Shape is one of the most important property that is perceived about objects. It allows predicting more facts about an object when compared with other features. Thus recognizing shape is crucial for object recognition. This paper proposes an optimal morphological shape decomposition scheme that represents the object accurately and efficiently. The high level of redundancy in representation is th...

Roots provide plants with mechanical stability and pure water. Wind and gravitational forces on plants are spread out by the roots over a large volume of soil. In a similar manner, roots absorb pure water and nutrients from moist soil. These processes are mathematically similar and have similar optimal solutions, unless the soil is inhomogeneous -i.e. if one part is wetter, whereas another part...

We propose an approach to accurately detecting two-dimensional (2-D) shapes. The cross section of the shape boundary is modeled as a step function. We first derive a one-dimensional (1-D) optimal step edge operator, which minimizes both the noise power and the mean squared error between the input and the filter output. This operator is found to be the derivative of the double exponential (DODE)...

This paper presents the solution to the following optimization problem: What is the shape of the region that minimizes the average Lp distance between all pairs of points if the area of this region is held fixed? (The Lp-distance between two points x = (x1, x2) and y = (y1, y2) in < 2 is (|x1 − y1| p + |x2 − y2| p).) We use variational methods to determine the shape of the region that minimizes...

With the objective of minimizing the total execution time of a parallel program on a distributed memory parallel computer, this paper discusses the selection of an optimal supernode shape of a supernode transformation (also known as tiling). We assume that the communication cost is dominated by the startup penalty and therefore, can be approximated by a constant. We identify three parameters of...

Shape deformation analysis is concerned with determining a deformation of a given shape into another one, which is optimal for a certain cost. We provide the main ideas for a new general approach to shape deformation analysis, using the framework of optimal control theory. This point of view can be made independent from the parametrization of the shape, and allows to model general constrained s...

This paper investigates how context-based DPCM techniques can be used in conjunction with an operationally rate-distortion (ORD) optimized shape coder. Object contours are approximated by connected second-order spline segments, each defined by three consecutive control points, and, in the case of inter mode, by segments of the motion-compensated reference contours. In scalable intra mode and no...

We consider a system given by a second order elliptic equation with jumps in the coeecients. This models a body made of two diierent materials and we study the question of the material distribution that minimizes a certain cost functional. We introduce a local compactness condition for a class of characteristic functions to obtain the existence of the optimum. We also indicate a new approximati...