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Shape Modeling with Front Propagation: A Level Set Approach
February 1995 (vol. 17 no. 2)
pp. 158-175

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 retains some of the attractive features of existing methods and overcomes 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 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 and 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. It is moved by solving a “Hamilton-Jacobi” type equation written for a function in which the interface is a particular level set. A speed term synthesized from the image is used to stop the interface in the vicinity 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.

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Index Terms:
Shape modeling, shape recovery, interface motion, level sets, hyperbolic conservation laws, Hamilton-Jacobi equation, entropy condition.
Ravikanth Malladi, James A. Sethian, Baba C. Vemuri, "Shape Modeling with Front Propagation: A Level Set Approach," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 2, pp. 158-175, Feb. 1995, doi:10.1109/34.368173
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