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A novel statistical method is presented for shape modeling by exploiting an extended class of the flexible skew-symmetric shape model (FSSM) distributions, where each is represented by a distribution. FSSM is formulated as a joint bimodal distribution of angle and distance from the centroid of an aggregate of random points.

Robust variants of Wald, Rao and likelihood ratio (LR) tests for the detection of a signal subspace in a signal interference subspace corrupted by contaminated Gaussian noise are proposed in this paper. They are derived using the $\alpha -$ divergence, and the trade-off between the robustness and the power (the probability of detection) of the tests is adjustable using a single hyperparameter $\alpha $. It is shown that when $\alpha \rightarrow 1$ , these tests are equivalent to their well known classical counterparts. For example the robust LR test coincides with the LR test or the matched subspace detector (MSD). Asymptotic results are provided to support the proposed tests and robustness to outliers is obtained using values of $\alpha < 1$. Numerical experiments illustrating the performance of these tests on simulated, real functional magnetic resonance imaging (fMRI), hyperspectral and synthetic aperture radar (SAR) data are also presented. [ABSTRACT FROM AUTHOR]

A new methodology is proposed for three-dimensional (3-D) object matching based on a global geodesic measure. The object matching can be carried out by information-theoretic dissimilarity measure calculations between geodesic shape distributions and is also computationally efficient and inexpensive.

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

The method for identifying a discrete planar symmetric shape from an arbitrary viewpoint is described. It is shown that the proposed method can be extended to the case of noisy data to yield an optimal estimate of a shape in question.

The addition of a prediction step to active contour-based visual tracking using an optical flow is considered, and the local computation of the latter along the boundaries of continuous active contours with appropriate regularizers is clarified. The need of adding 'ad hoc' regularizing terms to the optical flow computations, and the inevitably arbitrary associated weighting parameters are avoided.

A new nonlinear smoothness-constrained filtering technique is described. Numerical experiments show that the approach is effective and efficient.

Image-segmentation and edge-enhancement has been applied to signals and images with very high noise levels and to blurry signals. The approach is based on a new class of evolution equations for processing of imagery and signals. They are called stabilized inverse diffusion equations (SIDEs) and are a family of first-order multidimensional ordinary differential equations with discontinuous right-hand sides. Such an equation is an inverse diffusion everywhere other than at local extreme. At these extreme some stabilization is introduced.

Multiscale stochastic models can be used for segmentation of natural clutters of grass and forest terrains and for enhancement of anomalous pixel regions for man-made object detection in synthetic aperture radar (SAR) imagery. The models take advantage of the coherent nature of SAR sensors and the differences in interscale variability and predictability of different images. The models have a scale-autoregressive nature, and are applicable to image pixel classification and grass-forest boundary detection. The algorithmic calculations involved are simple and efficient.

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

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

A new algorithm for maximum-likelihood blind image restoration is presented in this paper. It is obtained by modeling the original image and the additive noise as multivariate Gaussian processes with unknown covariance matrices. The blurring process is specified by its point spread function, which is also unknown. Estimations of the original image and the blur are derived by alternating minimization of the Kullback–Leibler divergence between a model family of probability distributions defined using the linear image degradation model and a desired family of probability distributions constrained to be concentrated on the observed data. The algorithm presents the advantage to provide closed form expressions for the parameters to be updated and to converge only after few iterations. A simulation example that illustrates the effectiveness of the proposed algorithm is presented. [ABSTRACT FROM AUTHOR]

Existing polyp detection methods rely heavily on curvature-based characteristics to differentiate between lesions. These assume that the discrete triangulated surface mesh or volume closely approximates a smooth continuous surface. However, this is often not the case and because curvature is computed as a local feature and a second-order differential quantity, the presence of noise significantly affects its estimation. For this reason, a more global feature is required to provide an accurate description of the surface at hand. In this paper, a novel method incorporating a local neighborhood around the centroid of a surface patch is proposed. This is done using geodesic rings which accumulate curvature information in a neighborhood around this centroid. This geodesic-ring neighborhood approximates a single smooth, continuous surface upon which curvature and orientation estimation methods can be applied. A new global shape index, S is also introduced and computed. These curvature and orientation values will be used to classify the surface as either a bulbous polyp, ridge-like fold or semiplanar structure. Experimental results show that this method is promising (100% sensitivity, 100% specificity for lesions >10 mm) for distinguishing between bulbous polyps, folds and planar-like structures in the colon. [ABSTRACT FROM AUTHOR]

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

Presents a study which examined a novel nonlinear filtering technique for denoising or signal enhancement in a wavelet-based framework. Theoretical background; Computational approach used; Findings.

Wavelet denoising is a classical and effective approach for reducing noise in images and signals. Suggested in 1994, this approach is carried out by rectifying the coefficients of a noisy image, in the transform domain, using a set of shrinkage functions (SFs). A plethora of papers deals with the optimal shape of the SFs and the transform used. For example, it is widely known that applying SFs in a redundant basis improves the results. However, it is barely known that the shape of the SFs should be changed when the transform used is redundant. In this paper, we introduce a complete picture of the interrelations between the transform used, the optimal shrinkage functions, and the domains in which they are optimized. We suggest three schemes for optimizing the SFs and provide bounds of the remaining noise, in each scheme, with respect to the other alternatives. In particular, we show that for subband optimization, where each SF is optimized independently for a particular band, optimizing the SFs in the spatial domain is always better than or equal to optimizing the SFs in the transform domain. Furthermore, for redundant bases, we provide the expected denoising gain that can be achieved, relative to the unitary basis, as a function of the redundancy rate. [ABSTRACT FROM AUTHOR]

Snapshot compressive imaging (SCI) is a promising approach to capture high-dimensional data with low dimensional sensors. With modest modifications to off-the-shelf cameras, SCI cameras encode multiple frames into a single measurement frame. These correlated frames can then be retrieved by reconstruction algorithms. Existing reconstruction algorithms suffer from low speed or low fidelity. In this paper, we propose a novel reconstruction algorithm, namely, Shearlet enhanced Snapshot Compressive Imaging (SeSCI), which exploits the sparsity of the image representation in both frequency domain and shearlet domain. Towards this end, we first derive our SeSCI algorithm under the alternating direction method of multipliers (ADMM) framework. We then propose an efficient solution of SeSCI algorithm. Moreover, we prove that the improved SeSCI algorithm converges to a fixed point. Experimental results on both synthetic data and real data captured by SCI cameras demonstrate the significant advantages of SeSCI, which outperforms the conventional algorithms by more than 2dB in PSNR. At the same time, the SeSCI achieves a speed-up more than $100\times $ over the state-of-the-art algorithm. [ABSTRACT FROM AUTHOR]

Image decomposition is crucial for many image processing tasks, as it allows to extract salient features from source images. A good image decomposition method could lead to a better performance, especially in image fusion tasks. We propose a multi-level image decomposition method based on latent low-rank representation(LatLRR), which is called MDLatLRR. This decomposition method is applicable to many image processing fields. In this paper, we focus on the image fusion task. We build a novel image fusion framework based on MDLatLRR which is used to decompose source images into detail parts(salient features) and base parts. A nuclear-norm based fusion strategy is used to fuse the detail parts and the base parts are fused by an averaging strategy. Compared with other state-of-the-art fusion methods, the proposed algorithm exhibits better fusion performance in both subjective and objective evaluation. [ABSTRACT FROM AUTHOR]

This paper presents a special matrix factorization based on sparse representation that detects anomalies in video sequences generated with moving cameras. Such representation is made by associating the frames of the target video, that is a sequence to be tested for the presence of anomalies, with the frames of an anomaly-free reference video, which is a previously validated sequence. This factorization is done by a sparse coefficient matrix, and any target-video anomaly is encapsulated into a residue term. In order to cope with camera trepidations, domain-transformations are incorporated into the sparse representation process. Approximations of the transformed-domain optimization problem are introduced to turn it into a feasible iterative process. Results obtained from a comprehensive video database acquired with moving cameras on a visually cluttered environment indicate that the proposed algorithm provides a better geometric registration between reference and target videos, greatly improving the overall performance of the anomaly-detection system. [ABSTRACT FROM AUTHOR]

As one of the most widely used clustering techniques, the fuzzy $k$ -means (FKM) assigns every data point to each cluster with a certain degree of membership. However, conventional FKM approach relies on the square data fitting term, which is sensitive to the outliers with ignoring the prior information. In this paper, we develop a novel and robust fuzzy $k$ -means clustering algorithm, namely, joint learning of fuzzy $k$ -means and nonnegative spectral clustering with side information. The proposed method combines fuzzy $k$ -means and nonnegative spectral clustering into a unified model, which can further exploit the prior knowledge of data pairs such that both the quality of affinity graph and the clustering performance can be improved. In addition, for the purpose of enhancing the robustness, the adaptive loss function is adopted in the objective function, since it smoothly interpolates between $\ell _{1}$ -norm and $\ell _{2}$ -norm. Finally, experimental results on benchmark datasets verify the effectiveness and the superiority of our clustering method. [ABSTRACT FROM AUTHOR]

Person re-identification is a fundamental task in many computer vision and image understanding systems. Due to appearance variations from different camera views, person re-identification still poses an important challenge. In the literature, KISSME has already been introduced as an effective distance metric learning method using pairwise constraints to improve the re-identification performance. Computationally, it only requires two inverse covariance matrix estimations. However, the linear transformation induced by KISSME is not powerful enough for more complex problems. We show that KISSME can be kernelized, resulting in a nonlinear transformation, which is suitable for many real-world applications. Moreover, the proposed kernel method can be used for learning distance metrics from structured objects without having a vectorial representation. The effectiveness of our method is validated on five publicly available data sets. To further apply the proposed kernel method efficiently when data are collected sequentially, we introduce a fast incremental version that learns a dissimilarity function in the feature space without estimating the inverse covariance matrices. The experiments show that the latter variant can obtain competitive results in a computationally efficient manner. [ABSTRACT FROM AUTHOR]

We propose novel convolutional sparse and low-rank coding-based methods for cartoon and texture decomposition. In our method, we first learn a set of generic filters that can efficiently represent cartoon-and texture-type images. Then, using these learned filters, we propose two optimization frameworks to decompose a given image into cartoon and texture components: convolutional sparse coding-based image decomposition; and convolutional low-rank coding-based image decomposition. By working directly on the whole image, the proposed image separation algorithms do not need to divide the image into overlapping patches for leaning local dictionaries. The shift-invariance property is directly modeled into the objective function for learning filters. Extensive experiments show that the proposed methods perform favorably compared with state-of-the-art image separation methods. [ABSTRACT FROM PUBLISHER]

Kernel-based nonlinear mixing models have been applied to unmix spectral information of hyperspectral images when the type of mixing occurring in the scene is too complex or unknown. Such methods, however, usually require the inversion of matrices of sizes equal to the number of spectral bands. Reducing the computational load of these methods remains a challenge in large-scale applications. This paper proposes a centralized band selection (BS) method for supervised unmixing in the reproducing kernel Hilbert space. It is based upon the coherence criterion, which sets the largest value allowed for correlations between the basis kernel functions characterizing the selected bands in the unmixing model. We show that the proposed BS approach is equivalent to solving a maximum clique problem, i.e., searching for the biggest complete subgraph in a graph. Furthermore, we devise a strategy for selecting the coherence threshold and the Gaussian kernel bandwidth using coherence bounds for linearly independent bases. Simulation results illustrate the efficiency of the proposed method. [ABSTRACT FROM PUBLISHER]