We introduce new transforms for efficient compression of image blocks with directional preferences. Each transform, which is an orthogonal basis for a specific direction, is constructed from an eigen-decomposition of a discrete directional Laplacian system matrix. The method is a natural extension of the DCT, expressing the Laplacian in Cartesian coordinates rotated to some predetermined angles. Symmetry properties of the transforms over square domains lead to efficient computation and compact storage of the directional transforms. A version of the directional transforms was implemented within the beyond HEVC software and demonstrated significant improvement for intra block coding.

We present a new active contour model in spatio-velocity space which is based on the probability data association filter (PDAF) approach. It employs a directional-based measurement model of image potential and of optical-flow along the contour points. The proposed directional approach of measurements is the basis for the velocity-based discrimination between measurements of the object to that of image clutter. The model chooses the appropriate measurements which are most consistent with previous estimation of motion in the sense of the PDAF approach. In order to obtain reliable measurements of image motion and of gradient-based image potential, we propose a directional smoothing operator which is the basis for discriminating the objects measurements from that of image clutter. The method was applied to real world tracking problems such as a walking leg and a waving hand.

A new Kalman-filter based active contour model is proposed for tracking of nonrigid objects in combined spatio-velocity space. The model employs measurements of gradient-based image potential and of optical-flow along the contour as system measurements. In order to improve robustness to image clutter and to occlusions an optical-flow based detection mechanism is proposed. The method detects and rejects spurious measurements which are not consistent with previous estimation of image motion.

Using results from robust Kalman filtering, we present a new Kalman filter-based snake model for tracking of nonrigid objects in combined spatio-velocity space. The proposed model is the stochastic version of the velocity snake which is an active contour model for combined tracking of position and velocity of nonrigid boundaries. The proposed model uses image gradient and optical flow measurements along the contour as system measurements. An optical-flow based measurement error is used to detect and reject image measurements which correspond to image clutter or to other objects. The method was applied to object tracking of both rigid and nonrigid objects, resulting in good tracking results and robustness to image clutter, occlusions and numerical noise.

This paper is concerned with image representation by data distributed nonuniformly and in particular with a representation scheme suitable for "area-of-interest" imaging. The class of signals under consideration, whose information density varies with position, can be represented according to a nonuniform sampling scheme. Position-varying projection operators are presented as simple low-pass filtering operations in a Fourier-like domain. Sequential projections are used for pyramidal representation of nonuniformly sampled images. It is shown that irregular random sampling, prevents, under certain mild restrictions, aliasing effects.

We present a method for analyzing the convergence properties of nonlinear dynamical systems yielding second-order bounds on the domain of attraction of an asymptotically stable equilibrium point and on the time of convergence in the estimated domain. We show that under certain conditions on the system, there exists an analytic solution to the corresponding optimization problem. The method is applied in analyzing the dynamics of a neural network model.