It has been known that Reproducing Kernel Particle (RKP) shape functions with Kronecker delta property are not available in simple forms. Thus, in this paper, we construct highly regular piecewise polynomial Reproducing Polynomial Particle (RPP) shape functions that satisfy the Kronecker Delta Property. Like RKP shape functions, the RPP shape functions reproduce the complete polynomials of degr...

Small particles on supports have been of interest for many years both scientifically and with respect to their uses in heterogeneous catalysis. One of the common and often critical questions is the shape of a small particle, i.e., spherical or faceted, since many of the properties depend upon the relative populations of different surface planes and edges. The question of the equilibrium shape o...

This paper presents a new method for constructing statistical representations of ensembles of similar shapes. The proposed method relies on an optimal distribution of a large set of surface point correspondences, rather than the manipulation of a specific surface parameterization. The optimal configuration is defined as one in which the entropy or information content of each shape is balanced a...

Tracking deforming objects involves estimating the global motion of the object and its local deformations as functions of time. Tracking algorithms using Kalman filters or particle filters have been proposed for tracking such objects, but these have limitations due to the lack of dynamic shape information. In this paper, we propose a novel method based on employing a locally linear embedding in...