Abstract- Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which re-tains some of the attractive features of existing methods and over-comes some of their limitations. Our techniques can be applied to model arbitrarily complex shapes, which include shapes with significant protrusions, and to situations where no a priori as-sumption about the object’s topology is made. A single instance of our model, when presented with an image having more than one object of interest, has the ability to split freely to represent each object. This method is based on the ideas developed by Osher and Sethian to model propagating solidhiquid interfaces with curva-ture-dependent speeds. The interface (front) is a closed, noninter-secting, hypersurface flowing along its gradient field with con-stant speed or a speed that depends on the curvature. It is moved by solving a “Hamilton-Jacob? ’ type equation written for a func-tion in which the interface is a particular level set. A speed term synthesizpd from the image is used to stop the interface in the vi-cinity of object boundaries. The resulting equation of motion is solved by employing entropy-satisfying upwind finite difference schemes. We present a variety of ways of computing evolving front, including narrow bands, reinitializations, and different stopping criteria. The efficacy of the scheme is demonstrated with numerical experiments on some synthesized images and some low contrast medical images. Index Terms- Shape modeling, shape recovery, interface mo-tion, level sets, hyperbolic conservation laws, Hamilton-Jacobi

In this paper, we propose a snake-based approach that lets a user specify only the distant end points of the curve he wishes to delineate without having to supply an almost complete polygonal approximation. We achieve much better convergence properties than those of traditional snakes by using the image information around these end points to provide boundary conditions and by introducing an optimization schedule that allows the snake to take image information into account first only near its extremities and then, progressively, towards its center.

Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains the most attractive features of existing methods, and overcomes their prominent limitations. Our technique can be applied to model arbitrarily complex shapes, which include shapes with significant protrusions, and to situations where no a priori assumption about the object's topology is made. A single instance of our model, when presented with an image having more than one object of interest, has the ability to split freely to represent each object. This method is based on the ideas developed by Osher & Sethian to model propagating solid/liquid interfaces with curvature-dependent speeds. The interface (front) is a closed, nonintersecting, hypersurface flowing along its gradient field with constant speed or a speed that depends on the curvature...

We show that any algorithm that maintains the connected components of a digital image must take #(log n/ log log n) time per change to the image. The problem can be solved in O(log n) time per change using dynamic planar graph techniques. We discuss applications to computer Go and other games. Keywords: dynamic planar connectivity, percolation, lower bounds, image processing, go, lines of action. # Work supported in part by NSF grant CCR-9258355 and by matching funds from Xerox Corp. 1 1 Introduction A basic problem in image processing consists of finding the connected components of a bitmap image (where each component consists of pixels of a common color adjacent vertically, horizontally, or sometimes diagonally; the same problem applies also to finding regions of an image separated from each other by an edge detection operator). This is a special case of graph connectivity, and can easily be solved in linear time by depth-first search, but there has been some research on fas...

In this paper, we propose a snake-based approach that lets a user specify only the distant end points of the curve he wishes to delineate without having to supply an almost complete polygonal approximation. We achieve much better convergence properties than those of traditional snakes by using the image information around these end points to provide boundary conditions and by introducing an optimization schedule that allows the snake to take image information into account first only near its extremities and then, progressively, towards its center.

A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analysis is then applied to four particular active contour formulations, revealing important characteristics of their convexity, and suggesting that external potentials involving center of mass computations may be better behaved than the ususal potentials based on image gradients. Most importantly, our analysis provides an explanation for the poor convergence behavior at concave boundaries and suggests an alternate algorithm for approaching these types of boundaries. I. Introduction Active contours, originally described by Kass, Witkin, and Terzopoulos [1], have been successfully used in a wide variety of applications. Their main advantage is that they are topologically isomorphic to the feature...