Analysis Dictionary Learning Based Classification: Structure for Robustness.

A discriminative structured analysis dictionary is proposed for the classification task. A structure of the union of subspaces (UoS) is integrated into the conventional analysis dictionary learning to enhance the capability of discrimination. A simple classifier is also simultaneously included into the formulated function to ensure a more complete consistent classification.

Metric Driven Classification: A Non-Parametric Approach Based on the Henze-Penrose Test Statistic.

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.

Subspace learning of dynamics on a shape manifold: a generative modeling approach.

In this paper, we propose a novel subspace learning algorithm of shape dynamics. Compared to the previous works, our method is invertible and better characterizes the nonlinear geometry of a shape manifold while retaining a good computational efficiency. In this paper, using a parallel moving frame on a shape manifold, each path of shape dynamics is uniquely represented in a subspace spanned by the moving frame, given an initial condition (the starting point and starting frame).

Human activity as a manifold valued random process.

Most of previous shape based human activity models were built with either a linear assumption or an extrinsic interpretation of the nonlinear geometry of the shape space, both of which proved to be problematic on account of the nonlinear intrinsic geometry of the associated shape spaces. In this paper we propose an intrinsic stochastic modeling of human activity on a shape manifold. More importantly, within an elegant and theoretically sound framework, our work effectively bridges the nonlinear modeling of human activity on a nonlinear space, with the classic stochastic modeling in a Euclidean space, and thereby provides a foundation for a more effective and accurate analysis of the nonlinear feature space of activity models.

Multiphase joint segmentation-registration and object tracking for layered images.

In this paper we propose to jointly segment and register objects of interest in layered images. Layered imaging refers to imageries taken from different perspectives and possibly by different sensors. Registration and segmentation are therefore the two main tasks which contribute to the bottom level, data alignment, of the multisensor data fusion hierarchical structures.

Object recognition through topo-geometric shape models using error-tolerant subgraph isomorphisms.

We propose a method for 3-D shape recognition based on inexact subgraph isomorphisms, by extracting topological and geometric properties of a shape in the form of a shape model, referred to as topo-geometric shape model (TGSM). In a nutshell, TGSM captures topological information through a rigid transformation invariant skeletal graph that is constructed in a Morse theoretic framework with distance function as the Morse function. Geometric information is then retained by analyzing the geometric profile as viewed through the distance function.

Squigraphs for fine and compact modeling of 3-D shapes.

We propose to superpose global topological and local geometric 3-D shape descriptors in order to define one compact and discriminative representation for a 3-D object. While a number of available 3-D shape modeling techniques yield satisfactory object classification rates, there is still a need for a refined and efficient identification/recognition of objects among the same class. In this paper, we use Morse theory in a two-phase approach.

Joint brain parametric T1-map segmentation and RF inhomogeneity calibration.

We propose a constrained version of Mumford and Shah's (1989) segmentation model with an information-theoretic point of view in order to devise a systematic procedure to segment brain magnetic resonance imaging (MRI) data for parametric T(1)-Map and T(1)-weighted images, in both 2-D and 3D settings. Incorporation of a tuning weight in particular adds a probabilistic flavor to our segmentation method, and makes the 3-tissue segmentation possible. Moreover, we proposed a novel method to jointly segment the T(1)-Map and calibrate RF Inhomogeneity (JSRIC).

A shearlet approach to edge analysis and detection.

It is well known that the wavelet transform provides a very effective framework for analysis of multiscale edges. In this paper, we propose a novel approach based on the shearlet transform: a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges. Indeed, unlike traditional wavelets, shearlets are theoretically optimal in representing images with edges and, in particular, have the ability to fully capture directional and other geometrical features.

Stochastic differential equations and geometric flows.

In previous years, curve evolution, applied to a single contour or to the level sets of an image via partial differential equations, has emerged as an important tool in image processing and computer vision. Curve evolution techniques have been utilized in problems such as image smoothing, segmentation, and shape analysis. We give a local stochastic interpretation of the basic curve smoothing equation, the so called geometric heat equation, and show that this evolution amounts to a tangential diffusion movement of the particles along the contour.

Multiscale signal enhancement: beyond the normality and independence assumption.

Current approaches to denoising or signal enhancement in a wavelet-based framework have generally relied on the assumption of normally distributed perturbations. In practice, this assumption is often violated and sometimes prior information of the probability distribution of a noise process is not even available. To relax this assumption, we propose a novel nonlinear filtering technique in this paper.

Flexible skew-symmetric shape model for shape representation, classification, and sampling.

Skewness of shape data often arises in applications (e.g., medical image analysis) and is usually overlooked in statistical shape models.

Geodesic matching of triangulated surfaces.

Recognition of images and shapes has long been the central theme of computer vision. Its importance is increasing rapidly in the field of computer graphics and multimedia communication because it is difficult to process information efficiently without its recognition. In this paper, we propose a new approach for object matching based on a global geodesic measure.

An independent component analysis approach for minimizing effects of recirculation in dynamic susceptibility contrast magnetic resonance imaging.

In dynamic susceptibility contrast (DSC) perfusion-weighted imaging, effects of recirculation are normally minimized by a gamma-variate fitting procedure of the concentration curves before estimating hemodynamic parameters. The success of this method, however, hinges largely on the extent to which magnetic resonance signal is altered in the presence of a contrast agent and a temporal separation between the first and subsequent passages of the contrast agent. Moreover, important physiologic information might be compromised by imposing an analytic equation to all measured concentration curves.

Identification of a discrete planar symmetric shape from a single noisy view.

In this paper, we propose a method for identifying a discrete planar symmetric shape from an arbitrary viewpoint. Our algorithm is based on a newly proposed notion of a view's skeleton. We show that this concept yields projective invariants which facilitate the identification procedure.

Fast incorporation of optical flow into active polygons.

In this paper, we first reconsider, in a different light, the addition of a prediction step to active contour-based visual tracking using an optical flow and clarify the local computation of the latter along the boundaries of continuous active contours with appropriate regularizers. We subsequently detail our contribution of computing an optical flow-based prediction step directly from the parameters of an active polygon, and of exploiting it in object tracking. This is in contrast to an explicitly separate computation of the optical flow and its ad hoc application.

Smart nonlinear diffusion: a probabilistic approach.

In this paper, a stochastic interpretation of nonlinear diffusion equations used for image filtering is proposed. This is achieved by relating the problem of evolving/smoothing images to that of tracking the transition probability density functions of an underlying random process. We show that such an interpretation of, e.