The emphasis of the two approaches described in this chapter is on determining shape skeletons in the presence of noise. The parts of the skeleton which are most robust in the presence of noise correspond to the parts of the shape where its width varies slowly. In contrast, singular points of the skeleton such as junctions tend to be sensitive to noise. The strategy therefore is to concentrate ...

This paper presents a new theory of multipath shape factors that greatly simplifies the description of small-scale fading statistics of a wireless receiver. A method is presented for reducing a multipath channel with arbitrary spatial complexity to three shape factors that have simple intuitive geometrical interpretations. Furthermore, these shape factors are shown to describe the statistics of...

BACKGROUND The shape diversity of 16.4 million biologically relevant molecules from the PubChem Compound database and their 1.46 billion diverse conformers was explored as a function of molecular volume. RESULTS The diversity of shape space was investigated by determining the shape similarity threshold to achieve a maximum on the count of reference shapes per unit of conformer volume. The rat...

A static shape analysis is presented that can prove the absence of NULLand dangling pointer dereferences in standard algorithms on lists, trees and graphs. It is conceptually simpler than other analyses that use symbolically represented logic to describe the heap. Instead, it represents the heap as a single graph and a Boolean formula. The key idea is to summarize two nodes by calculating their...

Shape similarity assessment is a fundamental geometric reasoning problem that finds application in several different product design and manufacturing applications. A computationally efficient way to assess shape similarity is to first abstract 3D object shapes into shape signatures and use shape signatures to perform similarity assessment. Several different types of shape signatures have been d...

The problem of efficiently finding images that are similar to a target image has attracted much attention in the image processing community and is rightly considered an information retrieval task. However, the problem of finding structure and regularities in large image datasets is an area in which data mining is beginning to make fundamental contributions. In this work, we consider the new pro...

Pixel brightness variations in an image sequence depend both on the objects’ surface reflectance and on the motion of the camera and object. In the case of rigid shapes some proposed models have been very successful explaining the relation among these strongly coupled components. On the other hand, shapes which deform pose new challenges since the relation between pixel brightness variation wit...

We present a framework for shape alignment that generalizes several existing methods. We assume that the shape is a closed genus zero surface. Our framework requires a diffeomorphic surface mapping to the 2-sphere which preserves rotation. Our similarity measure is a global spherical cross-correlation function of surface-intrinsic scalar attributes, weighted by the cross-correlation of the para...

We propose a method of using shape adaptation for compression of light fields of 3-D objects. Shape adaptation is incorporated into two light field coders, both applying disparity compensation with an explicit geometry model, to improve the compression efficiency. The shape information can be derived at the decoder from an accurate geometry model. If the available geometry is inaccurate, we pro...