Contour estimation using global shape constraints and local forces

Abstract

This paper describes an object contour approximation method and its applications. It is assumed there is a rule R that locally estimates the boundaries of objects. Given a specified set of parameters, p1, ..., pn, and an index t (epsilon) {1, ..., M}, an object is abstracted as a closed curve described by a function C(p1, ..., pn, t) or simply C(t) where the other parameters are understood. An image strip centered at C(ti) and oriented along the normal to the curve at C(ti) is denoted by S(i). Boundary estimation further requires the specification of a function f(i), which is interpreted as a force applied to C(ti). F denotes the force vector (f(1), ..., f(m)). Given a initial curve C(p1(0), ..., pn(0), t), estimates for p1, ..., pn are refined iteratively by minimizing a nonnegative quantity (Epsilon) until pi(n) - 1) < (epsilon) for all i. In this paper, (Epsilon) takes the form: (omega) F2 + (1 - (omega) )F(infinity) , where the 2-norm favors point-group energy minimization fitting of the curve, and to (infinity) -norm favors individual point energy minimization fitting, and 0 &le; <i>w</i> &le; determines the relative importance of each type of fitting. A sequence of such curves initialized near an object will move and deform to fit the object and become fixed during the minimization process. Furthermore, we propose a method to describe the object contour when C(<i>t</i>) is stabilized. We also compare this method with the traditional curve fitting method, Fourier descriptors, dynamic splines, and deformable templates. Details are given for a simple form of this method using elliptical approximation. Finally, we present two applications of this method. The first one is for real-time object tracking, exploring the global shape. The other is for 2-D shape description using the feature vector once the global shape has been determined.