Limited data availability in machine learning significantly impacts performance and generalization. Traditional augmentation methods enhance moderately sufficient datasets. GANs struggle with convergence when generating diverse samples. Diffusion models, while effective, have high computational costs. We introduce an Expansive Synthesis model generating large-scale, information-rich datasets from minimal samples. It uses expander graph mappings and feature interpolation to preserve data distribution and feature relationships. The model leverages neural networks' non-linear latent space, captured by a Koopman operator, to create a linear feature space for dataset expansion. An autoencoder with self-attention layers and optimal transport refines distributional consistency. We validate by comparing classifiers trained on generated data to those trained on original datasets. Results show comparable performance, demonstrating the model's potential to augment training data effectively. This work advances data generation, addressing scarcity in machine learning applications.1

This work tackles an intriguing and fundamental open challenge in representation learning: Given a well-trained deep learning model, can it be reprogrammed to enhance its robustness against adversarial or noisy input perturbations without altering its parameters? To explore this, we revisit the core feature transformation mechanism in representation learning and propose a novel non-linear robust pattern matching technique as a robust alternative. Furthermore, we introduce three model reprogramming paradigms to offer flexible control of robustness under different efficiency requirements. Comprehensive experiments and ablation studies across diverse learning models ranging from basic linear model and MLPs to shallow and modern deep ConvNets demonstrate the effectiveness of our approaches. This work not only opens a promising and orthogonal direction for improving adversarial defenses in deep learning beyond existing methods but also provides new insights into designing more resilient AI systems with robust statistics. Our implementation is available at https://github.com/chris-hzc/Robustness-Reprogramming.

In the era of big data, the sheer volume and complexity of datasets pose significant challenges in machine learning, particularly in image processing tasks. This paper introduces an innovative Autoencoder-based Dataset Condensation Model backed by Koopman operator theory that effectively packs large datasets into compact, information-rich representations. Inspired by the predictive coding mechanisms of the human brain, our model leverages a novel approach to encode and reconstruct data, maintaining essential features and label distributions. The condensation process utilizes an autoencoder neural network architecture, coupled with Optimal Transport theory and Wasserstein distance, to minimize the distributional discrepancies between the original and synthesized datasets. We present a two-stage implementation strategy: first, condensing the large dataset into a smaller synthesized subset; second, evaluating the synthesized data by training a classifier and comparing its performance with a classifier trained on an equivalent subset of the original data. Our experimental results demonstrate that the classifiers trained on condensed data exhibit comparable performance to those trained on the original datasets, thus affirming the efficacy of our condensation model. This work not only contributes to the reduction of computational resources but also paves the way for efficient data handling in constrained environments, marking a significant step forward in data-efficient machine learning.11Thanks to the generous support of ARO grant W911NF-23-2-0041

The importance of inference in Machine Learning (ML) has led to an explosive number of different proposals, particularly in Deep Learning. In an attempt to reduce the complexity of Convolutional Neural Networks, we propose a Volterra filter-inspired Network architecture. This architecture introduces controlled non-linearities in the form of interactions between the delayed input samples of data. We propose a cascaded implementation of Volterra Filtering so as to significantly reduce the number of parameters required to carry out the same classification task as that of a conventional Neural Network. We demonstrate an efficient parallel implementation of this Volterra Neural Network (VNN), along with its remarkable performance while retaining a relatively simpler and potentially more tractable structure. Furthermore, we show a rather sophisticated adaptation of this network to nonlinearly fuse the RGB (spatial) information and the Optical Flow (temporal) information of a video sequence for action recognition. The proposed approach is evaluated on UCF-101 and HMDB-51 datasets for action recognition, and is shown to outperform state of the art CNN approaches.

The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability distributions by some optimal metric, has been creatively exploited and shown to hold promise for many real-world data challenges. In a related theme in the present work, we posit that domain adaptation robustness is rooted in the intrinsic (latent) representations of the respective data, which are inherently lying in a non-linear submanifold embedded in a higher dimensional Euclidean space. We account for the geometric properties by refining the l2Euclidean metric to better reflect the geodesic distance between two distinct representations. We integrate a metric correction term as well as a prior cluster structure in the source data of the OT-driven adaptation. We show that this is tantamount to an implicit Bayesian framework, which we demonstrate to be viable for a more robust and better-performing approach to domain adaptation. Substantiating experiments are also included for validation purposes.

In this paper, we address the problem of unsupervised Domain Adaptation. The need for such an adaptation arises when the distribution of the target data differs from that which is used to develop the model and the ground truth information of the target data is unknown. We propose an algorithm that uses optimal transport theory with a verifiably efficient and implementable solution to learn the best latent feature representation. This is achieved by minimizing the cost of transporting the samples from the target domain to the distribution of the source domain.

We develop a novel theoretical framework for understating Optimal Transport (OT) schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class structure under geometric assumptions. Furthermore, we derive an accelerated proximal algorithm with a closed-form projection and proximal operator scheme, thereby affording a more scalable algorithm for computing optimal transport plans. We provide a novel argument for the uniqueness of the optimum even in the absence of strong convexity. Our experiments show that the new regularizer not only results in a better preservation of the class structure in the data but also yields additional robustness to the data geometry, compared to previous regularizers.

We introduce in this paper a new statistical perspective, exploiting the Jaccard similarity metric, as a measure-based metric to effectively invoke non-linear features in the loss of self-supervised contrastive learning. Specifically, our proposed metric may be interpreted as a dependence measure between two adapted projections learned from the so-called latent representations. This is in contrast to the cosine similarity measure in the conventional contrastive learning model, which accounts for correlation information. To the best of our knowledge, this effectively non-linearly fused information embedded in the Jaccard similarity, is novel to self-supervision learning with promising results. The proposed approach is compared to two state-of-the-art self-supervised contrastive learning methods on three image datasets. We not only demonstrate its amenable applicability in current ML problems, but also its improved performance and training efficiency.

The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work lies in the search for a connectome model which properly captures brain functionality upon observing activities in different regions of the brain and possibly of individual neurons. We formulate the problem as a quadratic objective functional of observed node signals over short time intervals, subjected to the proper regularization reflecting the graph smoothness and other dynamics involving the underlying graph’s Laplacian, as well as the time evolution smoothness of the underlying graph. The resulting joint optimization is solved by a continuous relaxation and an introduced novel gradient-projection scheme. We apply our algorithm to a real-world dataset comprising recorded activities of individual brain cells. The resulting model is shown to not only be viable but also efficiently computable.

Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer dictionaries, the recently improved Deep DL methods have also fallen short on a number of issues. We hence propose a novel Deep DL approach where each DL layer can be formulated and solved as a combination of one linear layer and a Recurrent Neural Network, where the RNN is flexibly regraded as a layer-associated learned metric. Our proposed work unveils new insights between the Neural Networks and Deep DL, and provides a novel, efficient and competitive approach to jointly learn the deep transforms and metrics. Extensive experiments are carried out to demonstrate that the proposed method can not only outperform existing Deep DL, but also state-of-the-art generic Convolutional Neural Networks.

In this work, we demonstrate the ability to exploit sensing modalities for mitigating an unrepresented modality or for potentially re-targeting resources. This is tantamount to developing proxy sensing capabilities for multi-modal learning. In classical fusion, multiple sensors are required to capture different information about the same target. Maintaining and collecting samples from multiple sensors can be financially demanding. Additionally, the effort necessary to ensure a logical mapping between the modalities may be prohibitively limiting. We examine the scenario where we have access to all modalities during training, but only a single modality at testing. In our approach, we initialize the parameters of our single modality inference network with weights learned from the fusion of multiple modalities through both classification and GANs losses. Our experiments show that emulating a multi-modal system by perturbing a single modality with noise can help us achieve competitive results compared to using multiple modalities.

This article presents Egeria, the first automatic synthesizer of advising tools for High-Performance Computing (HPC). When one provides it with some HPC programming guides as inputs, Egeria automatically constructs a text retrieval tool that can advise on what to do to improve the performance of a given program. The advising tool provides a concise list of essential rules automatically extracted from the documents and can retrieve relevant optimization knowledge for optimization questions. Egeria is built based on a distinctive multi-layered design that leverages natural language processing (NLP) techniques and extends them with HPC-specific knowledge and considerations. This article presents the design, implementation, and both quantitative and qualitative evaluation results of Egeria.

This paper presents a data driven approach to multi-modal fusion where a hidden latent sub-space between the different modalities is learned. The hidden space is estimated via a bank of Conditional GANs which also commute with each other, leading to an output that lies in a common subspace. Experimental results show improved detection performance compared to existing fusion techniques in ideal as well as noisy sensor condition.

Discriminative Dictionary Learning (DL) methods have been widely advocated for image classification problems. To further sharpen their discriminative capabilities, most state-of-the-art DL methods have additional constraints included in the learning stages. These various constraints, however, lead to additional computational complexity. We hence propose an efficient Discriminative Convolutional Analysis Dictionary Learning (DCADL) method, as a lower cost Discriminative DL framework, to both characterize the image structures and refine the interclass structure representations. The proposed DCADL jointly learns a convolutional analysis dictionary and a universal classifier, while greatly reducing the time complexity in both training and testing phases, and achieving a competitive accuracy, thus demonstrating great performance in many experiments with standard databases.

We propose a deep learning architecture capable of performing up to 8× single image super-resolution. Our architecture incorporates an adversarial component from the super-resolution generative adversarial networks (SRGANs) and a multi-scale learning component from the multiple scale super-resolution network (MSSRNet), which only together can recover smaller structures inherent in satellite images. To further enhance our performance, we integrate progressive growing and training to our network. This, aided by feed forwarding connections in the network to move along and enrich information from previous inputs, produces super-resolved images at scaling factors of 2, 4, and 8. To ensure and enhance the stability of GANs, we employ Wasserstein GANs (WGANs) during training. Experimentally, we find that our architecture can recover small objects in satellite images during super-resolution whereas previous methods cannot.

Deep dictionary learning seeks multiple dictionaries at different image scales to capture complementary coherent characteristics. We propose a method for learning a hierarchy of synthesis dictionaries with an image classification goal. The dictionaries and classification parameters are trained by a classification objective, and the sparse features are extracted by reducing a reconstruction loss in each layer. The reconstruction objectives in some sense regularize the classification problem and inject source signal information in the extracted features. The performance of the proposed hierarchical method increases by adding more layers, which consequently makes this model easier to tune and adapt. The proposed algorithm furthermore, shows remarkably lower fooling rate in presence of adversarial perturbation. The validation of the proposed approach is based on its classification performance using four benchmark datasets and is compared to a CNN of similar size.

A discriminative structured analysis dictionary is proposed for the classification task. A structure of the union of subspaces (UoS) is integrated into the conventional analysis dictionary learning to enhance the capability of discrimination. A simple classifier is also simultaneously included into the formulated function to ensure a more complete consistent classification. The solution of the algorithm is efficiently obtained by the linearized alternating direction method of multipliers. Moreover, a distributed structured analysis dictionary learning is also presented to address large-scale datasets. It can group-(class-) independently train the structured analysis dictionaries by different machines/cores/threads, and therefore avoid a high computational cost. A consensus structured analysis dictionary and a global classifier are jointly learned in the distributed approach to safeguard the discriminative power and the efficiency of classification. Experiments demonstrate that our method achieves a comparable or better performance than the state-of-the-art algorithms in a variety of visual classification tasks. In addition, the training and testing computational complexity are also greatly reduced.

Parametric approaches to Learning, such as deep learning (DL), are highly popular in nonlinear regression, in spite of their extremely difficult training with their increasing complexity (e.g. number of layers in DL). In this paper, we present an alternative semi-parametric framework which foregoes the ordinarily required feedback, by introducing the novel idea of geometric regularization. We show that certain deep learning techniques such as residual network (ResNet) architecture are closely related to our approach. Hence, our technique can be used to analyze these types of deep learning. Moreover, we present preliminary results which confirm that our approach can be easily trained to obtain complex structures.

In this paper, we propose to use a Conditional Generative Adversarial Network (CGAN) for distilling (i.e. transferring) knowledge from sensor data and enhancing low-resolution target detection. In unconstrained surveillance settings, sensor measurements are often noisy, degraded, corrupted, and even missing/absent, thereby presenting a significant problem for multi-modal fusion. We therefore specifically tackle the problem of a missing modality in our attempt to propose an algorithm based on CGANs to generate representative information from the missing modalities when given some other available modalities. Despite modality gaps, we show that one can distill knowledge from one set of modalities to another. Moreover, we demonstrate that it achieves better performance than traditional approaches and recent teacher-student models.

We propose a computationally efficient and high-performance classification algorithm by incorporating class structural information in analysis dictionary learning. To achieve more consistent classification, we associate a class characteristic structure of independent subspaces and impose it on the classification error constrained analysis dictionary learning. Experiments demonstrate that our method achieves a comparable or better performance than the state-of-the-art algorithms in a variety of visual classification tasks. In addition, our method greatly reduces the training and testing computational complexity.

K-means configuration is a time-consuming process due to the iterative nature of k-means. This paper proposes reuse-centric k-means configuration to accelerate k-means configuration. It is based on the observation that the explorations of different configurations share lots of common or similar computations. Effectively reusing the computations from prior trials of different configurations could largely shorten the configuration time. The paper presents a set of novel techniques to materialize the idea, including reuse-based filtering, center reuse, and a two-phase design to capitalize on the reuse opportunities on three levels: validation, k, and feature sets. Experiments show that our approach can accelerate some common configuration tuning methods by 5-9X.

We consider subspace clustering under sparse noise, for which a non-convex optimization framework based on sparse data representations has been recently developed. This setup is suitable for a large variety of applications with high dimensional data, such as image processing, which is naturally decomposed into a sparse unstructured foreground and a background residing in a union of low-dimensional subspaces. In this framework, we further discuss both performance and implementation of the key optimization problem. We provide an analysis of this optimization problem demonstrating that our approach is capable of recovering linear subspaces as a local optimal solution for sufficiently large data sets and sparse noise vectors. We also propose a sequential algorithmic solution, which is particularly useful for extremely large data sets and online vision applications such as video processing.

Data heterogeneity can pose a great challenge to process and systematically fuse low-level data from different modalities with no recourse to heuristics and manual adjustments and refinements. In this paper, a new methodology is introduced for the fusion of measured data for detecting and predicting weather-driven natural hazards. The proposed research introduces a robust theoretical and algorithmic framework for the fusion of heterogeneous data in near real time. We establish a flexible information-based fusion framework with a target optimality criterion of choice, which for illustration, is specialized to a maximum entropy principle and a least effort principle for semisupervised learning with noisy labels. We develop a methodology to account for multimodality data and a solution for addressing inherent sensor limitations. In our case study of interest, namely, that of flood density estimation, we further show that by fusing remote sensing and social media data, we can develop well founded and actionable flood maps. This capability is valuable in situations where environmental hazards, such as hurricanes or severe weather, affect very large areas. Relative to the state of the art working with such data, our proposed information-theoretic solution is principled and systematic, while offering a joint exploitation of any set of heterogeneous sensor modalities with minimally assuming priors. This flexibility is coupled with the ability to quantitatively and clearly state the fusion principles with very reasonable computational costs. The proposed method is tested and substantiated with the multimodality data of a 2013 Boulder Colorado flood event.

Entropy-based divergence measures have proven their effectiveness in many areas of computer vision and pattern recognition. However, the complexity of their implementation might be prohibitive in resource-limited applications, as they require estimates of probability densities which are expensive to compute directly for high-dimensional data. In this paper, we investigate the usage of a non-parametric distribution-free metric, known as the Henze-Penrose test statistic to obtain bounds for the $k$ -nearest neighbors ( $k$ -NN) classification accuracy. Simulation results demonstrate the effectiveness and the reliability of this metric in estimating the inter-class separability. In addition, the proposed bounds on the $k$ -NN classification are exploited for evaluating the efficacy of different pre-processing techniques as well as selecting the least number of features that would achieve the desired classification performance.

We further delay embedding framework application to multiple time series for extraction of their potential causal interactions. We introduce a novel geometric model-free causality measure that can efficiently detect linear and nonlinear causal interactions between time series with no prior information or parameter estimation. Using multivariate delay embedding, we construct a point cloud from a set of time domain signals and propose the inverse of its fractal dimension as a causal interaction measure between the corresponding time series. Correlation dimension estimation is fully exploited as a fractal-based method for uncovering the dimensions of generated point clouds. Extensive simulation results are presented to substantiate the capabilities of the proposed approach.

Hierarchical dictionary learning seeks multiple dictionaries at different image scales to capture complementary coherent characteristics. We propose a method to learn a hierarchy of two overcomplete synthesis dictionaries with an image classification goal. The classification objective in some sense regularizes the joint optimization of the hierarchical dictionaries and injects refinement feedback. The validation of the proposed approach is based on its classification performance using two well-known data sets.

In this paper, we are interested in modeling the diffusion of information in a multilayer network of agents using a thermodynamic diffusion approach. The state of each agent is viewed as a topic mixture, to describe his/her resources, and represented by a distribution over multiple topics. We observe and learn diffusion-related thermodynamical patterns in the training data set, and we use the estimated diffusion structure to predict the future states of the agents. With a priori knowledge of a fraction of the state of all agents, the problem is shown to turn into a Kalman predictor problem that refines the predicted system states using the estimation error of the agents' states. A real world Twitter data set is then used to evaluate and validate our information diffusion model.

The detection of abandoned objects in videos from moving cameras is of great importance to automatic surveillance systems that monitor large and visually complex areas. This paper proposes a new method based on sparse decompositions to identify video anomalies associated with abandoned objects. The proposed scheme inherently incorporates synchronization between the reference (anomaly-free) and target (under analysis) sequences thus reducing the implementation complexity of the overall surveillance system. Results indicate that the proposed video-processing scheme can lead to 95% complexity reduction while maintaining excellent detection capability of foreground objects.

Achieving high performance on modern systems is challenging. Even with a detailed profile from a performance tool, writing or refactoring a program to remove its performance issues is still a daunting task for application programmers: it demands lots of program optimization expertise that is often system specific.

Topological Data Analysis (TDA) is a topic which has recently seen many applications. The goal of this special session is to highlight the bridge between signal processing, machine learning and techniques in topological data analysis. In this way, we hope to encourage more engineers to start exploring TDA and its applications. This paper briefly introduces the standard techniques used in this area, delineates the common theme connecting the works presented in this session, and concludes with a brief summary of each of the papers presented.

In the pharmaceutical industry, quality is often measured by the impact of a product on a population. Knowledge about the behaviour of mosquitos responding to a repellent is a case in point in helping to improve the effect of insect repellent. It is ideally carried out using 3D videos which require a stereoscopic apparatus. To do so using 2D video and effectively evaluate the repellent is an difficult problem as is known in the biotechnology research field. In this paper, we propose a general framework for the swarm motion analysis of multiple mosquitos based on 2D videos. The effectiveness and robustness of our algorithm are verified by multiple 2D videos capturing mosquitos behavior in different experimental conditions.

Discovering the underlying structure of a high-dimensional signal or big data has always been a challenging topic, and has become harder to tackle especially when the observations are exposed to arbitrary sparse perturbations. In this paper, built on the model of a union of subspaces (UoS) with sparse outliers and inspired by a basis pursuit strategy, we exploit the fundamental structure of a Grassmann manifold, and propose a new technique of pursuing the subspaces systematically by solving a non-convex optimization problem using the alternating direction method of multipliers. This problem as noted is further complicated by non-convex constraints on the Grassmann manifold, as well as the bilinearity in the penalty caused by the subspace bases and coefficients. Nevertheless, numerical experiments verify that the proposed algorithm, which provides elegant solutions to the sub-problems in each step, is able to de-couple the subspaces and pursue each of them under time-efficient parallel computation.

Data fusion is the operation of integrating data from different modalities to construct a single consistent representation. This paper proposes variations of coupled dictionary learning through an additional factorization. One variation of this model is applicable to the pansharpening data fusion problem. Real world pansharpening data was applied to train and test our proposed formulation. The results demonstrate that the data fusion model can successfully be applied to the pan-sharpening problem.

Analysis procedures for higher-dimensional data are generally computationally costly; thereby justifying the high research interest in the area. Entropy-based divergence measures have proven their effectiveness in many areas of computer vision and pattern recognition. However, the complexity of their implementation might be prohibitive in resource-limited applications, as they require estimates of probability densities which are very difficult to compute directly for high-dimensional data. In this paper, we investigate the usage of a non-parametric distribution-free metric, known as the Henze-Penrose test statistic, to estimate the divergence between different classes of vehicles. In this regard, we apply some common feature extraction techniques to further characterize the distributional separation relative to the original data. Moreover, we employ the Henze-Penrose metric to obtain bounds for the Nearest Neighbor (NN) classification accuracy. Simulation results demonstrate the effectiveness and the reliability of this metric in estimating the inter-class separability. In addition, the proposed bounds are exploited for selecting the least number of features that would retain sufficient discriminative information.

Sparse models in dictionary learning have been successfully applied in a wide variety of machine learning and computer vision problems, and as a result have recently attracted increased research interest. Another interesting related problem based on linear equality constraints, namely the sparse null space (SNS) problem, first appeared in 1986 and has since inspired results on sparse basis pursuit. In this paper, we investigate the relation between the SNS problem and the analysis dictionary learning (ADL) problem, and show that the SNS problem plays a central role, and may be utilized to solve dictionary learning problems. Moreover, we propose an efficient algorithm of sparse null space basis pursuit (SNS-BP) and extend it to a solution of ADL. Experimental results on numerical synthetic data and real-world data are further presented to validate the performance of our method.

Indoor localization of multiple speech sources in wireless acoustic sensor networks (WASNs) is an open and interesting problem with many practical applications, but the presence of noise and reverberations complicates the problem. In this paper, a distributed algorithm for multiple DOA estimation of speech sources in WASNs is presented. The method exploits the sparsity of speech sources in the time-frequency domain to obtain DOA estimations locally in each node of the network. The DOA estimations of different nodes are further combined to increase the accuracy of the local DOA estimations. Since the local DOAs are estimated using only the microphones of the same node, the synchronization between input channels and localization of the microphones from different nodes are not an issue.

Sparse models in dictionary learning have been successfully applied in a wide variety of machine learning and computer vision problems, and have also recently been of increasing research interest. Another interesting related problem based on a linear equality constraint, namely the sparse null space problem (SNS), first appeared in 1986, and has since inspired results on sparse basis pursuit. In this paper, we investigate the relation between the SNS problem and the analysis dictionary learning problem, and show that the SNS problem plays a central role, and may be utilized to solve dictionary learning problems. Moreover, we propose an efficient algorithm of sparse null space basis pursuit, and extend it to a solution of analysis dictionary learning. Experimental results on numerical synthetic data and real-world data are further presented to validate the performance of our method.

We consider the application of sparse-representation and robust-subspace-recovery techniques to detect abandoned objects in a target video acquired with a moving camera. In the proposed framework, the target video is compared to a previously acquired reference video, which is assumed to have no abandoned objects. The detection method explores the low-rank similarities among the reference and target videos, as well as the sparsity of the differences between the two video sequences caused by the unexpected object in the target video. A three-step procedure is then presented adapting a previous low-rank and sparse image representation to the problem at hand. Performance of the proposed technique is verified using a large video database for abandoned-object detection in a cluttered environment. Results demonstrate the technique effectiveness even in the presence of some significant camera shake along its trajectory.

The success of sparse models in computer vision and machine learning in many real-world applications, may be attributed in large part, to the fact that many high dimensional data are distributed in a union of low dimensional subspaces. The underlying structure may, however, be adversely affected by sparse errors, thus inducing additional complexity in recovering it. In this paper, we propose a bi-sparse model as a framework to investigate and analyze this problem, and provide as a result, a novel algorithm to recover the union of subspaces in presence of sparse corruptions. We additionally demonstrate the effectiveness of our method by experiments on real-world vision data.

This work presents a framework to be used in the detection of abandoned objects and other video events in a cluttered environment with a moving camera. In the proposed method a target video, that may have features we would like to detect, is compared with a pre-acquired reference video, which is assumed to have no objects nor video events of interest. The comparison is carried out by way of the achieved optimized operators, generated from the reference video, that produce Gaussian outputs when applied to it. Any anomaly of interest in the target video leads to a non-Gaussian output. The method dispenses with the target and reference videos being either synchronized or precisely registered, being robust to rotations and translations between the frames. Experiments show its good performance in the proposed environment.

Four characteristic points of pulse pressure waves-the systolic peak, the anacrotic notch, the dicrotic notch, and the diastolic foot-are used to estimate various aspects of cardiovascular function, such as heart rate and augmentation index. We propose a novel approach to extracting these characteristic points using a topological signal processing framework. We characterize the topology of the signals using a collection of persistence intervals, which are encapsulated in a persistence diagram. The characteristic points are identified based on their time of occurrence and their distance from the identity line in the persistence diagram. We validate this approach by collecting radial pulse pressure data from twenty-eight participants using a wearable tonometer, and computing the peripheral augmentation index using a traditional derivative-based method and our novel persistence-based method. The augmentation index values computed using the two methods are statistically indistinguishable, suggesting that this representation merits further exploration as a tool for analyzing pulse pressure waves.

The goal of this study is to find evidence of cyclicity or periodicity in data with low computational complexity and high accuracy. Using delay embeddings, we transform the timedomain signal into a point cloud, whose topology reflects the periodic behavior of the signal. Persistent homology is employed to determine the underlying manifold of the point cloud, and the Euler characteristic provides for a fast computation of topology of the resulting manifold. We apply the introduced approach to breathing sound signals for wheeze detection. Our experiments substantiate the capabilities of the proposed method.

Persistent homology has become one of the most popular tools used in topological data analysis for analyzing big data sets. In an effort to minimize the computational complexity of finding the persistent homology of a data set, we develop a simplicial collapse algorithm called the selective collapse. This algorithm works by representing the previously developed strong collapse as a forest and uses that forest data to improve the speed of both the strong collapse and of persistent homology. Finally, we demonstrate the savings in computational complexity using geometric random graphs.

In applications where the use of video surveillance is necessary and/or beneficial, it is a common goal to identify the contents of the video automatically. Of particular interest in such applications is the ability to recognize locations in the environment, where events occur, and describe the events common to those locations. This is one of the goals of scene understanding. Scene understanding is traditionally addressed from one of two separate points-of-view: the description of the underlying environment or the action taking-place throughout the scene. Each of these facets is required to address the overarching goal but, is insufficient independently to address the problem entirely. These facets are, in fact, dependent and by considering both, a more complete description becomes available. In this paper, we describe a novel, data-driven scene understanding and classification technique that captures and utilizes information about both the environment and activity within a scene.

We propose a new approach to detect and quantify the periodic structure of dynamical systems using topological methods. We propose to use delay-coordinate embedding as a tool to detect the presence of harmonic structures by using persistent homology for robust analysis of point clouds of delay-coordinate embeddings. To discover the proper delay, we propose an autocorrelation like (ACL) function of the signals, and apply the introduced topological approach to analyze breathing sound signals for wheeze detection. Experiments have been carried out to substantiate the capabilities of the proposed method.

In this paper, we propose a novel subspace learning algorithm of shape dynamics. Compared to the previous works, our method is invertible and better characterizes the nonlinear geometry of a shape manifold while retaining a good computational efficiency. In this paper, using a parallel moving frame on a shape manifold, each path of shape dynamics is uniquely represented in a subspace spanned by the moving frame, given an initial condition (the starting point and starting frame). Mathematically, such a representation may be formulated as solving a manifold-valued differential equation, which provides a generative modeling of high-dimensional shape dynamics in a lower dimensional subspace. Given the parallelism and a path on a shape manifold, the parallel moving frame along the path is uniquely determined up to the choice of the starting frame. With an initial frame, we minimize the reconstruction error from the subspace to shape manifold. Such an optimization characterizes well the Riemannian geometry of the manifold by imposing parallelism (equivalent as a Riemannian metric) constraints on the moving frame. The parallelism in this paper is defined by a Levi-Civita connection, which is consistent with the Riemannian metric of the shape manifold. In the experiments, the performance of the subspace learning is extensively evaluated using two scenarios: 1) how the high dimensional geometry is characterized in the subspace and 2) how the reconstruction compares with the original shape dynamics. The results demonstrate and validate the theoretical advantages of the proposed approach.

The solution of speech related problems such as source location or separation relies on a prior estimation of the number of sources. In this paper we propose a method for speech source enumeration based on the different relative delays that sources at different locations register at two microphones. The Probability Density Function (PDF) of the estimated delays exhibits peaks associated with each source. The Minimum Description Length (MDL) criterion is applied to the prediction error of a linear model fitted to the delay estimates. The method is validated for the estimation of different number of sources and different mixtures.

There has recently been increased interest in applications of topology to areas ranging from control and sensing, to social network analysis, to high-dimensional point cloud data analysis. Here we use simplicial complexes to represent the group relationship structure in a network. We detail a novel algorithm for simplifying homology and “hole location” computations on a complex by reducing it to its core using a strong collapse. We show that the homology and hole locations are preserved and provide motivation for interest in this reduction technique with applications in sensor and social networks. Since the complexity of finding “holes” is quintic in the number of simplices, the proposed reduction leads to significant savings in complexity.

This paper proposes a new social network classification method by comparing statistics of their centralities and clustering coefficients. Specifically, the proposed method uses the statistics of Degree Centralities and clustering coefficients of networks as a classification criterion. A theoretical justification to this method is also given. In relation to the widely held belief that a social network graph is solely defined by its degree distribution, the novelty of this paper consists in revealing the strong dependence of social networks on Degree Centralities and clustering coefficients, and in using them as minimal information to classify social networks. In addition, experimental classification demonstrates a very good performance of the proposed method on real social network data, and validates the hypothesis that Degree Centralities and clustering coefficients are the only two viable independent properties of a social network.

Most of previous shape based human activity models were built with either a linear assumption or an extrinsic interpretation of the nonlinear geometry of the shape space, both of which proved to be problematic on account of the nonlinear intrinsic geometry of the associated shape spaces. In this paper we propose an intrinsic stochastic modeling of human activity on a shape manifold. More importantly, within an elegant and theoretically sound framework, our work effectively bridges the nonlinear modeling of human activity on a nonlinear space, with the classic stochastic modeling in a Euclidean space, and thereby provides a foundation for a more effective and accurate analysis of the nonlinear feature space of activity models. From a video sequence, human activity is extracted as a sequence of shapes. Such a sequence is considered as one realization of a random process on a shape manifold. Different activities are then modeled as manifold valued random processes with different distributions. To address the problem of stochastic modeling on a manifold, we first construct a nonlinear invertible map of a manifold valued process to a Euclidean process. The resulting process is then modeled as a global or piecewise Brownian motion. The mapping from a manifold to a Euclidean space is known as a stochastic development. The advantage of such a technique is that it yields a one-one correspondence, and the resulting Euclidean process intrinsically captures the curvature on the original manifold. The proposed algorithm is validated on two activity databases [15], [5] and compared with the related works on each of these. The substantiating results demonstrate the viability and high accuracy of our modeling technique in characterizing and classifying different activities.

In this paper, we develop a procedure to factorize a broadband signal into the product of a narrow-band modulator and a wide-band carrier. The approach is based on using the Singular Value Decomposition theorem and the Discrete Fourier Transform. Finally, some experiments on synthetic and speech signals are provided to show the effectiveness of the proposed approach.

This paper presents a novel 3D face recognition method by means of the evolution of iso-geodesic distance curves. Specifically, the proposed method compares two neighboring iso-geodesic distance curves, and formalizes the evolution between them as a one-dimensional function, named evolution angle function, which is Euclidean invariant. The novelty of this paper consists in formalizing 3D face by an evolution angle functions, and in computing the distance between two faces by that of two functions. Experiments on Face Recognition Grand Challenge (FRGC) ver2.0 shows that our approach works very well on both neutral faces and non-neutral faces. By introducing a weight function, we also show a very promising result on non-neutral face database.

We define a new adaptive embedding approach for data dimension reduction applications. Our technique entails a local learning of the manifold of the initial data, with the objective of defining local distance metrics that take into account the different correlations between the data points. We choose to illustrate the properties of our work on the isomap algorithm. We show through multiple simulations that the new adaptive version of isomap is more robust to noise than the original non-adaptive one.

Sensor Networks are inherently complex networks, and associated problems where analysis of some global features becomes more important than local ones, often arise. Localizing the holes in the overall coverage is one such problem. We present here, a distributed algorithm in a generalized combinatorial setting to localize holes in the coverage, with no a priori localization information for the nodes. We follow a divide and conquer approach, strategically dissecting the network so that the overall topology is preserved, while simultaneously minimizing the computational complexity. The detection of holes is enabled by first attributing a combinatorial object called a "Rips Complex" to each network segment, and by then checking for the triviality of the first homology class of this complex. Our estimate approaches the location of the holes exponentially with each iteration leading to a very fast convergence coupled with optimal usage of valuable resources such as power and memory. We demonstrate the effectiveness of the presented algorithm with simulations.

We propose to superpose global topological and local geometric 3-D shape descriptors in order to define one compact and discriminative representation for a 3-D object. While a number of available 3-D shape modeling techniques yield satisfactory object classification rates, there is still a need for a refined and efficient identification/recognition of objects among the same class. In this paper, we use Morse theory in a two-phase approach. To ensure the invariance of the final representation to isometric transforms, we choose the Morse function to be a simple and intrinsic global geodesic function defined on the surface of a 3-D object. The first phase is a coarse representation through a reduced topological Reeb graph. We use it for a meaningful decomposition of shapes into primitives. During the second phase, we add detailed geometric information by tracking the evolution of Morse function's level curves along each primitive. We then embed the manifold of these curves into [Formula: see text], and obtain a single curve. By combining phase one and two, we build new graphs rich in topological and geometric information that we refer to as squigraphs. Our experiments show that squigraphs are more general than existing techniques. They achieve similar classification rates to those achieved by classical shape descriptors. Their performance, however, becomes clearly superior when finer classification and identification operations are targeted. Indeed, while other techniques see their performances dropping, squigraphs maintain a performance rate of the order of 97%.

We propose a method for 3-D shape recognition based on inexact subgraph isomorphisms, by extracting topological and geometric properties of a shape in the form of a shape model, referred to as topo-geometric shape model (TGSM). In a nutshell, TGSM captures topological information through a rigid transformation invariant skeletal graph that is constructed in a Morse theoretic framework with distance function as the Morse function. Geometric information is then retained by analyzing the geometric profile as viewed through the distance function. Modeling the geometric profile through elastic yields a weighted skeletal representation, which leads to a complete shape signature. Shape recognition is carried out through inexact subgraph isomorphisms by determining a sequence of graph edit operations on model graphs to establish subgraph isomorphisms with a test graph. Test graph is recognized as a shape that yields the largest subgraph isomorphism with minimal cost of edit operations. In this paper, we propose various cost assignments for graph edit operations for error correction that takes into account any shape variations arising from noise and measurement errors.

In this paper we propose to jointly segment and register objects of interest in layered images. Layered imaging refers to imageries taken from different perspectives and possibly by different sensors. Registration and segmentation are therefore the two main tasks which contribute to the bottom level, data alignment, of the multisensor data fusion hierarchical structures. Most exploitations of two layered images assumed that scanners are at very high altitudes and that only one transformation ties the two images. Our data are however taken at mid-range and therefore requires segmentation to assist us examining different object regions in a divide-and-conquer fashion. Our approach is a combination of multiphase active contour method with a joint segmentation-registration technique (which we called MPJSR) carried out in a local moving window prior to a global optimization. To further address layered video sequences and tracking objects in frames, we propose a simple adaptation of optical flow calculations along the active contours in a pair of layered image sequences. The experimental results show that the whole integrated algorithm is able to delineate the objects of interest, align them for a pair of layered frames and keep track of the objects over time.

We present a new similarity invariant signature for space curves. This signature is based on the information contained in the turning angles of both the tangent and the binormal vectors at each point on the curve. For an accurate comparison of these signatures, we define a Riemannian metric on the space of the invariant. We show through relevant examples that, unlike classical invariants, the one we define in this paper enjoys multiple important properties at the same time, namely, a high discrimination level, independence of any reference point, uniqueness property, as well as a good preservation of the correspondence between curves. Moreover, we illustrate how to match 3D objects by extracting and comparing the invariant signatures of their curved skeletons.

In this paper we propose a constrained version of Mumford-Shah's[1] segmentationwith an information-theoretic point of view[2] in order to devise a systematic procedure to segment brain MRI data for two modalities of parametric T1-Map and T1-weighted images in both 2-D and 3-D settings. The incorporation of a tuning weight in particular adds a probabilistic flavor to our segmentation method, and makes the three-tissue segmentation possible. Our method uses region based active contours which have proven to be robust. The method is validated by two real objects which were used to generate T1-Maps and also by two simulated brains of T1-weighted data from the BrainWeb[3] public database.

To simplify the matching and recognition of 3D objects, we propose to decompose a complex 3D shape into simpler primitive parts. Our partitioning of objects relies on their topological Reeb graphs. Taking advantage of the properties of Morse theory, we detect the critical points of the global geodesic function. These points define the levels at which the segmentation happens. To preserve the geometry of objects, we choose to use level curves instead of intervals. To proceed with object matching, we propose a kernel-based technique to register Reeb graphs. This optimal positioning of two Reeb graphs prepares for a pairwise comparison of the geometry of their primitives.

One of the main challenges of human behavior analysis is the high dimensionality of the representation space. In shape representation, however, a specific human behavior may naturally be described by a 1D path which lies in shape space. According to Whitney Embedding Theorem, such a 1D manifold may be embedded in R3. Motivated by the potential of reducing the dimensionality of behavior representation, we construct an embedding to map the path of evolution of the silhouette in shape space to a representational curve in R3. In contrast to other behavioral embedding, where each point of the path in shape space is projected to lower dimension, we embed the homotopy function of the whole path to be a planar curve function. The proposed embedding utilizes sampling theory to provide computational efficiency and simple reconstruction from the embedding space. Upon validating such a representation, we proceed to model different activities by an AR model of the representative curve. Experiments are provided to illustrate our technique and to demonstrate its viability.

It is well known that the wavelet transform provides a very effective framework for analysis of multiscale edges. In this paper, we propose a novel approach based on the shearlet transform: a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges. Indeed, unlike traditional wavelets, shearlets are theoretically optimal in representing images with edges and, in particular, have the ability to fully capture directional and other geometrical features. Numerical examples demonstrate that the shearlet approach is highly effective at detecting both the location and orientation of edges, and outperforms methods based on wavelets as well as other standard methods. Furthermore, the shearlet approach is useful to design simple and effective algorithms for the detection of corners and junctions

We present in this paper a solution to the graph isomorphism problem, by a unique decomposition of a graph into a set of atoms via its clique minimal separators. The resulting set of atoms is then used to collapse the original graph into a bipartite attributed relational graph, having a fewer number of vertices. Finally a probabilistic matching algorithm operates on the reduced graphs, simulating a belief propagation run, and decides whether the original graphs are isomorphic, in which case their corresponding atoms match. The complete approach yields a good suboptimal solution, while retaining a polynomial time complexity.

Mathematically wavelets are not very effective in representing images containing distributed discontinuities such as edges. This paper deals with a new multiscale directional representation called the shearlet transform that has been shown to represent specific classes of images with edges optimally. Techniques based on this transform for edge detection and analysis are presented. Unlike previously developed directional filter based techniques for edge detection, shearlets provide a theoretical basis for characterizing how edges will behave in such representations. Experiments demonstrate that this novel approach is very competitive for the purpose of edge detection and analysis.

Abstract In this paper, we present a probabilistic approach for 3D object's smoothing. The core idea behind the proposed method is to relate the problem of smoothing objects to that of tracking the transition probability density functions of an underlying random process. We show that such an approach allows for additional insight and sufficient flexibility compared with existing standard smoothing techniques. In particular, we are able to propose a newer, faster, and simpler smoothing approach that retains and enhances important manifold features. Furthermore, it is demonstrated to improve performance over existing smoothing techniques.

This paper presents a novel classification strategy for 3D objects. Our technique is based on using a global geodesic function to intrinsically describe the surface of an object. The choice of the global geodesic function ensures the invariance of the classification procedure to scaling and all isometric transformations. Using the Jensen-Shannon divergence, feature parameters are extracted from the probability distribution functions of the global geodesic function for each one of the classes. These parameters are used in the decision of a class membership of an object. This approach demonstrates low computational cost, efficiency, and robustness to resolution over many different data sets.

A new integro-differential invariant for curves in 3D transformed by affine group action is presented in this paper. The derivatives involved are of the first order, and therefore this invariant is significantly less sensitive to noise than classical affine differential invariants, the simplest of which involves derivatives of order 5. A classification procedure based on characteristic curves of an object surface is considered using our proposed mixed invariants. Substantiating examples are provided to verify efficiency and discriminant power of the characteristic spatial curve based 3D object classification.

In this paper, we study a problem of global optimization of an energy functional by a stochastic dynamics with a general diffusion coefficient. The main result is that adapting the diffusion coefficient to the shape of the functional enables the dynamics to escape wide local minima, and attracts it to narrower global minima that are missed by conventional diffusions. We discuss how to properly choose the diffusion coefficient and show numerically the superior performance of the resulting optimization algorithm.

In this paper we obtain, for the first time, explicit formulae for integral invariants for curves in 3D with respect to the special and the full affine groups. Using an inductive approach we first compute Euclidean integral invariants and use them to build the affine invariants. The motivation comes from problems in computer vision. Since integration diminishes the effects of noise, integral invariants have advantage in such applications. We use integral invariants to construct signatures that characterize curves up to the special affine transformations.

Skewness of shape data often arises in applications (e.g., medical image analysis) and is usually overlooked in statistical shape models. In such cases, a Gaussian assumption is unrealistic and a formulation of a general shape model which accounts for skewness is in order. In this paper, we present a novel statistical method for shape modeling, which we refer to as the flexible skew-symmetric shape model (FSSM). The model is sufficiently flexible to accommodate a departure from Gaussianity of the data and is fairly general to learn a "mean shape" (template), with a potential for classification and random generation of new realizations of a given shape. Robustness to skewness results from deriving the FSSM from an extended class of flexible skew-symmetric distributions. In addition, we demonstrate that the model allows us to extract principal curves in a point cloud. The idea is to view a shape as a realization of a spatial random process and to subsequently learn a shape distribution which captures the inherent variability of realizations, provided they remain, with high probability, within a certain neighborhood range around a mean. Specifically, given shape realizations, FSSM is formulated as a joint bimodal distribution of angle and distance from the centroid of an aggregate of random points. Mean shape is recovered from the modes of the distribution, while the maximum likelihood criterion is employed for classification.

A new 3D face representation and recognition approach is presented in this paper. Two sets of facial curves are extracted from a face range image, and a novel facial feature representation, the affine integral invariant, is introduced to mitigate the effect of pose on the facial curves. A human face is shown to be representable by a small subset of those affine integral invariant curves. A recognition procedure based on the discriminant analysis and Jensen-Shannon divergence analysis is proposed. Substantiating examples are provided with an achieved classification accuracy of 92.57%

Recognition of images and shapes has long been the central theme of computer vision. Its importance is increasing rapidly in the field of computer graphics and multimedia communication because it is difficult to process information efficiently without its recognition. In this paper, we propose a new approach for object matching based on a global geodesic measure. The key idea behind our methodology is to represent an object by a probabilistic shape descriptor that measures the global geodesic distance between two arbitrary points on the surface of an object. In contrast to the Euclidean distance which is more suitable for linear spaces, the geodesic distance has the advantage to be able to capture the intrinsic geometric structure of the data. The matching task therefore becomes a one-dimensional comparison problem between probability distributions which is clearly much simpler than comparing three-dimensional structures. Object matching can then be carried out by an information-theoretic dissimilarity measure calculations between geodesic shape distributions, and is additionally computationally efficient and inexpensive.

In dynamic susceptibility contrast perfusion weighted imaging, the recirculation effect is normally removed by gamma-variate fitting from concentration curves before estimating hemodynamic parameters. At lower SNR, however, many fitting failures may result. Moreover, when cerebral hemodynamics is compromised e.g., cerebral ischemia, a substantially broadened concentration curve is anticipated, resulting in the first passage overlapping with recirculation, which again causes a gamma-fit to fail to consistently discern recirculation contributions from the first passage. We propose to exploit independent component analysis to obviate the recirculation effect. We demonstrate that such a technique can remove recirculation in normal and ischemic brain tissues while preserving the first passage. This in turn allows for accurate recirculation elimination and hence improved estimation of cerebral blood volume particularly when overlapping between first passage and recirculation is suspected as in the case of an ischemic lesion.

In this paper, we propose a numerical algorithm for extracting the topology of a three-dimensional object (2 dimensional surface) embedded in a three-dimensional space /spl Ropf//sup 3/. The method is based on capturing the topology of a modified Reeb graph by tracking the critical points of a distance function. As such, the approach employs Morse theory in the study of translation, rotation, and scale invariant skeletal graphs. The latter are useful in the representation and classification of objects in /spl Ropf//sup 3/.

Three dimensional objects viewed as surfaces or volumes embedded in /spl Ropf//sup 3/, are usually sampled along the z-dimension by planes for rendering or modeling purposes. The resulting intersections are curves or planar shapes which may in turn be modeled for parsimony of representation. Each curve or planar shape may be viewed as a point in a high dimensional manifold, thereby providing the notion of interpolation between two curves or two points on this manifold to reconstruct the subsurface that lies between the two slices. We exploit some recent results in formulating this interpolation problem as an optimization problem in /spl Ropf//sup 3/ to yield a simple interpolating spline, known as elasticae, which when evaluated at intermediate points yields curves which can in turn be instrumental in 3D reconstruction. The approach is particularly suited for interpolation between MRI slices and for modeling and reconstruction of 3D shapes.

The importance of shape recognition is increasing rapidly in the field of computer graphics and multimedia communication because it is difficult to process information efficiently without its recognition. In this paper, we present a 3D object recognition approach based on a global geodesic measure. The key idea behind our methodology is to represent an object by a probabilistic shape descriptor that measures the global geodesic distance between two arbitrary points on the surface of an object. The geodesic distance has the advantage to be able to capture the intrinsic geometric structure of the data. Object matching can then be carried out by an information-theoretic dissimilarity measure calculations between geodesic shape distributions.

In this paper, we propose a method for identifying a discrete planar symmetric shape from an arbitrary viewpoint. Our algorithm is based on a newly proposed notion of a view's skeleton. We show that this concept yields projective invariants which facilitate the identification procedure. It is, furthermore, shown that the proposed method may be extended to the case of noisy data to yield an optimal estimate of a shape in question. Substantiating examples are provided.

In this paper, we first reconsider, in a different light, the addition of a prediction step to active contour-based visual tracking using an optical flow and clarify the local computation of the latter along the boundaries of continuous active contours with appropriate regularizers. We subsequently detail our contribution of computing an optical flow-based prediction step directly from the parameters of an active polygon, and of exploiting it in object tracking. This is in contrast to an explicitly separate computation of the optical flow and its ad hoc application. It also provides an inherent regularization effect resulting from integrating measurements along polygon edges. As a result, we completely avoid the need of adding ad hoc regularizing terms to the optical flow computations, and the inevitably arbitrary associated weighting parameters. This direct integration of optical flow into the active polygon framework distinguishes this technique from most previous contour-based approaches, where regularization terms are theoretically, as well as practically, essential. The greater robustness and speed due to a reduced number of parameters of this technique are additional and appealing features.

Shape modeling and template learning form an important area of research in image analysis. The paper addresses the problem from a novel viewpoint /sup s/ing a new class of semiparametric skew distributions. Given several realizations of a shape, we represent its template as a joint distribution of angle and distance from the centroid for all points on the boundary. The shape boundary may be arbitrary and irregular but simple. Its corresponding distribution is learned from the scattered data points of the available boundary realizations. We first obtained a bimodal distribution of the radii distances for given angles and subsequently synthesize the overall joint distributions according to some prior on the angles. We substantiate our proposed methodology with a number of examples.

Law enforcement officers on mobile duty are often confronted with ID authentication of subjects entailing the transmission of a driver's license picture over wireless channels that are very narrowband. To access mug shots in a reliable and timely manner, a real time compression and decompression method with high compression ratios is required at the server database and the mobile client unit. The presented technique minimizes the size of the data sent over the channel by locally storing common features of the human face in the client computers. Pre-processing of server database images, such as facial feature extraction, are used to extract these common facial features, obtained via ravines and image singularities. The implemented file transfer protocols are based on basic TCP/IP client-server models and make use of socket programming. Experimental results show a 5/spl times/ improvement in transfer time over typically saturated channels.

We present a novel nearest neighbor rule-based implementation of the structural risk minimization principle to address a generic classification problem. We propose a fast reference set thinning algorithm on the training data set similar to a support vector machine approach. We then show that the nearest neighbor rule based on the reduced set implements the structural risk minimization principle, in a manner which does not involve selection of a convenient feature space. Simulation results on real data indicate that this method significantly reduces the computational cost of the conventional support vector machines, and achieves a nearly comparable test error performance.

Automatic facial feature extraction is one of the most important and attempted problems in computer vision. It is a necessary step in face recognition, facial image compression and low-bit video coding. The methodology presented in this paper, considers the facial image as a surface. Topological properties of the facial surface, such as principal curvatures are used to extract the eyes and mouth, which form deep valleys on the surface. Ravines are points on the surface where the maximum curvature is a local maximum in the corresponding principal direction. The basic idea of the proposed method is to model the facial features as ravines on the facial surface. Experimental results have shown accurate extraction of the eye boundaries and the mouth opening in a very small computational time.

We present a feature-based object representation for topological modeling of three-dimensional illuminated surfaces. The proposed approach encodes an object into the Reeb graph concept from computational topology. This skeletal structure is based on the generalized height function in the light direction defined on the illuminated surface. In this paper, the topological properties of the proposed representation are analyzed in the Morse theoretic framework, and its close relationship to the shading problem is also highlighted. Some numerical simulations with synthetic and real 3D data are provided to demonstrate the potential of object singularities in topological modeling.

Based on nonparametric statistics, we propose robust variational filters for image denoising. The approach is a result of optimizing smooth statistical influence functionals subject to some noise constraints. Substantiating numerical examples are provided to demonstrate the potential and the good performance of the proposed algorithms in environmental image filtering.

We present a novel nearest neighbor rule-based implementation of the structural risk minimization principle to address a generic classification problem. We propose a fast reference set thinning algorithm on the training data set similar to a support vector machine approach. We then show that the nearest neighbor rule based on the reduced set implements the structural risk minimization principle, in a manner, which does not involve selection of a convenient feature space. Simulation results on real data indicate that this method significantly reduces the computational cost of the conventional support vector machines, and achieves a nearly comparable test error performance.

In this letter, we revisit a number of concepts that have recently proven to be useful in multiresolution signal analysis, specifically by replacing the now classical linear-scale transition operators by nonlinear ones. More precisely, we address the problem of designing appropriate operators associated to nonlinear filter banks using multiscale analysis. We first establish a connection between nonlinear filter banks and partial differential equations operators used in scale-space theory. Toward this end, we propose specific structures of nonlinear three-band decompositions ensuring a perfect reconstruction. The behavior of the proposed structures is analyzed for a step-like signal in a high SNR scenario, and a simulation is proposed for a more complex scenario.

In this paper, we present a novel nearest neighbor rule-based implementation of the structural risk minimization principle to address a generic classification problem. We propose a fast reference set thinning algorithm on the training data set similar to a support vector machine (SVM) approach. We then show that the nearest neighbor rule based on the reduced set implements the structural risk minimization principle, in a manner which does not involve selection of a convenient feature space. Simulation results on real data indicate that this method significantly reduces the computational cost of the conventional SVMs, and achieves a nearly comparable test error performance.

Image segmentation is a crucial step in computer vision, medical imaging and image processing. There has been recently an interest in a nonlinear partial differential equation based approach, motivated by a more systematic approach for image segmentation. In this paper, a novel active contour model expressed in terms of an energy functional is formulated in a calculus of variations framework. The key idea behind the proposed technique is to segment objects from the background of images that may have non-uniform brightness because of illumination. Simulation results showing a much improved performance of the proposed method in image segmentation are analyzed and illustrated.

Image singularities are prominent landmarks and their detection, recognition, and classification is a crucial step in image processing and computer vision. Such singularities carry important information for further operations, such as image registration, shape analysis, motion estimation, and object recognition. We propose a topological gradient descent flow for image singularities. The approach is expressed in the higher order variational framework as a minimizer of a variational integral involving the gradient and the Hessian matrix of the height function defined on a manifold. We demonstrate through numerical simulations the power of the proposed technique in preserving image singularities.

Novel polygon evolution models are introduced in this paper for capturing polygonal object boundaries in images which have one or more objects that have statistically different distributions on the intensity values. The key idea in our approach is to design evolution equations for vertices of a polygon that integrate both local and global image characteristics. Our method naturally provides an efficient representation of an object through a few number of vertices, which also leads to a significant amount of compression of image content. This methodology can effectively be used in the context of MPEG-7. We also propose usage of the Jensen-Shannon criterion as an information measure between the densities of regions of an image to capture more general statistical characteristics of the data.

This paper presents an approach to the fusion of SSM/I (Special Sensor Microwave/Imager) data from different resolutions, based on the prior statistical information about the data. The result is an estimated field that lives in a finer scale than any of the measurements. We apply a Wavelet Transform that increases speed and decreases memory requirements by sparsifying and preconditioning the statistics. This approach makes feasible the use of reprogrammable FPGA implementations for onboard satellite data processing, which greatly enhances flexibility and, most importantly, reduces communication burdens by limiting the extent to which raw, unprocessed data are transmitted to the ground.

Current approaches to denoising or signal enhancement in a wavelet-based framework have generally relied on the assumption of normally distributed perturbations. In practice, this assumption is often violated and sometimes prior information of the probability distribution of a noise process is not even available. To relax this assumption, we propose a novel nonlinear filtering technique in this paper. The key idea is to project a noisy signal onto a wavelet domain and to suppress wavelet coefficients by a mask derived from curvature extrema in its scale space representation. For a piecewise smooth signal, it can be shown that filtering by this curvature mask is equivalent to preserving the signal pointwise Hölder exponents at the singular points and lifting its smoothness elsewhere.

In previous years, curve evolution, applied to a single contour or to the level sets of an image via partial differential equations, has emerged as an important tool in image processing and computer vision. Curve evolution techniques have been utilized in problems such as image smoothing, segmentation, and shape analysis. We give a local stochastic interpretation of the basic curve smoothing equation, the so called geometric heat equation, and show that this evolution amounts to a tangential diffusion movement of the particles along the contour. Moreover, assuming that a priori information about the shapes of objects in an image is known, we present modifications of the geometric heat equation designed to preserve certain features in these shapes while removing noise. We also show how these new flows may be applied to smooth noisy curves without destroying their larger scale features, in contrast to the original geometric heat flow which tends to circularize any closed curve.

We address a well known problem of nonlinear image diffusion techniques, namely the loss of texture information. We do so by first determining that it is due to unaccounted correlation structure in the image which we subsequently mitigate by proposing a wavelet frame-based technique. This, by the same token, establishes a theoretical bridge between the scale space methodology and the multiscale analysis approach. We provide examples to illustrate the effectiveness of the proposed approach.

The high sensitivity of many specific filters to an accurate modeling of the noise that is to be removed led us to investigate the existence of a new class of filters using the theory of robust estimation. The latter class includes a large number of filters whose optimality when given a specific noise distribution is attained by merely adjusting weights. We also show that a convex combination of the mean and relaxed median filters exhibits many good properties. Some deterministic and asymptotic properties are studied, and comparisons with other filtering schemes are performed. Experimental results showing a much improved performance of the proposed filters in the presence of mixed Gaussian and heavy-tailed noise are analyzed and illustrated.

A connection between the maximum a posteriori (MAP) estimation and the variational formulation based on the minimization of a given variational integral subject to some noise constraints is established in this paper. A MAP estimator which uses a Markov or a maximum entropy random field model for the prior distribution can be viewed as a minimizer of a variational problem. Inspired by the maximum entropy principle, a nonlinear variational filter called improved entropic gradient descent flow is proposed. It minimizes a hybrid functional between the neg-entropy variational integral and the total variation subject to some noise constraints. Simulation results showing a much improved performance of the proposed filter in the presence of Gaussian and Laplacian noise are analyzed and illustrated.

Over the years the evolution of level sets of two-dimensional functions or images in time through a partial differential equation has emerged as an important tool in image processing. Curve evolution, which may be viewed as an evolution of a single level curve, has been applied to a wide variety of problems such as smoothing of shapes, shape analysis and shape recovery. We give a stochastic interpretation of the basic curve smoothing equation, the so called geometric heat equation, and show that this evolution amounts to a rotational diffusion movement of the particles along the contour. Moreover, assuming that a priori information about the orientation of objects to be preserved is known, we present new flows which amount to weighting the geometric heat equation nonlinearly as a function of the angle of the normal to the curve at each point.

Evolution equations have proven to be useful in tracking fine to coarse features in a single level curve and/or in an image. We give a stochastic insight to a specific evolution equation, namely the geometric heat equation, and subsequently use this insight to develop a class of feature-driven diffusions. A progressive smoothing along desired features of a level curve is aimed at overcoming effects of noisy environment during feature extraction and denoising applications.

We introduce a family of first-order multidimensional ordinary differential equations (ODEs) with discontinuous right-hand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diffusion everywhere except at local extrema, where some stabilization is introduced. For this reason, we call these equations "stabilized inverse diffusion equations" (SIDEs). Existence and uniqueness of solutions, as well as stability, are proven for SIDEs. A SIDE in one spatial dimension may be interpreted as a limiting case of a semi-discretized Perona-Malik equation. In an experiment, SIDE's are shown to suppress noise while sharpening edges present in the input signal. Their application to image segmentation is also demonstrated.

We present a stochastic formulation of a linear diffusion equation (or heat equation), and in light of the potential applications ranging from signal denoising to image enhancement/segmentation of its nonlinear extensions, we propose a more general nonlinear stochastic diffusion. The constructed stochastic framework, in contrast to traditional deterministic approaches, unveils the sources of existing limitations and allows us to further significantly improve the performance by addressing the key problem. Substantiating examples are provided.

A nonlinear diffusion process known to be effective for image segmentation is analyzed in 1-D. It is shown that it optimally solves certain edge detection problems. A fast implementation of the algorithm is introduced.

A probabilistic view of diffusion is presented. A discrete symmetric random walk is shown to be equivalent to a heat equation evolution, and an extension to nonlinear evolutions including Perona-Malik equation is shown to be of utmost importance for analysis. Upon unraveling the limitations as well as the advantages of such an equation, we are able to propose a new approach which is demonstrated to outperform existing approaches, and to lift the long-standing problem of when to stop the evolution. Substantiating examples of image enhancement and segmentation are provided.

Approaches to wavelet-based denoising (or signal enhancement) have generally relied on the assumption of normally distributed perturbations. To relax this assumption, which is often violated in practice, we derive a robust wavelet thresholding technique based on the minimax description length (MMDL) principle. We first determine the least favorable distribution in the /spl epsiv/-contaminated normal family as the member that maximizes the entropy. We show that this distribution, and the best estimate based upon it, namely the maximum-likelihood estimate, together constitute a saddle point. The MMDL approach results in a thresholding scheme that is resistant to heavy tailed noise. We further extend this framework and propose a novel approach to selecting an adapted or best basis (BB) that results in optimal signal reconstruction. Finally, we address the practical case where the underlying signal is known to be bounded, and derive a two-sided thresholding technique that is resistant to outliers and has bounded error.

We propose a best basis algorithm for signal enhancement in white Gaussian noise. The best basis search is performed in families of orthonormal bases constructed with wavelet packets or local cosine bases. We base our search for the "best" basis on a criterion of minimal reconstruction error of the underlying signal. This approach is intuitively appealing, because the enhanced or estimated signal has an associated measure of performance, namely, the resulting mean-square error. Previous approaches in this framework have focused on obtaining the most "compact" signal representations, which consequently contribute to effective denoising. These approaches, however, do not possess the inherent measure of performance which our algorithm provides. We first propose an estimator of the mean-square error, based on a heuristic argument and subsequently compare the reconstruction performance based upon it to that based on the Stein (1981) unbiased risk estimator. We compare the two proposed estimators by providing both qualitative and quantitative analyses of the bias term. Having two estimators of the mean-square error, we incorporate these cost functions into the search for the "best" basis, and subsequently provide a substantiating example to demonstrate their performance.

Some wavelet-based methods for signal estimation in the presence of noise are reviewed in the context of the parsimonious representation of the underlying signal. Three approaches are considered. The first is based on the application of the minimum description length (MDL) principle. The robustness of this method is improved in the second approach, by relaxing the assumption of known noise distribution following Huber's (1967) work. In the third approach, a Bayesian strategy is adopted in order to incorporate prior information pertaining to the signal of interest; this method is especially useful at low signal-to-noise ratios.

We present an estimation-theoretic approach for reducing motion effects in SAR imaging. Our approach may be viewed as a multi-dimensional matched-filter, whose parameters are determined by the relative motion between the SAR antenna and the target. In contrast to similar multi-dimensional matched filter methods, we propose a fast and easily implementable solution.

Adapted wavelet analysis of signals is achieved by optimizing a selected criterion. We previously introduced a majorization framework for constructing selection functionals, which can be as well suited to compression as to entropy or other methods. We show how these functionals operate on the basis selection and their effect on the statistics of the resulting representation.

Approaches to wavelet-based denoising (or signal enhancement) have so far relied on the assumption of normally distributed perturbations. To relax this assumption, which is often violated in practice, we derive a robust wavelet thresholding technique based on the minimax description length principle. We first determine the least favorable distribution in the /spl epsi/-contaminated normal family as the member that maximizes the entropy. We show that this distribution and the best estimate based upon it, namely the maximum likelihood estimate, constitute a saddle point. This results in a threshold that is more resistant to heavy-tailed noise, but for which the estimation error is still potentially unbounded. We address the practical case where the underlying signal is known to be bounded, and derive a two-sided thresholding technique that is resistant to outliers and has bounded error. We provide illustrative examples.

To abate the enormous costs incurred in the transmission and storage of SAR data, we present a segmentation driven compression technique using hierarchical stochastic modeling within a multiscale framework. Our approach to SAR image compression is unique in that we exploit the multiscale stochastic structure inherent in SAR imagery. This structure is well captured by a set of scale auto-regressive models that accurately characterize the evolution in scale. We thus use the local evolution in scale of SAR imagery to generate a segmentation map which is then used in tandem with the corresponding models to provide a robust, hierarchical compression technique.

We present efficient multiscale approaches to the segmentation of natural clutter, specifically grass and forest, and to the enhancement of anomalies in synthetic aperture radar (SAR) imagery. The methods we propose exploit the coherent nature of SAR sensors. In particular, they take advantage of the characteristic statistical differences in imagery of different terrain types, as a function of scale, due to radar speckle. We employ a class of multiscale stochastic processes that provide a powerful framework for describing random processes and fields that evolve in scale. We build models representative of each category of terrain of interest (i.e., grass and forest) and employ them in directing decisions on pixel classification, segmentation, and anomalous behaviour. The scale-autoregressive nature of our models allows extremely efficient calculation of likelihoods for different terrain classifications over windows of SAR imagery. We subsequently use these likelihoods as the basis for both image pixel classification and grass-forest boundary estimation. In addition, anomaly enhancement is possible with minimal additional computation. Specifically, the residuals produced by our models in predicting SAR imagery from coarser scale images are theoretically uncorrelated. As a result, potentially anomalous pixels and regions are enhanced and pinpointed by noting regions whose residuals display a high level of correlation throughout scale. We evaluate the performance of our techniques through testing on 0.3-m resolution SAR data gathered with Lincoln Laboratory's millimeter-wave SAR.

Automatic segmentation of the electrocardiogram (ECG) is important in both clinical and research settings. Past algorithms have relied on incorporation of detailed heuristics. We avoid heuristics by employing a best-basis algorithm. As large variability of the local SNR causes the standard entropy criterion to produce an overly-fine segmentation, we introduce a novel optimality criterion which is based on a linear combination of the entropy measure and a function of a smoothness measure, and is quite general in form. We tested the algorithm on the MIT-BIH arrythmia database and body surface potential maps.

Wavelet packets and local trigonometric bases provide an efficient framework and fast algorithms to obtain a "best basis" or "best representation" of deterministic signals. Applying these deterministic techniques to stochastic processes may, however, lead to variable results. We revisit this problem and introduce a prior model on the underlying signal in noise and account for the contaminating noise model as well. We thus develop a Bayesian-based approach to the best basis problem, while preserving the classical tree search efficiency.

We present an efficient multiscale approach to the segmentation of natural clutter, specifically grass and forest, in synthetic aperture imagery (SAR) and to the enhancement of anomalous image regions therein. The methods we propose exploit the coherent nature of SAR sensors. In particular, they characterize the scale-to-scale statistical differences in imagery of various terrain categories due to radar speckle. To achieve this, we employ a recently introduced class of multiscale stochastic processes that provide a powerful framework for describing random processes and fields that evolve in scale. We build models representative of each relevant category of terrain and use them to direct subsequent decisions on pixel classification, segmentation, and anomaly presence.

We propose a best basis algorithm for signal enhancement in white Gaussian noise. We base our search of best basis on a criterion of minimal reconstruction error of the underlying signal. We subsequently compare our simple error criterion to the Stein (1981) unbiased risk estimator, and provide a substantiating example to demonstrate its performance. A review is also given of noise removal by thresholding and of wavepacket orthonormal bases.

Processing nonstationary signals is an important and challenging problem. We focus on the class of nonstationary processes with stationary increments of an arbitrary order, and place them in a multiscale framework. Unlike other related studies, we concentrate on the discrete-time analysis and derive a number of new results in addition to placing the related existing ones in the same framework. We extend the study to various parametric models for which we derive the resulting multiresolution description. We show that wide-sense stationarity may be achieved by adequately selecting the analysis wavelet. After generalizing the study to wavelet packet analysis, we show that the latter possesses additional properties which are useful in the presence of other types of nonstationarities.>

Two different approaches for estimating the direction of arrival (DOA) of two coherent signals impinging on a uniform linear array are analyzed. Simple asymptotic expressions for the variance as well as for the bias of the estimated angles are derived. The simplicity of the method allows much insight and an easy analytic comparison is achieved. Examples are also provided.>

A formal approach is presented to carry out a performance analysis of subspace-based estimation techniques applied to the problem of the direction of arrival of plane waves. This approach was inspired by the operator formalism, on account of its algebraic simplicity. It is a generalized approach that can be easily modified to analyze any subspace-based technique, as it uses a series expansion of projection operators on the signal and noise subspaces. A perturbation analysis is performed on the operators, thus avoiding a direct use of the eigenvectors and eigenvalues. This allows the analysis to be carried out to any desired order. This is made possible by using an original recurrence formula developed for the higher order terms in the expansion of the projection operators. This method is applied to study the root-min-norm algorithm with uncorrelated signals impinging from distinct directions on a uniform linear array and then extended to the correlated signal scenario. Simulations which verify the analytical derivations are provided.>

The relationship between Cadzow's signal subspace algorithm and the spatially smoothed minimum-norm algorithm of Tufts-Kumaresan is investigated. It is shown that Cadzow's algorithm can be realized by subarray averaging lower rank approximations to the array covariance matrix. A data-domain algorithm that is applicable in a correlated signal environment is formulated. This algorithm offers the advantage of lower word length requirements, and obviates the necessity of computing higher order statistics. It may also be extended in a straightforward way to incorporate signal enumeration. Simulation results are given that contrast the performance of this algorithm to the signal eigenvector approach.>