Abstract. This work considers a time domain inverse acoustic obstacle scattering problem due to passive data. Motivated by the Helmholtz–Kirchhoff identity in the frequency domain, we propose to relate the time domain measurement data in passive imaging to an approximate data set given by the subtraction of two scattered wave fields. We propose a time domain linear sampling method for the approximate data set and show how to tackle the measurement data in passive imaging. An imaging functional is built based on the linear sampling method, which reconstructs the support of the unknown scattering object using directly the time domain measurements. The functional framework is based on the Laplace transform, which relates the mapping properties of Laplace domain factorized operators to their counterparts in the time domain. Numerical examples are provided to illustrate the capability of the proposed method.

Abstract. This paper is concerned with the problem of inverse scattering of time-harmonic acoustic plane waves by a two-layered medium with a locally rough interface in two dimensions. A direct imaging method is proposed to reconstruct the locally rough interface from the phaseless total-field data measured on the upper half of the circle with a large radius at a fixed frequency or from the phased far-field data measured on the upper half of the unit circle at a fixed frequency. The presence of the locally rough interface poses challenges in the theoretical analysis of the imaging methods. To address these challenges, a technically involved asymptotic analysis is provided for the relevant oscillatory integrals involved in the imaging methods, based mainly on the techniques and results in our recent work [L. Li, J. Yang, B. Zhang, and H. Zhang, arXiv:2208.00456 , 2022] on the uniform far-field asymptotics of the scattered field for acoustic scattering in a two-layered medium. Finally, extensive numerical experiments are conducted to demonstrate the feasibility and robustness of our imaging algorithms.

We present a memory and computation efficient ternary weight networks (TWNs) - with weights constrained to +1, 0 and -1. The Euclidian distance between full (float or double) precision weights and the ternary weights along with a scaling factor is minimized in training stage. Besides, a threshold-based ternary function is optimized to get an approximated solution which can be fast and easily computed. TWNs have shown better expressive abilities than binary precision counterparts. Meanwhile, TWNs achieve up to 16× model compression rate and need fewer multiplications compared with the float32 precision counterparts. Extensive experiments on MNIST, CIFAR-10, and ImageNet datasets show that the TWNs achieve much better result than the Binary-Weight-Networks (BWNs) and the classification performance on MNIST and CIFAR-10 is very close to the full precision networks. We also verify our method on object detection task and show that TWNs significantly outperforms BWN by more than 10% mAP on PASCAL VOC dataset. The pytorch version of source code is available at: https://github.com/Thinklab-SJTU/twns.

Imbalanced classification tasks are widespread in many real-world applications. For such classification tasks, in comparison with the accuracy rate (AR), it is usually much more appropriate to use nondecomposable performance measures such as the area under the receiver operating characteristic curve (AUC) and the$F_β$measure as the classification criterion since the label class is imbalanced. On the other hand, the minimax probability machine is a popular method for binary classification problems and aims at learning a linear classifier by maximizing the AR, which makes it unsuitable to deal with imbalanced classification tasks. The purpose of this article is to develop a new minimax probability machine for the$F_β$measure, called minimax probability machine for the$F_β$-measures (MPMF), which can be used to deal with imbalanced classification tasks. A brief discussion is also given on how to extend the MPMF model for several other nondecomposable performance measures listed in the article. To solve the MPMF model effectively, we derive its equivalent form which can then be solved by an alternating descent method to learn a linear classifier. Further, the kernel trick is employed to derive a nonlinear MPMF model to learn a nonlinear classifier. Several experiments on real-world benchmark datasets demonstrate the effectiveness of our new model.

Synthetic Aperture Radar (SAR) systems work in the open and dynamic environment, and capture new data or new targets continually over time. It requires that SAR target recognition algorithms should have the capability to learn new targets incrementally without forgetting the previously learned targets. Besides, SAR targets of different classes usually have subtle differences which makes the recognition more challenging. In this paper, we propose a fine-grained continual learning algorithm for SAR incremental target recognition. Since data imbalance between old and new classes results in the forgetting of old classes, class-balanced loss is introduced to alleviate this phenomenon. In addition, covariance pooling network is utilized to explore the higher-order statistical information to improve the discrimination of features. Experimental results on real SAR datasets validate the effectiveness of the proposed method.

Polarimetric synthetic aperture radar (PolSAR) data are sequentially acquired and have multiple views obtained from different feature extractors or multiple frequency bands. The fast and accurate classification of PolSAR data in dynamically changing environments is a critical and challenging task. Online learning can handle this task by learning a classifier incrementally from a stream of samples. In this article, we propose an online semisupervised active learning framework for multiview PolSAR data classification, called OSAM. First, a novel online active learning strategy is designed based on the relationships among multiple views and a randomized rule, which allows to only query the labels of some informative incoming samples. Then, in order to utilize both the incoming labeled and unlabeled samples to update the classifiers, a novel online semisupervised learning model is proposed based on co-regularized multiview learning and graph regularization. In addition, the proposed method can deal with the dynamic large-scale multifeature or multifrequency PolSAR data where not only the amount of data but also the number of classes gradually increases in the learning process. Moreover, the mistake bound of the proposed method is derived rigorously. Extensive experiments are conducted on real PolSAR data to evaluate the performance of our algorithm, and the results demonstrate the effectiveness of the proposed method.

Image scene classification aiming to assign specific semantic labels for each image is vital important for the applications of remote sensing (RS) data. In real world, since the observation environment is open and dynamic, RS images are collected sequentially and the numbers of images and classes grow rapidly over time. Most existing scene classification methods are offline learning algorithms which are inefficient and unscalable for this scenario. In this paper, an incremental learning with open set recognition framework is proposed for RS image scene classification in the open and dynamic environment, called ILOSR, which can identify the unknown classes from a stream of data and learn these new classes incrementally. Specifically, a controllable convex hull-based exemplar selection strategy is designed to address the catastrophic forgetting issue in incremental learning, which can reduce training time and memory footprint effectively. In addition, a new loss function based on prototype learning and uncertainty measurement is proposed for open set recognition to enhance the inter-class discrimination and intra-class compactness of the learned deep features. Experimental results on real remote sensing datasets demonstrate that the proposed method can not only outperform the state-of-the-art approaches on offline classification, incremental learning and OSR problem separately, but also achieve better and more stable performance in the experiments for incremental learning with OSR.

For polarimetric synthetic aperture radar (PolSAR) image classification, each pixel can be represented by multiple features from different perspectives, such as polarimetric feature (PF), texture feature (TF) and color feature (CF). Both multi-view canonical correlation analysis (MCCA) and multi-view spectral embedding (MSE) are two unsupervised multi-view subspace learning methods which search for different projection matrices for different features to combine multiple features in a common low-dimensional feature space. However, MCCA emphasizes the correlation of multiple features and MSE learns the complementarity of multiple features. To deeply learn the relation of multiple features, we incorporate MCCA with MSE based on the label information and a symmetric version of revised Wishart (SRW) distance for supervised PolSAR image feature extraction. Experimental results confirm that the proposed method can improve the classification performance.

Spatial information helps improve the performance of polarimetric synthetic aperture radar (PolSAR) image classification. Some existing methods have combined the spatial information and polarimetric features by the third-order tensor representation for feature extraction. They describe a pixel with the patch centered on this pixel. But they neglect the spatial heterogeneity, which may influence the classification performance. Therefore, we firstly seek k nearest samples based on the polarimetric feature similarity for each pixel to construct the second-order tensor, whose first order denotes the nearest samples and the second order denotes the polarimetric features. Moreover, k nearest samples are searched in a spatial local region rather than the full image, which can exploit the spatial information and reduce the computational burden. Then we employ tensor principal component analysis (TPCA) to extract low-dimensional features. Experimental results demonstrate that the proposed method can improve the classification performance compared with other methods.

An important property of the phaseless far field patterns with incident plane waves is the translation invariance. Thus it is impossible to reconstruct the location of the underlying scatterers. By adding a reference point scatterer into the model, we design a novel direct sampling method using the phaseless data directly. The reference point technique not only overcomes the translation invariance, but also brings a practical phase retrieval algorithm. Based on this, we propose a hybrid method combining the novel phase retrieval algorithm and the classical direct sampling methods. Numerical examples in two dimensions are presented to demonstrate their effectiveness and robustness.

The well-known translation invariance property of the phaseless far field patterns with incident plane waves make it is impossible to reconstruct the location of the underlying scatterers even for multiple incident directions and frequencies. To overcome this difficulty, we take the superpositions of plane waves and point sources as the incident fields. The point sources have fixed source location with at most three different scattering strengths. By adding a reference sound-soft obstacle into the scattering system, we show some uniqueness results with phaseless far field data. Of possibly even more interest are the phase retrieval technique and direct sampling methods, without using the reference obstacle. With the help of the point sources, we propose a simple and stable phase retrieval algorithm and design some novel direct sampling methods using the phaseless data directly. The novel phase retrieval algorithm can then be combined with the classical sampling methods for scatterer reconstruction. Finally, we present a variant of numerical examples in two dimensions to verify the effectiveness and robustness of the proposed algorithms.

The fast and accurate classification of polarimetric synthetic aperture radar (PolSAR) data in dynamically changing environments is an important and challenging task. In this paper, we propose an Incremental Multi-view Passive-Aggressive Active learning algorithm, named IMPAA, for PolSAR data classification. This algorithm can deal with online two-view multi-class categorization problem by exploiting the relationship between the polarimetric-color and texture feature sets of PolSAR data. In addition, the IMPAA algorithm can handle the dynamic large-scale datasets where not only the amount of data but also the number of classes gradually increases. Moreover, this algorithm only queries the class labels of some informative incoming samples to update the classifier based on the disagreement of different views' predictors and a randomized rule. Experiments on real PolSAR data demonstrate that the proposed method can use a smaller fraction of queried labels to achieve low online classification errors compared with previously known methods.

Feature extraction is a very important step for polarimetric synthetic aperture radar (PolSAR) image classification. Many dimensionality reduction (DR) methods have been employed to extract features for supervised PolSAR image classification. However, these DR-based feature extraction methods only consider each single pixel independently and thus fail to take into account the spatial relationship of the neighboring pixels, so their performance may not be satisfactory. To address this issue, we introduce a novel tensor local discriminant embedding (TLDE) method for feature extraction for supervised PolSAR image classification. The proposed method combines the spatial and polarimetric information of each pixel by characterizing the pixel with the patch centered at this pixel. Then each pixel is represented as a third-order tensor, of which the first two modes indicate the spatial information of the patch (i.e. the row and the column of the patch) and the third mode denotes the polarimetric information of the patch. Based on the label information of samples and the redundance of the spatial and polarimetric information, a supervised tensor-based dimensionality reduction technique, called TLDE, is introduced to find three projections which project each pixel, that is, the third-order tensor into the low-dimensional feature. Finally, classification is completed based on the extracted features using the nearest neighbor (NN) classifier and the support vector machine (SVM) classifier. The proposed method is evaluated on two real PolSAR data sets and the simulated PolSAR data sets with various number of looks. The experimental results demonstrate that the proposed method not only improves the classification accuracy greatly, but also alleviates the influence of speckle noise on classification.

Reducing samples through convex hull vertices selection (CHVS) within each class is an important and effective method for online classification problems, since the classifier can be trained rapidly with the selected samples. However, the process of CHVS is NP-hard. In this paper, we propose a fast algorithm to select the convex hull vertices, based on the convex hull decomposition and the property of projection. In the proposed algorithm, the quadratic minimization problem of computing the distance between a point and a convex hull is converted into a linear equation problem with a low computational complexity. When the data dimension is high, an approximate, instead of exact, convex hull is allowed to be selected by setting an appropriate termination condition in order to delete more nonimportant samples. In addition, the impact of outliers is also considered, and the proposed algorithm is improved by deleting the outliers in the initial procedure. Furthermore, a dimension convention technique via the kernel trick is used to deal with nonlinearly separable problems. An upper bound is theoretically proved for the difference between the support vector machines based on the approximate convex hull vertices selected and all the training samples. Experimental results on both synthetic and real data sets show the effectiveness and validity of the proposed algorithm.

Polarimetric synthetic aperture radar (PolSAR) plays an indispensable part in remote sensing. With its development and application, rapid and accurate online classification for PolSAR data becomes more and more important. PolSAR data can be depicted by different features such as polarimetric, texture and color features, which can be considered as multiple views. In this paper, we propose an online multiview learning method based on the passive aggressive algorithm, named OMVPA, for PolSAR data real-time classification. The OMVPA method makes full use of the consistency and complementary properties of different views. Experimental results on real PolSAR data demonstrate that the proposed method maintain a smaller mistake rate compared with other methods.

This letter proposes a novel multiview feature extraction method for supervised polarimetric synthetic aperture radar (PolSAR) image classification. PolSAR images can be characterized by multiview feature sets, such as polarimetric features and textural features. Canonical correlation analysis (CCA) is a well-known dimensionality reduction (DR) method to extract valuable information from multiview feature sets. However, it cannot exploit the discriminative information, which influences its performance of classification. Local discriminant embedding (LDE) is a supervised DR method, which can preserve the discriminative information and the local structure of the data well. However, it is a single-view learning method, which does not consider the relation between multiple view feature sets. Therefore, we propose local discriminant CCA by incorporating the idea of LDE into CCA. Specific to PolSAR images, a symmetric version of revised Wishart distance is used to construct the between-class and within-class neighboring graphs. Then, by maximizing the correlation of neighboring samples from the same class and minimizing the correlation of neighboring samples from different classes, we find two projection matrices to achieve feature extraction. Experimental results on the real PolSAR data sets demonstrate the effectiveness of the proposed method.

Generalization ability is widely acknowledged as one of the most important criteria to evaluate the quality of unsupervised models. The objective of our research is to find a better dropout method to improve the generalization ability of convolutional deep belief network (CDBN), an unsupervised learning model for vision tasks. In this paper, the phenomenon of low feature diversity during the training process is investigated. The attention mechanism of human visual system is more focused on rare events and depresses well-known facts. Inspired by this mechanism, No Feature Left Behind Dropout (NFLB Dropout), an adaptive dropout method is firstly proposed to automatically adjust the dropout rate feature-wisely. In the proposed method, the algorithm drops well-trained features and keeps poorly-trained ones with a high probability during training iterations. In addition, we apply two approximations of the quality of features, which are inspired by theory of saliency and optimization. Compared with the model trained by standard dropout, experiment results show that our NFLB Dropout method improves not only the accuracy but the convergence speed as well.

This letter proposes a method that can preserve the global and local discriminative information based on the tensor representation to achieve feature extraction for synthetic aperture radar (SAR) target configuration recognition. We model SAR images of targets with different configurations as different manifolds, and each manifold is represented as a collection of maximal linear patches (MLPs), each depicted by a subspace. The manifold-to-manifold distance and subspace-to-subspace distance are used to maintain the global discriminative structure of data. Meanwhile, point-to-point distance (PPD) in an MLP is exploited to keep the local discriminative information of data. These two terms are then integrated to maintain the structure of data. Experimental results on the moving and stationary target automatic recognition (MSTAR) database demonstrate the effectiveness of the proposed method.

The Wishart fidelity and total variation (TV) based variational model (WisTV) with the positive definite (PD) constraint has shown to be effective for the whole PolSAR covariance data speckle reduction. However, the existing algorithms for solving the WisTV model only give approximation solutions by projecting the results onto the set of PD matrices, and their parameters depend strongly on the data. The purpose of this letter is to propose a new optimization algorithm to address the issues. To keep the uniformity of the parameters for different PolSAR data, a sigmoid function-based normalization method is designed, which ensures the applicability of the WisTV model for the normalized data. By using the orthogonal decomposition of the PD variables, the WisTV model is converted into an unconstrained optimization problem which is further transformed into a multivariable problem based on the equivalent representations of the trace and logdet functions. The alternative minimization technique is then utilized to solve the final optimization problem. The subproblems for each individual variable are convex and their solutions have explicit expressions. Moreover, the computational complexity of the algorithm is discussed. Experimental results on both synthetic and real PolSAR data demonstrate the validity of the proposed algorithm.

In this paper, we propose a nonlocal total variation (NLTV)-based variational model for polarimetric synthetic aperture radar (PolSAR) data speckle reduction. This model, named WisNLTV, is obtained based on the Wishart fidelity term and the NLTV regularization defined for the complex-valued fourth-order tensor data. Since the proposed model is non-convex, an equivalent bi-convex model is obtained using the property of conjugate functions. Then, an efficient iteration algorithm is developed to solve the equivalent bi-convex model, based on the alternating minimization and the forward-backward operator splitting technique. The proposed iteration algorithm is proved to be convergent under certain conditions theoretically and numerically. Experimental results on both synthetic and real PolSAR data demonstrate that the proposed method can effectively reduce speckle noise and, meanwhile, better preserve the details and the repetitive structures such as textures and edges, and the polarimetric scattering characteristics, compared with the other methods.

Graph regularized Sparse Coding (GSC) considers data relationships during Sparse Coding (SC) and thus has better performance in certain image analysis tasks. However, it is very time consuming. This letter aims at speeding up GSC. The alternating optimization framework for GSC involves repeatedly solving a variant of${\ell _1}$minimization referred to as GSRsub in this letter. Traditional ways to deal with GSRsub are to generalize optimization strategies for${\ell _1}$minimization to solve its primal problem that is strongly convex but non-differentiable, thus converging slowly. We propose that GSC can be accelerated by solving a new dual problem of GSRsub called D-GSRsub. Compared with the primal form and the existing dual form of GSRsub, D-GSRsub has a strongly convex and smooth objective function with less variables. Based on these properties, four dual gradient ascent strategies with lower computational complexities are developed. Experimental results on real-world datasets demonstrate that these strategies can dramatically and stably speed up GSC without affecting its performance in the corresponding image analysis tasks.

In this paper, we propose a variational model for polarimetric synthetic aperture radar (PolSAR) data speckle reduction, which is based on the complex Wishart distribution of the covariance or coherency matrix and multichannel total variation (TV) regularization defined for complex-valued matrices. By assuming the TV regularization to be a prior and taking the statistical distribution of the covariance matrix in each resolution element into account, the variational model for PolSAR covariance data speckle suppression, named WisTV-C, is derived from the maximum a posteriori estimate. A similar variational model for PolSAR coherency data speckle reduction, named WisTV-T, is also obtained. As far as we know, this is the first variational model for the whole PolSAR covariance or coherency matrix data despeckling. Since the model is nonconvex, a convex relaxation iterative algorithm is designed to solve the variational problem, based on the variable splitting and alternating minimization techniques. Experimental results on both simulated and real PolSAR data demonstrate that the proposed approach notably removes speckles in the extended uniform areas and, meanwhile, better preserves the spatial resolution, the details such as edges and point scatterers, and the polarimetric scattering characteristics, compared with other methods.

Manifold learning is a hot research topic in the held of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there are no explicit mappings from the input data manifold to the output embedding. This prohibits the application of manifold learning methods in many practical problems such as classification and target detection. Previously, in order to provide explicit mappings for manifold learning methods, many methods have been proposed to get an approximate explicit representation mapping with the assumption that there exists a linear projection between the high-dimensional data samples and their low-dimensional embedding. However, this linearity assumption may be too restrictive. In this paper, an explicit nonlinear mapping is proposed for manifold learning, based on the assumption that there exists a polynomial mapping between the high-dimensional data samples and their low-dimensional representations. As far as we know, this is the hrst time that an explicit nonlinear mapping for manifold learning is given. In particular, we apply this to the method of locally linear embedding and derive an explicit nonlinear manifold learning algorithm, which is named neighborhood preserving polynomial embedding. Experimental results on both synthetic and real-world data show that the proposed mapping is much more effective in preserving the local neighborhood information and the nonlinear geometry of the high-dimensional data samples than previous work.

The support vector machine (SVM) method, as a promising classification technique, has been widely used in various fields due to its high efficiency. However, SVM cannot effectively solve online classification problems since, when a new sample is misclassified, the classifier has to be retrained with all training samples plus the new sample, which is time consuming. According to the geometric characteristics of SVM, in this paper we propose an online SVM classifier called VS-OSVM, which is based on convex hull vertices selection within each class. The VS-OSVM algorithm has two steps: 1) the samples selection process, in which a small number of skeleton samples constituting an approximate convex hull in each class of the current training samples are selected and 2) the online updating process, in which the classifier is updated with newly arriving samples and the selected skeleton samples. From the theoretical point of view, the first d+1 (d is the dimension of the input samples) selected samples are proved to be vertices of the convex hull. This guarantees that the selected samples in our approach keep the greatest amount of information of the convex hull. From the application point of view, the new algorithm can update the classifier without reducing its classification performance. Experimental results on benchmark data sets have shown the validity and effectiveness of the VS-OSVM algorithm.

Manifold learning is an important topic in pattern recognition and computer vision. However, most manifold learning algorithms implicitly assume the data are aligned on a single manifold, which is too strict in actual applications. Isometric feature mapping (Isomap), as a promising manifold learning method, fails to work on data which distribute on clusters in a single manifold or manifolds. In this paper, we propose a new multi-manifold learning algorithm (M-Isomap). The algorithm first discovers the data manifolds and then reduces the dimensionality of the manifolds separately. Meanwhile, a skeleton representing the global structure of whole data set is built and kept in low-dimensional space. Secondly, by referring to the low-dimensional representation of the skeleton, the embeddings of the manifolds are relocated to a global coordinate system. Compared with previous methods, these algorithms can keep both of the intra and inter manifolds geodesics faithfully. The features and effectiveness of the proposed multi-manifold learning algorithms are demonstrated and compared through experiments.

In this letter, we propose a semi-supervised dimensionality reduction method named Discriminative Sparsity Preserving Projection (DSPP). In order to get the feature mapping$f$which projects the high-dimensional data into a low-dimensional intrinsic space, DSPP attempts to maintain the prior low-dimensional representation constructed by the data points and the known class labels and, meanwhile, considers the complexity of$f$in the ambient space and the smoothness of$f$in preserving the sparse representation of data. On one hand, the DSPP method obtains an explicit nonlinear feature mapping for the out-of-sample extrapolation. On the other hand, the DSPP method has a high discriminative ability which is inherited from the sparse representation of data. Experiment results show the effectiveness of the proposed method.

Manifold learning is a fast growing area of research recently. The main purpose of manifold learning is to search for intrinsic variables underlying high-dimensional inputs which lie on or are close to a low-dimensional manifold. Different from current theoretical works and applications of manifold learning approaches, in our work manifold learning framework is transferred to tracking feature extraction for the first time. The contributions of this article include three aspects. Firstly, in this article, we focus on tracking feature extraction for dynamic visual tracking on dynamic systems. The feature extracted in this article is based on manifold learning framework and is particular for dynamic tracking purpose. It can be directly applied to system control of dynamic systems. This is different from most traditional tracking features which are used for recognition and detection. Secondly, the proposed tracking feature extraction method has been successfully applied to three different dynamic systems: dynamic robot system, intelligent vehicle system and aircraft visual navigation system. Thirdly, experimental results have proven the validity of the tracking method based on manifold learning framework. Particularly, in the tracking experiments the vision system is dynamic. The tracking method is also compared with the well-known mean-shift tracking method, and tracking results have shown that our method outperforms the latter.

Manifold learning has been a popular method in many areas such as classification and recognition. In this paper, we propose a novel algorithm for pedestrian tracking based on our previous work on manifold learning. A new kind of manifold subspace is introduced, in which the intrinsic features of the target's motion can be best preserved, and the dimensionality of feature is very low. In the proposed subspace, variations of continuous pedestrian postures can be represented well by these intrinsic features. This also validates our conjecture that the movement of pedestrians can be described by some intrinsic and low-dimensional features, which are significant for tracking. Although intrinsic features are useful for tracking, algorithms that directly apply intrinsic features could not guarantee stable performance due to the influence from a complicated background. To address this issue, a foreground extraction method is introduced to enhance tracking stability by selecting the most discriminative color features to automatically distinguish the foreground from the candidate image. This preprocessing stage is proven to promote the accuracy of low-dimensional feature representation in pedestrian tracking. The whole tracking procedure, particularly dimensionality reduction, is linear and fast without complicated calculations. The experimental results validate the effectiveness of our algorithm under challenging conditions, such as a complex background, various pedestrian postures, and even occlusion.

In general, localization is a very important step in the manufacturing process, which can be considered as a prior process of assembly, machining, transportation, etc. Localization can be achieved with or without sensors. Compared with localization with sensors, localization without sensors can be more reliable, cheaper, and can have lower requirements on the environment. For example, localization without sensors can be achieved in a dark environment. However, it is more restrictive to the condition of the system. Localization of 2-D objects without sensors has been deeply investigated. Some theoretical results on 3-D-object localization without sensors have been given. On the other hand, some work has been carried out that tries to find methods to reduce uncertainties in the 3-D orientation of a polyhedron (i.e., the orientation of the polyhedron in a 3-D space). However, to the best of our knowledge, no practical and effective methods have been proposed, so far, to localize a polyhedron from any initial 3-D orientation to a unique 3-D orientation without sensors. This paper aims to find conditions and strategies for 3-D objects to be rotated from an unknown initial stable state to a unique stable state without sensors. The main contributions of this paper are given as follows: 1) It is discovered and proved that there are two classes of 3-D objects that can be rotated into a unique state from an arbitrary initial state without sensory feedback. 2) For these two classes of objects, the practical strategies are presented, and one example for each class is given to show the validity of the strategy. 3) Based on the above results, the robotic system and localization operations are illustrated, and some experimental results are given.

Manifold learning is a hot topic in the field of computer science, particularly since nonlinear dimensionality reduction based on manifold learning was proposed in Science in 2000. The work has achieved great success. The main purpose of current manifold-learning approaches is to search for independent intrinsic variables underlying high dimensional inputs which lie on a low dimensional manifold. In this paper, a new manifold is built up in the training step of the process, on which the input training samples are set to be close to each other if the values of their intrinsic variables are close to each other. Then, the process of dimensionality reduction is transformed into a procedure of preserving the continuity of the intrinsic variables. By utilizing the new manifold, the dynamic tracking of a human who can move and rotate freely is achieved. From the theoretical point of view, it is the first approach to transfer the manifold-learning framework to dynamic tracking. From the application point of view, a new and low dimensional feature for visual tracking is obtained and successfully applied to the real-time tracking of a free-moving object from a dynamic vision system. Experimental results from a dynamic tracking system which is mounted on a dynamic robot validate the effectiveness of the new algorithm.

Sensorless localization of 3D objects has been a significant research topic for many years. Researchers have focused on this problem from both theoretical and practical perspective where the goal is to reduce uncertainties in the orientation of a 3D object. However, to the best of our knowledge, no effective practical methods have been proposed so far to localize a polyhedron from any initial orientation to a unique orientation without sensors. In our previous work [1], two broad classes of 3D objects have been introduced, which can be localized from an arbitrary state to a unique state on a flat plane (the surface resting on the flat plane is established) without sensors. In this paper, a much broader class of polyhedra is introduced, which can be localized to a unique state without sensors. The main contributions of this paper are given as follows: • It is found that a polyhedron with an arbitrary initial state on the flat plane can be rotated to a fixed orientation (the orientation of the surface resting on the flat plane is fixed), provided that the polygon corresponding to each surface of the polyhedron can be oriented to a unique orientation in a 2D space. The method of rotating the polyhedron to a fixed orientation is given. • Base on the above result, both conditions and the strategy are given for a polyhedron to be localized to a unique state. • An example is given to show the validity of the strategy.

Tracking multiple people in crowded and cluttered dynamic scenes is a very difficult task in robotic vision due to the highly frequent occlusion and lack of visibility of objects. In this paper, we present a manifold learning based multiple people tracking approach with occlusion reasoning to solve this problem. In our previous work, a new Intrinsic Variable Preserving Manifold Learning (IVPML) method is proposed, by which the continuity of the intrinsic motion variables for tracking is preserved on a new manifold after dimensionality reduction. In this paper, the IVPML method is extended to be applied to tracking multiple people with occlusion situations. Associated with spatio-temporal continuity of tracking and IVPML method, a novel robust occlusion reasoning method is proposed during the alternations of multiple people. For occlusion recovery, region covariance representation including both spatial and statistic properties of objects are used to detect people after occlusion. The multiple people tracking method has been successfully applied to mobile robotic visual tracking system in several complicated environments. Comparisons and experimental results have shown the effectiveness of the new algorithm in various situations.

Support vector machines (SVM) decomposition methods were proposed to solve high dimensional and/or large data classification problems. Two major decomposition algorithms: Karush-kuhn-Tucker (KKT) condition based algorithm, and 'Joachims' decomposition algorithm are popularly adopted. In this paper, both these two decomposition methods are analyzed and applied into face recognition with three basic mapping kernels. Numerical results showed that: a) face recognition with SVM performs better accuracy than other existed methods; b) the decomposition methods can perform face recognition efficiently; c) Joachims' decomposition method has better accuracy than that of decomposition algorithm based on KKT condition; d) linear kernel can provide much higher recognition accuracy than polynomial and slightly better accuracy than Gaussian radial based function (RBF) kernel; Also due to the fact that the linear kernel method is much simpler than others, it is most suitable for face recognition.

In this paper, a novel methodology called a reference model approach to stability analysis of neural networks is proposed. The core of the new approach is to study a neural network model with reference to other related models, so that different modeling approaches can be combinatively used and powerfully cross-fertilized. Focused on two representative neural network modeling approaches (the neuron state modeling approach and the local field modeling approach), we establish a rigorous theoretical basis on the feasibility and efficiency of the reference model approach. The new approach has been used to develop a series of new, generic stability theories for various neural network models. These results have been applied to several typical neural network systems including the Hopfield-type neural networks, the recurrent back-propagation neural networks, the BSB-type neural networks, the bound-constraints optimization neural networks, and the cellular neural networks. The results obtained unify, sharpen or generalize most of the existing stability assertions, and illustrate the feasibility and power of the new method.