Abstract Fast and differentiable solvers for anisotropic and asymmetric distance fields are a key primitive in geometry processing, enabling gradient‐based optimization over metrics, drift fields, and downstream objectives that depend on geodesic distances and geodesics. We present a differentiable Eikonal solver for Randers–Finsler metrics on Cartesian grids that combines the efficiency of a GPU‐friendly column/row fast sweeping with exact gradients obtained by implicit differentiation. Our forward pass uses local one‐ and two‐point upwind updates selected by a causality‐valid stencil; the backward pass exploits the induced arrival‐time ordering to solve the adjoint system via a single reverse‐time back‐substitution, avoiding unrolling (i.e., recording and differentiating through every solver iteration) and substantially reducing memory and runtime. We derive closed‐form derivatives of the discrete updates with respect to arrival times and Randers parameters, and we enforce metric feasibility with differentiable projections that guarantee positive definiteness and valid drift magnitude. Although stencil selection is piecewise‐smooth, we show gradients are stable under small perturbations and match finite differences away from stencil boundaries. We demonstrate accurate forward solutions and enable inverse problems such as recovering spatially varying anisotropic metrics and drift fields from sparse arrival‐time supervision. Finally, we apply the method to learning data‐driven spread models on real wildfire perimeters, illustrating scalability and the practical utility of differentiable Randers distance fields.

A central problem in quantum mechanics involves solving the Electronic Schrödinger Equation for a molecule or material. The Variational Monte Carlo approach to this problem approximates a particular variational objective via sampling, and then optimizes this approximated objective over a chosen parameterized family of wavefunctions, known as the ansatz. Recently neural networks have been used as the ansatz, with accompanying success. However, sampling from such wavefunctions has required the use of a Markov Chain Monte Carlo approach, which is inherently inefficient. In this work, we propose a solution to this problem via an ansatz which is cheap to sample from, yet satisfies the requisite quantum mechanical properties. We prove that a normalizing flow using the following two essential ingredients satisfies our requirements: (a) a base distribution which is constructed from Determinantal Point Processes; (b) flow layers which are equivariant to a particular subgroup of the permutation group. We then show how to construct both continuous and discrete normalizing flows which satisfy the requisite equivariance. We further demonstrate the manner in which the non-smooth nature (``cusps'') of the wavefunction may be captured, and how the framework may be generalized to provide induction across multiple molecules. The resulting theoretical framework entails an efficient approach to solving the Electronic Schrödinger Equation.

Building robotic prostheses requires a sensor-based interface designed to provide the robotic hand with the control required to perform hand gestures. Traditional Electromyography (EMG) based prosthetics and emerging alternatives often face limitations such as muscle-activation limitations, high cost, and complex calibrations. In this paper, we present a low-cost robotic system composed of a smart ankleband for intuitive, calibration-free control of a robotic hand, and a robotic prosthetic hand that executes actions corresponding to leg gestures. The ankleband integrates an Inertial Measurement Unit (IMU) sensor with a lightweight neural network to infer user-intended leg gestures from motion data. Our system represents a significant step towards higher adoption rates of robotic prostheses among arm amputees, as it enables one to operate a prosthetic hand using a low-cost, low-power, and calibration-free solution. To evaluate our work, we collected data from 10 subjects and tested our prototype ankleband with a robotic hand on an individual with an upper-limb amputation. Our results demonstrate that this system empowers users to perform daily tasks more efficiently, requiring few compensatory movements.

We introduce XTRA, a vision model pre-trained with a novel auto-regressive objective that significantly enhances both sample and parameter efficiency compared to previous auto-regressive image models. Unlike contrastive or masked image modeling methods, which have not been demonstrated as having consistent scaling behavior on unbalanced internet data, auto-regressive vision models exhibit scalable and promising performance as model and dataset size increase. In contrast to standard auto-regressive models, XTRA employs a Block Causal Mask, where each Block represents k × k tokens rather than relying on a standard causal mask. By reconstructing pixel values block by block, XTRA captures higher-level structural patterns over larger image regions. Predicting on blocks allows the model to learn relationships across broader areas of pixels, enabling more abstract and semantically meaningful representations than traditional next-token prediction. This simple modification yields two key results. First, XTRA is sample- efficient. Despite being trained on 152 fewer samples (13.1M vs. 2B), XTRA ViT-H/14 surpasses the×top-1 average accuracy of the previous state-of-the-art auto-regressive model across 15 diverse image recognition benchmarks. Second, XTRA is parameter-efficient. Compared to auto-regressive models trained on ImageNet-1k, XTRA ViT-B/16 outperforms in linear and attentive probing tasks, using 7–16× fewer parameters (85M vs. 1.36B/0.63B).

Proteins exist as a dynamic ensemble of multiple conformations, and these motions are often crucial for their functions. However, current structure prediction methods predominantly yield a single conformation, overlooking the conformational heterogeneity revealed by diverse experimental modalities. Here, we present a framework for building experiment-grounded protein structure generative models that infer conformational ensembles consistent with measured experimental data. The key idea is to treat state-of-the-art protein structure predictors (e.g., AlphaFold3) as sequence-conditioned structural priors, and cast ensemble modeling as posterior inference of protein structures given experimental measurements. Through extensive real-data experiments, we demonstrate the generality of our method to incorporate a variety of experimental measurements. In particular, our framework uncovers previously unmodeled conformational heterogeneity from crystallographic densities, generates high-accuracy NMR ensembles orders of magnitude faster than status quo, and incorporates pairwise cross-link constraints. Notably, we demonstrate that our ensembles outperform AlphaFold3 and sometimes better fit experimental data than publicly deposited structures to the protein database (PDB). We believe that this approach will unlock building predictive models that fully embrace experimentally observed conformational diversity.

Robust classification methods predominantly concen-trate on algorithms that address a specific threat model, resulting in ineffective defenses against other threat models. Real-world applications are exposed to this vulnerability, as malicious attackers might exploit alternative threat models. In this work, we propose a novel test-time threat model agnostic algorithm that enhances Adversarial-Trained (AT) models. Our method operates through COnditional image transformation and DIstance-based Prediction (CODIP) and includes two main steps: First, we transform the input image into each dataset class, where the input image might be either clean or attacked. Next, we make a prediction based on the shortest transformed distance. The conditional transformation utilizes the perceptually aligned gradients property possessed by AT models and, as a result, elimi-nates the need for additional models or additional training. Moreover, it allows users to choose the desired balance between clean and robust accuracy without training. The proposed method achieves state-of-the-art results demon-strated through extensive experiments on various models, AT methods, datasets, and attack types. Notably, applying CODIP leads to substantial robust accuracy improvement of up to$+23\%, +20\%, +26\%$, and +22% on CIFAR10, CIFAR100, ImageNet and Flowers datasets, respectively. For more details, visit the project page.

Quantile regression (QR) is a statistical tool for distribution-free estimation of conditional quantiles of a target variable given explanatory features. QR is limited by the assumption that the target distribution is univariate and defined on an Euclidean domain. Although the notion of quantiles was recently extended to multi-variate distributions, QR for multi-variate distributions on manifolds remains underexplored, even though many important applications inherently involve data distributed on, e.g., spheres (climate and geological phenomena), and tori (dihedral angles in proteins). By leveraging optimal transport theory and c-concave functions, we meaningfully define conditional vector quantile functions of high-dimensional variables on manifolds (M-CVQFs). Our approach allows for quantile estimation, regression, and computation of conditional confidence sets and likelihoods. We demonstrate the approach’s efficacy and provide insights regarding the meaning of non-Euclidean quantiles through synthetic and real data experiments.

Multi-rotor aerial autonomous vehicles (MAVs) primarily rely on vision for navigation purposes. However, visual localization and odometry techniques suffer from poor performance in low or direct sunlight, a limited field of view, and vulnerability to occlusions. Acoustic sensing can serve as a complementary or even alternative modality for vision in many situations, and it also has the added benefits of lower system cost and energy footprint, which is especially important for micro aircraft. This paper proposes actively controlling and shaping the aircraft propulsion noise generated by the rotors to benefit localization tasks, rather than considering it a harmful nuisance. We present a neural network architecture for self-noise-based localization in a known environment. We show that training it simultaneously with learning time-varying rotor phase modulation achieves accurate and robust localization. The proposed methods are evaluated using a computationally affordable simulation of MAV rotor noise in 2D acoustic environments that is fitted to real recordings of rotor pressure fields. Code3and data4are accompanied.

The high memory bandwidth demand of sparse embedding layers continues to be a critical challenge in scaling the performance of recommendation models. While prior works have exploited heterogeneous memory system designs and partial embedding sum memoization techniques, they offer limited benefits. This is because prior designs either target a very small subset of embeddings to simplify their analysis or incur a high processing cost to account for all embeddings, which does not scale with the large sizes of modern embedding tables. This paper proposes GRACE-a lightweight and scalable graph-based algorithm-system co-design framework to significantly improve the embedding layer performance of recommendation models. GRACE proposes a novel Item Co-occurrence Graph (ICG) that scalably records item co-occurrences. GRACE then presents a new system-aware ICG clustering algorithm to find frequently accessed item combinations of arbitrary lengths to compute and memoize their partial sums. High-frequency partial sums are stored in a software-managed cache space to reduce memory traffic and improve the throughput of computing sparse features. We further present a cache data layout and low-cost address computation logic to efficiently lookup item embeddings and their partial sums. Our evaluation shows that GRACE significantly outperforms the state-of-the-art techniques SPACE and MERCI by 1.5x and 1.4x, respectively.

A central challenge in building robotic prostheses is the creation of a sensor-based system able to read physiological signals from the lower limb and instruct a robotic hand to perform various tasks. Existing systems typically perform discrete gestures such as pointing or grasping, by employing electromyography (EMG) or ultrasound (US) technologies to analyze muscle states. While estimating finger gestures has been done in the past by detecting prominent gestures, we are interested in detection, or inference, done in the context of fine motions that evolve over time. Examples include motions occurring when performing fine and dexterous tasks such as keyboard typing or piano playing. We consider this task as an important step towards higher adoption rates of robotic prostheses among arm amputees, as it has the potential to dramatically increase functionality in performing daily tasks. To this end, we present an end-to-end robotic system, which can successfully infer fine finger motions. This is achieved by modeling the hand as a robotic manipulator and using it as an intermediate representation to encode muscles' dynamics from a sequence of US images. We evaluated our method by collecting data from a group of subjects and demonstrating how it can be used to replay music played or text typed. To the best of our knowledge, this is the first study demonstrating these downstream tasks within an end-to-end system.

Graph sparsification is a technique that approximates a given graph by a sparse graph with a subset of vertices and/or edges. The goal of an effective sparsification algorithm is to maintain specific graph properties relevant to the downstream task while minimizing the graph's size. Graph algorithms often suffer from long execution time due to the irregularity and the large real-world graph size. Graph sparsification can be applied to greatly reduce the run time of graph algorithms by substituting the full graph with a much smaller sparsified graph, without significantly degrading the output quality. However, the interaction between numerous sparsifiers and graph properties is not widely explored, and the potential of graph sparsification is not fully understood. In this work, we cover 16 widely-used graph metrics, 12 representative graph sparsification algorithms, and 14 real-world input graphs spanning various categories, exhibiting diverse characteristics, sizes, and densities. We developed a framework to extensively assess the performance of these sparsification algorithms against graph metrics, and provide insights to the results. Our study shows that there is no one sparsifier that performs the best in preserving all graph properties, e.g. sparsifiers that preserve distance-related graph properties (eccentricity) struggle to perform well on Graph Neural Networks (GNN). This paper presents a comprehensive experimental study evaluating the performance of sparsification algorithms in preserving essential graph metrics. The insights inform future research in incorporating matching graph sparsification to graph algorithms to maximize benefits while minimizing quality degradation. Furthermore, we provide a framework to facilitate the future evaluation of evolving sparsification algorithms, graph metrics, and ever-growing graph data.

What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on known matches or node or edge attributes is available, or utilize arbitrary graph features. Such methods fare poorly in the pure form of the problem, in which only graph structures are given. Other proposals translate the problem to one of aligning node embeddings, yet, by doing so, provide only a single-scale view of the graph. In this article, we transfer the shape-analysis concept of functional maps from the continuous to the discrete case, and treat the graph alignment problem as a special case of the problem of finding a mapping between functions on graphs. We present GRASP, a method that first establishes a correspondence between functions derived from Laplacian matrix eigenvectors, which capture multiscale structural characteristics, and then exploits this correspondence to align nodes. We enhance the basic form of GRASP by altering two of its components, namely the embedding method and the assignment procedure it employs, leveraging its modular, hence adaptable design. Our experimental study, featuring noise levels higher than anything used in previous studies, shows that the enhanced form of GRASP outperforms scalable state-of-the-art methods for graph alignment across noise levels and graph types, and performs competitively with respect to the best non-scalable ones. We include in our study another modular graph alignment algorithm, CONE, which is also adaptable thanks to its modular nature, and show it can manage graphs with skewed power-law degree distributions.

A variety of complex systems, including social and communication networks, financial markets, biology, and neuroscience are modeled using temporal graphs that contain a set of nodes and directed timestamped edges. Temporal motifs in temporal graphs are generalized from subgraph patterns in static graphs in that they also account for edge ordering and time duration, in addition to the graph structure. Mining temporal motifs is a fundamental problem used in several application domains. However, existing software frameworks offer suboptimal performance due to high algorithmic complexity and irregular memory accesses of temporal motif mining.This paper presents $\mathsf{Mint}$—a novel accelerator architecture and a programming model for mining temporal motifs efficiently. We first divide this workload into three fundamental tasks: search, book-keeping, and backtracking. Based on this, we propose a task-centric programming model that enables decoupled, asynchronous execution. This model unlocks massive opportunities for parallelism, and allows storing task context information on-chip. To best utilize the proposed programming model, we design a domain-specific hardware accelerator using its data path and memory subsystem design to cater to the unique workload characteristics of temporal motif mining. To further improve performance, we propose a novel optimization called search index memoization that significantly reduces memory traffic. We comprehensively compare the performance of $\mathsf{Mint}$ with state-of-the-art temporal motif mining software frameworks (both approximate and exact) running on both CPU and GPU, and show $9\times-2576\times$ benefit in performance.

The success of learning with noisy labels (LNL) methods relies heavily on the success of a warm-up stage where standard supervised training is performed using the full (noisy) training set. In this paper, we identify a "warm-up obstacle": the inability of standard warm-up stages to train high quality feature extractors and avert memorization of noisy labels. We propose "Contrast to Divide" (C2D), a simple framework that solves this problem by pre-training the feature extractor in a self-supervised fashion. Using self-supervised pre-training boosts the performance of existing LNL approaches by drastically reducing the warm-up stage's susceptibility to noise level, shortening its duration, and improving extracted feature quality. C2D works out of the box with existing methods and demonstrates markedly improved performance, especially in the high noise regime, where we get a boost of more than 27% for CIFAR-100 with 90% noise over the previous state of the art. In real-life noise settings, C2D trained on mini-WebVision outperforms previous works both in WebVision and ImageNet validation sets by 3% top-1 accuracy. We perform an in-depth analysis of the framework, including investigating the performance of different pre-training approaches and estimating the effective upper bound of the LNL performance with semi-supervised learning. Code for reproducing our experiments is available at https://github.com/ContrastToDivide/C2D.

Isometric feature mapping is an established time-honored algorithm in manifold learning and non-linear dimensionality reduction. Its prominence can be attributed to the output of a coherent global low-dimensional representation of data by preserving intrinsic distances. In order to enable an efficient and more applicable isometric feature mapping, a diverse set of sophisticated advancements have been proposed to the original algorithm to incorporate important factors like sparsity of computation, conformality, topological constraints and spectral geometry. However, a significant shortcoming of most approaches is the dependence on large-scale dense-spectral decompositions and the inability to generalize to points far away from the sampling of the manifold. In this paper, we explore an unsupervised deep learning approach for computing distance-preserving maps for non-linear dimensionality reduction. We demonstrate that our framework is general enough to incorporate all previous advancements and show a significantly improved local and non-local generalization of the isometric mapping. Our approach involves training with only a few landmark points and avoids the need for population of dense matrices as well as computing their spectral decomposition.

We introduce two constructions in geometric deep learning for 1) transporting orientation-dependent convolutional filters over a manifold in a continuous way and thereby defining a convolution operator that naturally incorporates the rotational effect of holonomy; and 2) allowing efficient evaluation of manifold convolution layers by sampling manifold valued random variables that center around a weighted diffusion mean. Both methods are inspired by stochastics on manifolds and geometric statistics, and provide examples of how stochastic methods - here horizontal frame bundle flows and non-linear bridge sampling schemes, can be used in geometric deep learning. We outline the theoretical foundation of the two methods, discuss their relation to Euclidean deep networks and existing methodology in geometric deep learning, and establish important properties of the proposed constructions.

One of the key factors of enabling machine learning models to comprehend and solve real-world tasks is to leverage multimodal data. Unfortunately, annotation of multimodal data is challenging and expensive. Recently, self-supervised multimodal methods that combine vision and language were proposed to learn multimodal representations without annotation. However, these methods often choose to ignore the presence of high levels of noise and thus yield sub-optimal results. In this work, we show that the problem of noise estimation for multimodal data can be reduced to a multimodal density estimation task. Using multimodal density estimation, we propose a noise estimation building block for multimodal representation learning that is based strictly on the inherent correlation between different modalities. We demonstrate how our noise estimation can be broadly integrated and achieves comparable results to state-of-the-art performance on five different benchmark datasets for two challenging multimodal tasks: Video Question Answering and Text-To-Video Retrieval. Furthermore, we provide a theoretical probabilistic error bound substantiating our empirical results and analyze failure cases. Code: https://github.com/elad-amrani/ssml.

Few-shot detection and classification have advanced significantly in recent years. Yet, detection approaches require strong annotation (bounding boxes) both for pre-training and for adaptation to novel classes, and classification approaches rarely provide localization of objects in the scene. In this paper, we introduce StarNet - a few-shot model featuring an end-to-end differentiable non-parametric star-model detection and classification head. Through this head, the backbone is meta-trained using only image-level labels to produce good features for jointly localizing and classifying previously unseen categories of few-shot test tasks using a star-model that geometrically matches between the query and support images (to find corresponding object instances). Being a few-shot detector, StarNet does not require any bounding box annotations, neither during pre-training nor for novel classes adaptation. It can thus be applied to the previously unexplored and challenging task of Weakly Supervised Few-Shot Object Detection (WS-FSOD), where it attains significant improvements over the baselines. In addition, StarNet shows significant gains on few-shot classification benchmarks that are less cropped around the objects (where object localization is key).

Mechanical image stabilization using actuated gimbals enables capturing long-exposure shots without suffering from blur due to camera motion. These devices, however, are often physically cumbersome and expensive, limiting their widespread use. In this work, we propose to digitally emulate a mechanically stabilized system from the input of a fast unstabilized camera. To exploit the trade-off between motion blur at long exposures and low SNR at short exposures, we train a CNN that estimates a sharp high-SNR image by aggregating a burst of noisy short-exposure frames, related by unknown motion. We further suggest learning the burst’s exposure times in an end-to-end manner, thus balancing the noise and blur across the frames. We demonstrate this method’s advantage over the traditional approach of deblurring a single image or denoising a fixed-exposure burst on both synthetic and real data.

Nowadays, there is an abundance of data involving images and surrounding free-form text weakly corresponding to those images. Weakly Supervised phrase-Grounding (WSG) deals with the task of using this data to learn to localize (or to ground) arbitrary text phrases in images without any additional annotations. However, most recent SotA methods for WSG assume an existence of a pre-trained object detector, relying on it to produce the ROIs for localization. In this work, we focus on the task of Detector-Free WSG (DF-WSG) to solve WSG without relying on a pre-trained detector. The key idea behind our proposed Grounding by Separation (GbS) method is synthesizing ‘text to image-regions’ associations by random alpha-blending of arbitrary image pairs and using the corresponding texts of the pair as conditions to recover the alpha map from the blended image via a segmentation network. At test time, this allows using the query phrase as a condition for a non-blended query image, thus interpreting the test image as a composition of a region corresponding to the phrase and the complement region. Our GbS shows an 8.5% accuracy improvement over previous DF-WSG SotA, for a range of benchmarks including Flickr30K, Visual Genome, and ReferIt, as well as a complementary improvement (above 7%) over the detector-based approaches for WSG.

One major obstacle hindering the ubiquitous use of CNNs for inference is their relatively high memory bandwidth requirements, which can be the primary energy consumer and throughput bottleneck in hardware accelerators. Inspired by quantization-aware training approaches, we propose a compression-aware training (CAT) method that involves training the model to allow better compression of weights and feature maps during neural network deployment. Our method trains the model to achieve low-entropy feature maps, enabling efficient compression at inference time using classical transform coding methods. CAT significantly improves the state-of-the-art results reported for quantization evaluated on various vision and NLP tasks, such as image classification (ImageNet), image detection (Pascal VOC), sentiment analysis (CoLa), and textual entailment (MNLI). For example, on ResNet-18, we achieve near baseline ImageNet accuracy with an average representation of only 1.5 bits per value with 5-bit quantization. Moreover, we show that entropy reduction of weights and activations can be applied together, further improving bandwidth reduction. Reference implementation is available.

Neural network quantization enables the deployment of large models on resource-constrained devices. Current post-training quantization methods fall short in terms of accuracy for INT4 (or lower) but provide reasonable accuracy for INT8 (or above). In this work, we study the effect of quantization on the structure of the loss landscape. We show that the structure is flat and separable for mild quantization, enabling straightforward post-training quantization methods to achieve good results. We show that with more aggressive quantization, the loss landscape becomes highly non-separable with steep curvature, making the selection of quantization parameters more challenging. Armed with this understanding, we design a method that quantizes the layer parameters jointly, enabling significant accuracy improvement over current post-training quantization methods. Reference implementation is available at https://github.com/ynahshan/nn-quantization-pytorch/tree/master/lapq .

Some face recognition methods are designed to utilize geometric information extracted from depth sensors to overcome the weaknesses of single-image based recognition technologies. However, the accurate acquisition of the depth profile is an expensive and challenging process. Here, we introduce a novel method that learns to recognize faces from stereo camera systems without the need to explicitly compute the facial surface or depth map. The raw face stereo images along with the location in the image from which the face is extracted allow the proposed CNN to improve the recognition task while avoiding the need to explicitly handle the geometric structure of the face. This way, we keep the simplicity and cost efficiency of identity authentication from a single image, while enjoying the benefits of geometric data without explicitly reconstructing it. We demonstrate that the suggested method outperforms both existing single-image and explicit depth based methods on largescale benchmarks, and even capable of recognize spoofing attacks. We also provide an ablation study that shows that the suggested method uses the face locations in the left and right images to encode informative features that improve the overall performance.

Magnetic Resonance Imaging (MRI) is considered today the golden-standard modality for soft tissues. The long acquisition times, however, make it more prone to motion artifacts as well as contribute to the relative high costs of this examination. Over the years, multiple studies concentrated on designing reduced measurement schemes and image reconstruction schemes for MRI, however these problems have been so far addressed separately. On the other hand, recent works in optical computational imaging have demonstrated growing success of simultaneous learning-based design of the acquisition and reconstruction schemes manifesting significant improvement in the reconstruction quality with a constrained time budget. Inspired by these successes, in this work, we propose to learn accelerated MR acquisition schemes (in the form of Cartesian trajectories) jointly with the image reconstruction operator. To this end, we propose an algorithm for training the combined acquisition-reconstruction pipeline end-to-end in a differentiable way. We demonstrate the significance of using the learned Cartesian trajectories at different speed up rates. Code available at https://github.com/tomer196/fastMRI-Cartesian.

Convolutional neural networks (CNNs) achieve state-of-the-art accuracy in a variety of tasks in computer vision and beyond. One of the major obstacles hindering the ubiquitous use of CNNs for inference on low-power edge devices is their high computational complexity and memory bandwidth requirements. The latter often dominates the energy footprint on modern hardware. In this paper, we introduce a lossy transform coding approach, inspired by image and video compression, designed to reduce the memory bandwidth due to the storage of intermediate activation calculation results. Our method does not require fine-tuning the network weights and halves the data transfer volumes to the main memory by compressing feature maps, which are highly correlated, with variable length coding. Our method outperform previous approach in term of the number of bits per value with minor accuracy degradation on ResNet-34 and MobileNetV2. We analyze the performance of our approach on a variety of CNN architectures and demonstrate that FPGA implementation of ResNet-18 with our approach results in a reduction of around 40% in the memory energy footprint, compared to quantized network, with negligible impact on accuracy. When allowing accuracy degradation of up to 2%, the reduction of 60% is achieved. A reference implementation accompanies the paper.

Neural network quantization methods often involve simulating the quantization process during training, making the trained model highly dependent on the target bit-width and precise way quantization is performed. Robust quantization offers an alternative approach with improved tolerance to different classes of data-types and quantization policies. It opens up new exciting applications where the quantization process is not static and can vary to meet different circumstances and implementations. To address this issue, we propose a method that provides intrinsic robustness to the model against a broad range of quantization processes. Our method is motivated by theoretical arguments and enables us to store a single generic model capable of operating at various bit-widths and quantization policies. We validate our method's effectiveness on different ImageNet Models. A reference implementation accompanies the paper.

Abstract Adversarial attacks have demonstrated remarkable efficacy in altering the output of a learning model by applying a minimal perturbation to the input data. While increasing attention has been placed on the image domain, however, the study of adversarial perturbations for geometric data has been notably lagging behind. In this paper, we show that effective adversarial attacks can be concocted for surfaces embedded in 3D, under weak smoothness assumptions on the perceptibility of the attack. We address the case of deformable 3D shapes in particular, and introduce a general model that is not tailored to any specific surface representation, nor does it assume access to a parametric description of the 3D object. In this context, we consider targeted and untargeted variants of the attack, demonstrating compelling results in either case. We further show how discovering adversarial examples, and then using them for adversarial training, leads to an increase in both robustness and accuracy. Our findings are confirmed empirically over multiple datasets spanning different semantic classes and deformations.

Intel® RealSense™ SR300 is a depth camera capable of providing a VGA-size depth map at 60 fps and 0.125mm depth resolution. In addition, it outputs an infrared VGA-resolution image and a 1080p color texture image at 30 fps. SR300 form-factor enables it to be integrated into small consumer products and as a front facing camera in laptops and Ultrabooks™. The SR300 depth camera is based on a coded-light technology where triangulation between projected patterns and images captured by a dedicated sensor is used to produce the depth map. Each projected line is coded by a special temporal optical code, that enables a dense depth map reconstruction from its reflection. The solid mechanical assembly of the camera allows it to stay calibrated throughout temperature and pressure changes, drops, and hits. In addition, active dynamic control maintains a calibrated depth output. An extended API LibRS released with the camera allows developers to integrate the camera in various applications. Algorithms for 3D scanning, facial analysis, hand gesture recognition, and tracking are within reach for applications using the SR300. In this paper, we describe the underlying technology, hardware, and algorithms of the SR300, as well as its calibration procedure, and outline some use cases. We believe that this paper will provide a full case study of a mass-produced depth sensing product and technology.

Vector fields arise in a variety of quantity measure and visualization techniques, such as fluid flow imaging, motion estimation, deformation measures, and color imaging, leading to a better understanding of physical phenomena. Recent progress in vector field imaging technologies has emphasized the need for efficient noise removal and reconstruction algorithms. A key ingredient in the successful extraction of signals from noisy measurements is prior information, which can often be represented as a parameterized model. In this work, we extend the overparameterization variational framework in order to perform model-based reconstruction of vector fields. The overparameterization methodology combines local modeling of the data with global model parameter regularization. By considering the vector field as a linear combination of basis vector fields and appropriate scale and rotation coefficients, we can reduce the denoising problem to a simpler form of coefficient recovery. We introduce two versions of the overparameterization framework: a total variation-based method and a sparsity-based method, which relies on the cosparse analysis model. We demonstrate the efficiency of the proposed frameworks for two- and three-dimensional vector fields with linear and quadratic overparameterization models.

Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami operator. In this paper, we propose to adapt the classical Hamiltonian operator from quantum mechanics to the field of shape analysis. To this end, we study the addition of a potential function to the Laplacian as a generator for dual spaces in which shape processing is performed. We present general optimization approaches for solving variational problems involving the basis defined by the Hamiltonian using perturbation theory for its eigenvectors. The suggested operator is shown to produce better functional spaces to operate with, as demonstrated on different shape analysis tasks.

We consider the problem of localizing relevant subsets of non-rigid geometric shapes given only a partial 3D query as the input. Such problems arise in several challenging tasks in 3D vision and graphics, including partial shape similarity, retrieval, and non-rigid correspondence. We phrase the problem as one of alignment between short sequences of eigenvalues of basic differential operators, which are constructed upon a scalar function defined on the 3D surfaces. Our method therefore seeks for a scalar function that entails this alignment. Differently from existing approaches, we do not require solving for a correspondence between the query and the target, therefore greatly simplifying the optimization process; our core technique is also descriptor-free, as it is driven by the geometry of the two objects as encoded in their operator spectra. We further show that our spectral alignment algorithm provides a remarkably simple alternative to the recent shape-from-spectrum reconstruction approaches. For both applications, we demonstrate improvement over the state-of-the-art either in terms of accuracy or computational cost.

Example synthesis is one of the leading methods to tackle the problem of few-shot learning, where only a small number of samples per class are available. However, current synthesis approaches only address the scenario of a single category label per image. In this work, we propose a novel technique for synthesizing samples with multiple labels for the (yet unhandled) multi-label few-shot classification scenario. We propose to combine pairs of given examples in feature space, so that the resulting synthesized feature vectors will correspond to examples whose label sets are obtained through certain set operations on the label sets of the corresponding input pairs. Thus, our method is capable of producing a sample containing the intersection, union or set-difference of labels present in two input samples. As we show, these set operations generalize to labels unseen during training. This enables performing augmentation on examples of novel categories, thus, facilitating multi-label few-shot classifier learning. We conduct numerous experiments showing promising results for the label-set manipulation capabilities of the proposed approach, both directly (using the classification and retrieval metrics), and in the context of performing data augmentation for multi-label few-shot learning. We propose a benchmark for this new and challenging task and show that our method compares favorably to all the common baselines.

We introduce the first completely unsupervised correspondence learning approach for deformable 3D shapes. Key to our model is the understanding that natural deformations (such as changes in pose) approximately preserve the metric structure of the surface, yielding a natural criterion to drive the learning process toward distortion-minimizing predictions. On this basis, we overcome the need for annotated data and replace it by a purely geometric criterion. The resulting learning model is class-agnostic, and is able to leverage any type of deformable geometric data for the training phase. In contrast to existing supervised approaches which specialize on the class seen at training time, we demonstrate stronger generalization as well as applicability to a variety of challenging settings. We showcase our method on a wide selection of correspondence benchmarks, where we outperform other methods in terms of accuracy, generalization, and efficiency.

Distance metric learning (DML) has been successfully applied to object classification, both in the standard regime of rich training data and in the few-shot scenario, where each category is represented by only a few examples. In this work, we propose a new method for DML that simultaneously learns the backbone network parameters, the embedding space, and the multi-modal distribution of each of the training categories in that space, in a single end-to-end training process. Our approach outperforms state-of-the-art methods for DML-based object classification on a variety of standard fine-grained datasets. Furthermore, we demonstrate the effectiveness of our approach on the problem of few-shot object detection, by incorporating the proposed DML architecture as a classification head into a standard object detection model. We achieve the best results on the ImageNet-LOC dataset compared to strong baselines, when only a few training examples are available. We also offer the community a new episodic benchmark based on the ImageNet dataset for the few-shot object detection task.

"Beauty is in the eye of the beholder." This maxim, emphasizing the subjectivity of the perception of beauty, has enjoyed a wide consensus since ancient times. In the digital era, data-driven methods have been shown to be able to predict human-assigned beauty scores for facial images. In this work, we augment this ability and train a generative model that generates faces conditioned on a requested beauty score. In addition, we show how this trained generator can be used to "beautify" an input face image. By doing so, we achieve an unsupervised beautification model, in the sense that it relies on no ground truth target images. Our implementation is available on: https://github.com/beholdergan/Beholder-GAN.

This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We use the Siamese configuration to train a neural network to solve the problem of least squares multidimensional scaling for generating maps that approximately preserve geodesic distances. By training with only a few landmarks, we show a significantly improved local and nonlocal generalization of the isometric mapping as compared to analogous non-parametric counterparts. Importantly, the combination of a deep-learning framework with a multidimensional scaling objective enables a numerical analysis of network architectures to aid in understanding their representation power. This provides a geometric perspective to the generalizability of deep learning.

Abstract We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.

We present DeepISP, a full end-to-end deep neural model of the camera image signal processing (ISP) pipeline. Our model learns a mapping from the raw low-light mosaiced image to the final visually compelling image and encompasses low-level tasks such as demosaicing and denoising as well as higher-level tasks such as color correction and image adjustment. The training and evaluation of the pipeline were performed on a dedicated dataset containing pairs of low-light and well-lit images captured by a Samsung S7 smartphone camera in both raw and processed JPEG formats. The proposed solution achieves state-of-the-art performance in objective evaluation of PSNR on the subtask of joint denoising and demosaicing. For the full end-to-end pipeline, it achieves better visual quality compared to the manufacturer ISP, in both a subjective human assessment and when rated by a deep model trained for assessing image quality.

We present a novel method for neural network quantization. Our method, named UNIQ , emulates a non-uniform k -quantile quantizer and adapts the model to perform well with quantized weights by injecting noise to the weights at training time. As a by-product of injecting noise to weights, we find that activations can also be quantized to as low as 8-bit with only a minor accuracy degradation. Our non-uniform quantization approach provides a novel alternative to the existing uniform quantization techniques for neural networks. We further propose a novel complexity metric of number of bit operations performed (BOPs), and we show that this metric has a linear relation with logic utilization and power. We suggest evaluating the trade-off of accuracy vs. complexity (BOPs). The proposed method, when evaluated on ResNet18/34/50 and MobileNet on ImageNet, outperforms the prior state of the art both in the low-complexity regime and the high accuracy regime. We demonstrate the practical applicability of this approach, by implementing our non-uniformly quantized CNN on FPGA.

The availability of affordable and portable depth sensors has made scanning objects and people simpler than ever. However, dealing with occlusions and missing parts is still a significant challenge. The problem of reconstructing a (possibly non-rigidly moving) 3D object from a single or multiple partial scans has received increasing attention in recent years. In this work, we propose a novel learning-based method for the completion of partial shapes. Unlike the majority of existing approaches, our method focuses on objects that can undergo non-rigid deformations. The core of our method is a variational autoencoder with graph convolutional operations that learns a latent space for complete realistic shapes. At inference, we optimize to find the representation in this latent space that best fits the generated shape to the known partial input. The completed shape exhibits a realistic appearance on the unknown part. We show promising results towards the completion of synthetic and real scans of human body and face meshes exhibiting different styles of articulation and partiality.

Accelerating iterative algorithms for solving inverse problems using neural networks have become a very popular strategy in the recent years. In this work, we propose a theoretical analysis that may provide an explanation for its success. Our theory relies on the usage of inexact projections with the projected gradient descent (PGD) method. It is demonstrated in various problems including image super-resolution.

Comparison among graphs is ubiquitous in graph analytics. However, it is a hard task in terms of the expressiveness of the employed similarity measure and the efficiency of its computation. Ideally, graph comparison should be invariant to the order of nodes and the sizes of compared graphs, adaptive to the scale of graph patterns, and scalable. Unfortunately, these properties have not been addressed together. Graph comparisons still rely on direct approaches, graph kernels, or representation-based methods, which are all inefficient and impractical for large graph collections. In this paper, we propose the Network Laplacian Spectral Descriptor (NetLSD): the first, to our knowledge, permutation- and size-invariant, scale-adaptive, and efficiently computable graph representation method that allows for straightforward comparisons of large graphs. NetLSD extracts a compact signature that inherits the formal properties of the Laplacian spectrum, specifically its heat or wave kernel; thus, it \em hears the shape of a graph. Our evaluation on a variety of real-world graphs demonstrates that it outperforms previous works in both expressiveness and efficiency.

Learning to classify new categories based on just one or a few examples is a long-standing challenge in modern computer vision. In this work, we propose a simple yet effective method for few-shot (and one-shot) object recognition. Our approach is based on a modified auto-encoder, denoted delta-encoder, that learns to synthesize new samples for an unseen category just by seeing few examples from it. The synthesized samples are then used to train a classifier. The proposed approach learns to both extract transferable intra-class deformations, or "deltas", between same-class pairs of training examples, and to apply those deltas to the few provided examples of a novel class (unseen during training) in order to efficiently synthesize samples from that new class. The proposed method improves the state-of-the-art of one-shot object-recognition and performs comparably in the few-shot case.

We propose a fully-convolutional neural-network architecture for image denoising which is simple yet powerful. Its structure allows to exploit the gradual nature of the denoising process, in which shallow layers handle local noise statistics, while deeper layers recover edges and enhance textures. Our method advances the state-of-the-art when trained for different noise levels and distributions (both Gaussian and Poisson). In addition, we show that making the denoiser class-aware by exploiting semantic class information boosts performance, enhances textures and reduces artifacts.

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior on the mapping, and propose a projected descent optimization procedure inspired by difference of convex functions (DC) programming.

Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used as a post-processing stage in the functional correspondence framework. Such frequently used techniques implicitly make restrictive assumptions (e.g., nearisometry) on the considered shapes and in practice suffer from lack of accuracy and result in poor surjectivity. We propose an alternative recovery technique capable of guaranteeing a bijective correspondence and producing significantly higher accuracy and smoothness. Unlike other methods our approach does not depend on the assumption that the analyzed shapes are isometric. We derive the proposed method from the statistical framework of kernel density estimation and demonstrate its performance on several challenging deformable 3D shape matching datasets.

We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label identifying a point on some reference domain; the correspondence is then constructed a posteriori by composing the label predictions of two input shapes. We propose a paradigm shift and design a structured prediction model in the space of functional maps, linear operators that provide a compact representation of the correspondence. We model the learning process via a deep residual network which takes dense descriptor fields defined on two shapes as input, and outputs a soft map between the two given objects. The resulting correspondence is shown to be accurate on several challenging benchmarks comprising multiple categories, synthetic models, real scans with acquisition artifacts, topological noise, and partiality.

The increasing demand for high image quality in mobile devices brings forth the need for better computational enhancement techniques, and image denoising in particular. To this end, we propose a new fully convolutional deep neural network architecture which is simple yet powerful and achieves state-of-the-art performance for additive Gaussian noise removal. Furthermore, we claim that the personal photo-collections can usually be categorized into a small set of semantic classes. However simple, this observation has not been exploited in image denoising until now. We show that a significant boost in performance of up to 0.4dB PSNR can be achieved by making our network class-aware, namely, by fine-tuning it for images belonging to a specific semantic class. Relying on the hugely successful existing image classifiers, this research advocates for using a class-aware approach in all image enhancement tasks.

We propose an efficient procedure for calculating partial dense intrinsic correspondence between deformable shapes performed entirely in the spectral domain. Our technique relies on the recently introduced partial functional maps formalism and on the joint approximate diagonalization (JAD) of the Laplace-Beltrami operators previously introduced for matching non-isometric shapes. We show that a variant of the JAD problem with an appropriately modified coupling term (surprisingly) allows to construct quasi-harmonic bases localized on the latent corresponding parts. This circumvents the need to explicitly compute the unknown parts by means of the cumbersome alternating minimization used in the previous approaches, and allows performing all the calculations in the spectral domain with constant complexity independent of the number of shape vertices. We provide an extensive evaluation of the proposed technique on standard non-rigid correspondence benchmarks and show state-of-the-art performance in various settings, including partiality and the presence of topological noise.

The L1norm has been tremendously popular in signal and image processing in the past two decades due to its sparsity-promoting properties. More recently, its generalization to non-Euclidean domains has been found useful in shape analysis applications. For example, in conjunction with the minimization of the Dirichlet energy, it was shown to produce a compactly supported quasi-harmonic orthonormal basis, dubbed as compressed manifold modes [14]. The continuous L1norm on the manifold is often replaced by the vector ℓ1norm applied to sampled functions. We show that such an approach is incorrect in the sense that it does not consistently discretize the continuous norm and warn against its sensitivity to the specific sampling. We propose two alternative discretizations resulting in an iteratively-reweighed ℓ2norm. We demonstrate the proposed strategy on the compressed modes problem, which reduces to a sequence of simple eigendecomposition problems not requiring non-convex optimization on Stiefel manifolds and producing more stable and accurate results.

We present a method to approximate pairwise distance on a graph, having an amortized sub-linear complexity in its size. The proposed method follows the so called heat method due to Crane et al. The only additional input are the values of the eigenfunctions of the graph Laplacian at a subset of the vertices. Using these values we estimate a random walk from the source points, and normalize the result into a unit gradient function. The eigenfunctions are then used to synthesize distance values abiding by these constraints at desired locations. We show that this method works in practice on different types of inputs ranging from triangular meshes to general graphs. We also demonstrate that the resulting approximate distance is accurate enough to be used as the input to a recent method for intrinsic shape correspondence computation.

The pursuit of smaller pixel sizes at ever increasing resolution in digital image sensors is mainly driven by the stringent price and form-factor requirements of sensors and optics in the cellular phone market. Recently, Eric Fossum proposed a novel concept of an image sensor with dense sub-diffraction limit one-bit pixels (jots), which can be considered a digital emulation of silver halide photographic film. This idea has been recently embodied as the EPFL Gigavision camera. A major bottleneck in the design of such sensors is the image reconstruction process, producing a continuous high dynamic range image from oversampled binary measurements. The extreme quantization of the Poisson statistics is incompatible with the assumptions of most standard image processing and enhancement frameworks. The recently proposed maximum-likelihood (ML) approach addresses this difficulty, but suffers from image artefacts and has impractically high computational complexity. In this work, we study a variant of a sensor with binary threshold pixels and propose a reconstruction algorithm combining an ML data fitting term with a sparse synthesis prior. We also show an efficient hardware-friendly real-time approximation of this inverse operator. Promising results are shown on synthetic data as well as on HDR data emulated using multiple exposures of a regular CMOS sensor.

Abstract The recent introduction of 3D shape analysis frameworks able to quantify the deformation of a shape into another in terms of the variation of real functions yields a new interpretation of the 3D shape similarity assessment and opens new perspectives. Indeed, while the classical approaches to similarity mainly quantify it as a numerical score, map‐based methods also define (dense) shape correspondences. After presenting in detail the theoretical foundations underlying these approaches, we classify them by looking at their most salient features, including the kind of structure and invariance properties they capture, as well as the distances and the output modalities according to which the similarity between shapes is assessed and returned. We also review the usage of these methods in a number of 3D shape application domains, ranging from matching and retrieval to annotation and segmentation. Finally, the most promising directions for future research developments are discussed.

Abstract Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo non‐rigid deformations and only partial views are available, the problem becomes very challenging. To this end, we present a non‐rigid multi‐part shape matching algorithm. We assume to be given a reference shape and its multiple parts undergoing a non‐rigid deformation. Each of these query parts can be additionally contaminated by clutter, may overlap with other parts, and there might be missing parts or redundant ones. Our method simultaneously solves for the segmentation of the reference model, and for a dense correspondence to (subsets of) the parts. Experimental results on synthetic as well as real scans demonstrate the effectiveness of our method in dealing with this challenging matching scenario.

3D models of humans are commonly used within computer graphics and vision, and so the ability to distinguish between body shapes is an important shape retrieval problem. We extend our recent paper which provided a benchmark for testing non-rigid 3D shape retrieval algorithms on 3D human models. This benchmark provided a far stricter challenge than previous shape benchmarks. We have added 145 new models for use as a separate training set, in order to standardise the training data used and provide a fairer comparison. We have also included experiments with the FAUST dataset of human scans. All participants of the previous benchmark study have taken part in the new tests reported here, many providing updated results using the new data. In addition, further participants have also taken part, and we provide extra analysis of the retrieval results. A total of 25 different shape retrieval methods are compared.

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.

This work presents a novel approach for detecting inliers in a given set of correspondences (matches). It does so without explicitly identifying any consensus set, based on a method for inlier rate estimation (IRE). Given such an estimator for the inlier rate, we also present an algorithm that detects a globally optimal transformation. We provide a theoretical analysis of the IRE method using a stochastic generative model on the continuous spaces of matches and transformations. This model allows rigorous investigation of the limits of our IRE method for the case of 2D-translation, further giving bounds and insights for the more general case. Our theoretical analysis is validated empirically and is shown to hold in practice for the more general case of 2D-affinities. In addition, we show that the combined framework works on challenging cases of 2D-homography estimation, with very few and possibly noisy inliers, where RANSAC generally fails.

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.

Intel's newly-announced low-cost RealSense 3D camera claims significantly better precision than other currently available low-cost platforms and is expected to become ubiquitous in laptops and mobile devices starting this year. In this paper, we demonstrate for the first time that the RealSense camera can be easily converted into a real low-cost gaze tracker. Gaze has become increasingly relevant as an input for human-computer interaction due to its association with attention. It is also critical in clinical mental health diagnosis. We present a novel 3D gaze and fixation tracker based on the eye surface geometry captured with the RealSense 3D camera. First, eye surface 3D point clouds are segmented to extract the pupil center and iris using registered infrared images. With non-ellipsoid eye surface and single fixation point assumptions, pupil centers and iris normal vectors are used to first estimate gaze (for each eye), and then a single fixation point for both eyes simultaneously using a RANSAC-based approach. With a simple learned bias field correction model, the fixation tracker demonstrates mean error of approximately 1 cm at 20-30 cm, which is sufficiently adequate for gaze and fixation tracking in human-computer interaction and mental health diagnosis applications.

Abstract We present a fast algorithm for global rigid symmetry detection with approximation guarantees. The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user‐specified threshold, with very high probability. Our method uses a carefully designed sampling of the transformation space, where each transformation is efficiently evaluated using a sublinear algorithm. We prove that the density of the sampling depends on the total variation of the shape, allowing us to derive formal bounds on the algorithm's complexity and approximation quality. We further investigate different volumetric shape representations (in the form of truncated distance transforms), and in such a way control the total variation of the shape and hence the sampling density and the runtime of the algorithm. A comprehensive set of experiments assesses the proposed method, including an evaluation on the eight categories of the COSEG data set. This is the first large‐scale evaluation of any symmetry detection technique that we are aware of.

We construct an extension of spectral and diffusion geometry to multiple modalities through simultaneous diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, object classification, and clustering, showing that the joint spectral geometry better captures the inherent structure of multi-modal data. We also show the relation of many previous approaches for multimodal manifold analysis to our framework.

Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with parsimony-promoting terms. The inherently sequential structure and data-dependent complexity and latency of iterative optimization constitute a major limitation in many applications requiring real-time performance or involving large-scale data. Another limitation encountered by these modeling techniques is the difficulty of their inclusion in discriminative learning scenarios. In this work, we propose to move the emphasis from the model to the pursuit algorithm, and develop a process-centric view of parsimonious modeling, in which a learned deterministic fixed-complexity pursuit process is used in lieu of iterative optimization. We show a principled way to construct learnable pursuit process architectures for structured sparse and robust low rank models, derived from the iteration of proximal descent algorithms. These architectures learn to approximate the exact parsimonious representation at a fraction of the complexity of the standard optimization methods. We also show that appropriate training regimes allow to naturally extend parsimonious models to discriminative settings. State-of-the-art results are demonstrated on several challenging problems in image and audio processing with several orders of magnitude speed-up compared to the exact optimization algorithms.

We propose a method and a prototype imaging system for real-time reconstruction of volumetric piecewise-smooth scattering media. The volume is illuminated by a sequence of structured binary patterns emitted from a fan beam projector, and the scattered light is collected by a two-dimensional sensor, thus creating an under-complete set of compressed measurements. We show a fixed-complexity and latency reconstruction algorithm capable of estimating the scattering coefficients in real-time. We also show a simple greedy algorithm for learning the optimal illumination patterns. Our results demonstrate faithful reconstruction from highly compressed measurements. Furthermore, a method for compressed registration of the measured volume to a known template is presented, showing excellent alignment with just a single projection. Though our prototype system operates in visible light, the presented methodology is suitable for fast x-ray scattering imaging, in particular in real-time vascular medical imaging.

Abstract We present a method for supervised learning of shape descriptors for shape retrieval applications. Many content‐based shape retrieval approaches follow the bag‐of‐features (BoF) paradigm commonly used in text and image retrieval by first computing local shape descriptors, and then representing them in a ‘geometric dictionary’ using vector quantization. A major drawback of such approaches is that the dictionary is constructed in an unsupervised manner using clustering, unaware of the last stage of the process (pooling of the local descriptors into a BoF, and comparison of the latter using some metric). In this paper, we replace the clustering with dictionary learning, where every atom acts as a feature, followed by sparse coding and pooling to get the final BoF descriptor. Both the dictionary and the sparse codes can be learned in the supervised regime via bi‐level optimization using a task‐specific objective that promotes invariance desired in the specific application. We show significant performance improvement on several standard shape retrieval benchmarks.

Informative and discriminative feature descriptors play a fundamental role in deformable shape analysis. For example, they have been successfully employed in correspondence, registration, and retrieval tasks. In recent years, significant attention has been devoted to descriptors obtained from the spectral decomposition of the Laplace-Beltrami operator associated with the shape. Notable examples in this family are the heat kernel signature (HKS) and the recently introduced wave kernel signature (WKS). The Laplacian-based descriptors achieve state-of-the-art performance in numerous shape analysis tasks; they are computationally efficient, isometry-invariant by construction, and can gracefully cope with a variety of transformations. In this paper, we formulate a generic family of parametric spectral descriptors. We argue that to be optimized for a specific task, the descriptor should take into account the statistics of the corpus of shapes to which it is applied (the "signal") and those of the class of transformations to which it is made insensitive (the "noise"). While such statistics are hard to model axiomatically, they can be learned from examples. Following the spirit of the Wiener filter in signal processing, we show a learning scheme for the construction of optimized spectral descriptors and relate it to Mahalanobis metric learning. The superiority of the proposed approach in generating correspondences is demonstrated on synthetic and scanned human figures. We also show that the learned descriptors are robust enough to be learned on synthetic data and transferred successfully to scanned shapes.

We introduce an efficient computational framework for hashing data belonging to multiple modalities into a single representation space where they become mutually comparable. The proposed approach is based on a novel coupled siamese neural network architecture and allows unified treatment of intra- and inter-modality similarity learning. Unlike existing cross-modality similarity learning approaches, our hashing functions are not limited to binarized linear projections and can assume arbitrarily complex forms. We show experimentally that our method significantly outperforms state-of-the-art hashing approaches on multimedia retrieval tasks.

In this paper we present a framework for real time enhancement of speech signals. Our method leverages a new process-centric approach for sparse and parsimonious models, where the representation pursuit is obtained applying a deterministic function or process rather than solving an optimization problem. We first propose a rank-regularized robust version of non-negative matrix factorization (NMF) for modeling time-frequency representations of speech signals in which the spectral frames are decomposed as sparse linear combinations of atoms of a low-rank dictionary. Then, a parametric family of pursuit processes is derived from the iteration of the proximal descent method for solving this model. We present several experiments showing successful results and the potential of the proposed framework. Incorporating discriminative learning makes the proposed method significantly outperform exact NMF algorithms, with fixed latency and at a fraction of it's computational complexity.

A method for removing impulse noise from audio signals by fusing multiple copies of the same recording is introduced in this paper. The proposed algorithm exploits the fact that while in general multiple copies of a given recording are available, all sharing the same master, most degradations in audio signals are record-dependent. Our method first seeks for the optimal non-rigid alignment of the signals that is robust to the presence of sparse outliers with arbitrary magnitude. Unlike previous approaches, we simultaneously find the optimal alignment of the signals and impulsive degradation. This is obtained via continuous dynamic time warping computed solving an Eikonal equation. We propose to use our approach in the derivative domain, reconstructing the signal by solving an inverse problem that resembles the Poisson image editing technique. The proposed framework is here illustrated and tested in the restoration of old gramophone recordings showing promising results; however, it can be used in other applications where different copies of the signal of interest are available and the degradations are copy-dependent.

In this paper, we propose a new and computationally efficient framework for learning sparse models. We formulate a unified approach that contains as particular cases models promoting sparse synthesis and analysis type of priors, and mixtures thereof. The supervised training of the proposed model is formulated as a bilevel optimization problem, in which the operators are optimized to achieve the best possible performance on a specific task, e.g., reconstruction or classification. By restricting the operators to be shift invariant, our approach can be thought as a way of learning analysis+synthesis sparsity-promoting convolutional operators. Leveraging recent ideas on fast trainable regressors designed to approximate exact sparse codes, we propose a way of constructing feed-forward neural networks capable of approximating the learned models at a fraction of the computational cost of exact solvers. In the shift-invariant case, this leads to a principled way of constructing task-specific convolutional networks. We illustrate the proposed models on several experiments in music analysis and image processing applications.

Abstract The use of Laplacian eigenbases has been shown to be fruitful in many computer graphics applications. Today, state‐of‐the‐art approaches to shape analysis, synthesis, and correspondence rely on these natural harmonic bases that allow using classical tools from harmonic analysis on manifolds. However, many applications involving multiple shapes are obstacled by the fact that Laplacian eigenbases computed independently on different shapes are often incompatible with each other. In this paper, we propose the construction of common approximate eigenbases for multiple shapes using approximate joint diagonalization algorithms, taking as input a set of corresponding functions (e.g. indicator functions of stable regions) on the two shapes. We illustrate the benefits of the proposed approach on tasks from shape editing, pose transfer, correspondence, and similarity.

Abstract We present a novel sparse modeling approach to non‐rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so the correspondence between the regions is not know, nor we know how many regions correspond in the two shapes. We show that even with such scarce information, it is possible to establish very accurate correspondence between the shapes by using methods from the field of sparse modeling, being this, the first non‐trivial use of sparse models in shape correspondence. We formulate the problem ofpermuted sparse coding, in which we solve simultaneously for an unknown permutation ordering the regions on two shapes and for an unknown correspondence in functional representation. We also propose a robust variant capable of handling incomplete matches. Numerically, the problem is solved efficiently by alternating the solution of a linear assignment and a sparse coding problem. The proposed methods are evaluated qualitatively and quantitatively on standard benchmarks containing both synthetic and scanned objects.

In this work, we present intrinsic shape context (ISC) descriptors for 3D shapes. We generalize to surfaces the polar sampling of the image domain used in shape contexts: for this purpose, we chart the surface by shooting geodesic outwards from the point being analyzed; `angle' is treated as tantamount to geodesic shooting direction, and radius as geodesic distance. To deal with orientation ambiguity, we exploit properties of the Fourier transform. Our charting method is intrinsic, i.e., invariant to isometric shape transformations. The resulting descriptor is a meta-descriptor that can be applied to any photometric or geometric property field defined on the shape, in particular, we can leverage recent developments in intrinsic shape analysis and construct ISC based on state-of-the-art dense shape descriptors such as heat kernel signatures. Our experiments demonstrate a notable improvement in shape matching on standard benchmarks.

We consider the problem of minimum distortion intrinsic correspondence between deformable shapes, many useful formulations of which give rise to the NP-hard quadratic assignment problem (QAP). Previous attempts to use the spectral relaxation have had limited success due to the lack of sparsity of the obtained “fuzzy” solution. In this paper, we adopt the recently introduced alternative L1relaxation of the QAP based on the principles of game theory. We relate it to the Gromov and Lipschitz metrics between metric spaces and demonstrate on state-of-the-art benchmarks that the proposed approach is capable of finding very accurate sparse correspondences between deformable shapes.

Dynamic Time Warping (DTW), is a simple but efficient technique for matching sequences with rigid deformation. Therefore, it is frequently used for matching shapes in general, and shapes of handwritten words in Document Image Analysis tasks. As DTW is computationally expensive, efficient algorithms for fast computation are crucial. Retrieving images from large scale datasets using DTW, suffers from the constraint of linear searching of all sample in the datasets. Fast approximation algorithms for image retrieval are mostly based on normed spaces where the triangle inequality holds, which is unfortunately not the case with the DTW metric. In this paper we present a novel approach for fast search of handwritten words within large datasets of shapes. The presented approach is based on the Boost-Map [1] algorithm, for embedding the feature space with the DTW measurement to an euclidean space and use the Local Sensitivity Hashing algorithm (LSH) to rank the k-nearest neighbors of a query image. The algorithm, first, processes and embeds objects of the large data sets to a normed space. Fast approximation of k-nearest neighbors using LSH on the embedding space, generates the top kranked samples which are examined using the real DTW distance to give final accurate results. We demonstrate our method on a database of 45; 800 images of word-parts extracted from the IFN/ENIT database [11] and images collected from 51 different writers. Our method achieves a speedup of 4 orders of magnitude over the exact method, at the cost of only a 2:2% reduction in accuracy.

SIFT-like local feature descriptors are ubiquitously employed in computer vision applications such as content-based retrieval, video analysis, copy detection, object recognition, photo tourism, and 3D reconstruction. Feature descriptors can be designed to be invariant to certain classes of photometric and geometric transformations, in particular, affine and intensity scale transformations. However, real transformations that an image can undergo can only be approximately modeled in this way, and thus most descriptors are only approximately invariant in practice. Second, descriptors are usually high dimensional (e.g., SIFT is represented as a 128-dimensional vector). In large-scale retrieval and matching problems, this can pose challenges in storing and retrieving descriptor data. We map the descriptor vectors into the Hamming space in which the Hamming metric is used to compare the resulting representations. This way, we reduce the size of the descriptors by representing them as short binary strings and learn descriptor invariance from examples. We show extensive experimental validation, demonstrating the advantage of the proposed approach.

We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant Laplacian from which local and global geometric structures are extracted. Applications of the proposed framework demonstrate its power in generalizing and enriching the existing set of tools for shape analysis.

In this paper we present a novel approach for fast search of handwritten Arabic word-parts within large lexicons. The algorithm runs through three steps to achieve the required results. First it warps multiple appearances of each word-part in the lexicon for embedding into the same euclidean space. The embedding is done based on the warping path produced by the Dynamic Time Warping (DTW) process while calculating the similarity distance. In the next step, all samples of different word-parts are resampled uniformly to the same size. The kd-tree structure is used to store all shapes representing word parts in the lexicon. Fast approximation of k-nearest neighbors generates a short list of candidates to be presented to the next step. In the third step, the Active-DTW [15] algorithm is used to examine each sample in the short list and give final accurate results. We demonstrate our method on a database of 23,500 images of word-parts extracted from the IFN/ENIT database [6] and 22,000 images collected from 93 writers. Our method achieves a speedup of 5 orders of magnitude over the exact method, at the cost of only a 3.8% reduction in accuracy.

Recent works have shown the use of diffusion geometry for various pattern recognition applications, including nonrigid shape analysis. In this paper, we introduce spectral shape distance as a general framework for distribution-based shape similarity and show that two recent methods for shape similarity due to Rustamov and Mahmoudi and Sapiro are particular cases thereof.

Detection and description of affine-invariant features is a cornerstone component in numerous computer vision applications. In this note, we analyze the notion of maximally stable extremal regions (MSERs) through the prism of the curvature scale space, and conclude that in its original definition, MSER prefers regular (round) regions. Arguing that interesting features in natural images usually have irregular shapes, we propose alternative definitions of MSER which are free of this bias, yet maintain their invariance properties.

The computer vision and pattern recognition communities have recently witnessed a surge of feature-based methods in object recognition and image retrieval applications. These methods allow representing images as collections of “visual words” and treat them using text search approaches following the “bag of features” paradigm. In this article, we explore analogous approaches in the 3D world applied to the problem of nonrigid shape retrieval in large databases. Using multiscale diffusion heat kernels as “geometric words,” we construct compact and informative shape descriptors by means of the “bag of features” approach. We also show that considering pairs of “geometric words” (“geometric expressions”) allows creating spatially sensitive bags of features with better discriminative power. Finally, adopting metric learning approaches, we show that shapes can be efficiently represented as binary codes. Our approach achieves state-of-the-art results on the SHREC 2010 large-scale shape retrieval benchmark.

International audience

We present an efficient O( n ) numerical algorithm for first-order approximation of geodesic distances on geometry images, where n is the number of points on the surface. The structure of our algorithm allows efficient implementation on parallel architectures. Two implementations on a SIMD processor and on a GPU are discussed. Numerical results demonstrate up to four orders of magnitude improvement in execution time compared to the state-of-the-art algorithms.

This paper explores similarity criteria between non-rigid shapes. Broadly speaking, such criteria are divided into intrinsic and extrinsic, the first referring to the metric structure of the objects and the latter to the geometry of the shapes in the Euclidean space. Both criteria have their advantages and disadvantages; extrinsic similarity is sensitive to non-rigid deformations of the shapes, while intrinsic similarity is sensitive to topological noise. Here, we present an approach unifying both criteria in a single distance. Numerical results demonstrate the robustness of our approach in cases where using only extrinsic or intrinsic criteria fail.

Symmetry and self-similarity is the cornerstone of Nature, exhibiting itself through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection of asymmetries is important in numerous practical applications, including crystallography, medical imaging, and face recognition, to mention a few. Conversely, the assumption of underlying shape symmetry can facilitate solutions to many problems in shape reconstruction and analysis. Traditionally, symmetries are described as extrinsic geometric properties of the shape. While being adequate for rigid shapes, such a description is inappropriate for non-rigid ones. Extrinsic symmetry can be broken as a result of shape deformations, while its intrinsic symmetry is preserved. In this paper, we pose the problem of finding intrinsic symmetries of non-rigid shapes and propose an efficient method for their computation.

Addressed here is the problem of constructing and analyzing expression-invariant representations of human faces. We demonstrate and justify experimentally a simple geometric model that allows to describe facial expressions as isometric deformations of the facial surface. The main step in the construction of expression-invariant representation of a face involves embedding of the facial intrinsic geometric structure into some low-dimensional space. We study the influence of the embedding space geometry and dimensionality choice on the representation accuracy and argue that compared to its Euclidean counterpart, spherical embedding leads to notably smaller metric distortions. We experimentally support our claim showing that a smaller embedding error leads to better recognition.

The experience of motion sickness in a virtual environment may be measured through pre and postexperiment self-reported questionnaires such as the Simulator Sickness Questionnaire (SSQ). Although research provides converging evidence that users of virtual environments can experience motion sickness, there have been no controlled studies to determine to what extent the user's subjective response is a demand characteristic resulting from pre and posttest measures. In this study, subjects were given either SSQ's both pre and postvirtual environment immersion, or only postimmersion. This technique tested for contrast effects due to demand characteristics in which administration of the questionnaire itself suggested to the participant that the virtual environment may produce motion sickness. Results indicate that reports of motion sickness after immersion in a virtual environment are much greater when both pre and postquestionnaires are given than when only a posttest questionnaire is used. The implications for assessments of motion sickness in virtual environments are discussed.

Recently, it was proven empirically that facial expressions can be modelled as isometries, that is, geodesic distances on the facial surface were shown to be significantly less sensitive to facial expressions compared to Euclidean ones. Based on this assumption, the 3DFACE face recognition system was built. The system efficiently computes expression invariant signatures based on isometry-invariant representation of the facial surface. One of the crucial steps in the recognition system was embedding of the face geometric structure into a Euclidean (flat) space. Here, we propose to replace the flat embedding by a spherical one to construct isometric invariant representations of the facial image. We refer to these new invariants as spherical canonical images. Compared to its Euclidean counterpart, spherical embedding leads to notably smaller metric distortion. We demonstrate experimentally that representations with lower embedding error lead to better recognition. In order to efficiently compute the invariants we introduce a dissimilarity measure between the spherical canonical images based on the spherical harmonic transform.

We pose the problem of tissue classification in MRI as a blind source separation (BSS) problem and solve it by means of sparse component analysis (SCA). Assuming that most MR images can be sparsely represented, we consider their optimal sparse representation. Sparse components define a physically-meaningful feature space for classification. We demonstrate our approach on simulated and real multi-contrast MRI data. The proposed framework is general in that it is applicable to other modalities of medical imaging as well, whenever the linear mixing model is applicable.

The relative Newton algorithm, previously proposed for quasi-maximum likelihood blind source separation and blind deconvolution of one-dimensional signals is generalized for blind deconvolution of images. Smooth approximation of the absolute value is used as the nonlinear term for sparse sources. In addition, we propose a method of sparsification, which allows blind deconvolution of arbitrary sources, and show how to find optimal sparsifying transformations by supervised learning.

We discuss the synthesis between the 3D and the 2D data in three-dimensional face recognition. We show how to compensate for the illumination and racial expressions using the 3D facial geometry and present the approach of canonical images, which allows us to incorporate geometric information into standard face recognition approaches.

We present an efficient Newton-like algorithm for quasimaximum likelihood (QML) blind deconvolution of images. This algorithm exploits the sparse structure of the Hessian. An optimal distribution-shaping approach by means of sparsification allows one to use simple and convenient sparsity prior for processing of a wide range of natural images. Simulation results demonstrate the efficiency of the proposed method.

We address the problem of blind source separation (BSS) of superimposed images and, in particular, consider the recovery of a scene recorded through a semireflective medium (e.g. glass windshield) from its mixture with a virtual reflected image. We extend the sparse ICA (SPICA) approach to BSS and apply it to the separation of the desired image from the superimposed images, without having any a priori knowledge about its structure and/or statistics. Advances in the SPICA approach are discussed. Simulations and experimental results illustrate the efficiency of the proposed approach, and of its specific implementation in a simple algorithm of a low computational cost. The approach and the algorithm are generic in that they can be adapted and applied to a wide range of BSS problems involving one-dimensional signals or images.

In this paper, we consider the problem of recovery of a scene recorded through a semireflective medium from its mixture with a virtual reflected image using the blind source separation (BSS) framework. We extend the sparse ICA (SPICA) approach and apply it to the separation of the desired image from the superimposed images, without having any a priory knowledge about its structure and/or statistics. Advances in the SPICA approach are discussed. Simulations and experimental results illustrate the efficiency of the proposed approach, and of its specific implementation in a simple algorithm of a low computational cost. The approach and the algorithm are generic and can be adapted and applied to a wide range of BSS problems involving one-dimensional signals or images.

We show an iterative reconstruction framework for diffraction ultrasound tomography. The use of broad-band illumination allows significant reduction of the number of projections compared to straight ray tomography. The proposed algorithm makes use of forward nonuniform fast Fourier transform (NUFFT) for iterative Fourier inversion. Incorporation of total variation regularization allows the reduction of noise and Gibbs phenomena while preserving the edges. The complexity of the NUFFT-based reconstruction is comparable to the frequency-domain interpolation (gridding) algorithm, whereas the reconstruction accuracy (in sense of the L2 and the L(infinity) norm) is better.