Shape representation using a generalized potential field model

Abstract

Abstract-This paper is concerned with efficient derivation of the medial axis transform of a two-dimensional polygonal region. Instead of using the shortest distance to the region border, a potential field model is used for computational efficiency. The region border is assumed to be charged and the valleys of the resulting potential field are used to estimate the axes for the medial axis transform. The potential valleys are found by following force field, thus, avoiding twodimensional search. The potential field is computed in closed form using the equations of the border segments. The simple Newtonian potential is shown to be inadequate for this purpose. A higher order potential is defined which decays faster with distance than as inverse of distance. It is shown that as the potential order becomes arbitrarily large, the axes approach those computed using the shortest distance to the border. Algorithms are given for the computation of axes, which can run in linear parallel time for part of the axes having initial guesses. Experimental results are presented for a number of examples.

The Evolution of Object Categorization and the Challenge of Image Abstraction

“…To help manage this complexity, feature hierarchies have re-emerged, in combination with powerful learning tools, to yield exciting new categorization frameworks [7,6,179,41,241,92,171,4,242,273]. 3 Figure 8 illustrates the system of Todorovic and Ahuja [242], in which a region-based hierarchical object model is learned from training examples and used to detect new instances of the model in query images.…”

<title>Generic force server for haptic devices</title>

“…Existing approaches to compute output forces use either a physical representation of the world (the output-force is computed regarding a given set of equations), or directly a given discrete force-field (for example the force-field can be computed from an elevation map. [10][11][12][13][14][15][16][17] The physical representation is well-suited for a haptic rendering of wide range of physical phenomenon, but the need to code the equations could be a real drawback when changing the world or adding/removing other properties is needed. In addition, this representation is not adequate to render other information not linked to a physical phenomenon, like a repulsive field generated by an hazardous area.…”

Force Field Energy Functionals for Image Feature Extraction

“…[9] describes the use of vector potential to extract corners by treating the Canny edge map of the image as a current density. Another recent approach [10] has used a potential ®eld model in a medial axis transform. The concepts underpinning the force ®eld transformation and the mathematics used to describe it can be found in various introductory works on physics [7] and electromagnetics [8].…”