On the representation of a digital contour with an unordered point set for visual perception

Abstract

In this paper, we study the problem of representing the boundary of a digital object with an unordered set of points (pixels) chosen from its 1-pixel wide contour such that its shape is visually perceptible and uniquely reconstructible. Extraction of such a set is important from the viewpoint of shape description and may also offer potential solutions to various applications like object representation, recognition, and discrimination. We propose a novel technique of determining an irredundant point set from a digital contour using the classical concept of pointillism. Pointillism, a movement of painting with dots that would blend in the viewer’s eye, was developed by certain Neo-Impressionists of France late in the 19th century. In order to extract the representative point set, we first consider the digitally straight pieces constituting the contour and then obtain a digital polygon P that approximates the bounding curve in a compact form. The polygon P , defined in terms of its ordered set of vertices, is replaced, in turn, with an irredundant set P ′ of pseudo-vertices lying on its digital edges, so that the union of P and P ′ produces an unordered point set that obviates the vertex ordering but captures the underlying geometric orderliness and the neighborhood relations defining the boundary of the original object. The pseudo-vertices may be chosen by controlling a parameter called pointillist factor that governs our visual perception with the nearest-neighbor correlation of a point set. The pointillist factor can be regulated to control the prominence of the underlying object with its unordered set of points — a strong outcome that establishes the technique about its ability to capture the shape information by an order-free point set of optimal or suboptimal size. We have also given a reconstruction procedure along with an error analysis related with the concerned descriptor. Experimental results on several databases demonstrate its elegance and effectiveness.