Shape Modeling with Front Propagation: A Level Set Approach

Shape Modeling with Front Propagation: A Level Set Approach

June 1994 | R. Malladi, J.A. Sethian, and B.C. Vemuri
This paper presents a new approach to shape modeling using front propagation and a level set method. The 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. The method is applied to model arbitrarily complex shapes, including those with significant protrusions, and to situations where no a priori assumption about the object's topology is made. A single instance of the model can split freely to represent each object when presented with an image having more than one shape of interest. The method is demonstrated with numerical experiments on synthesized images and low contrast medical images. The approach allows for the recovery of detailed structure from noisy data and can handle topological changes, such as splitting and merging of curves. The method is also capable of recovering shapes with holes in a seamless fashion. The paper discusses the application of the level set method to shape recovery, including various speed functions and approaches to the problem, such as the effect of global speed laws, narrow band formulations, reinitialization, and stopping criteria. The method is shown to be effective in recovering shapes from images, including complex structures like arterial trees and shapes with holes. The approach is also extended to three dimensions, demonstrating its versatility in handling a wide range of shape modeling tasks.This paper presents a new approach to shape modeling using front propagation and a level set method. The 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. The method is applied to model arbitrarily complex shapes, including those with significant protrusions, and to situations where no a priori assumption about the object's topology is made. A single instance of the model can split freely to represent each object when presented with an image having more than one shape of interest. The method is demonstrated with numerical experiments on synthesized images and low contrast medical images. The approach allows for the recovery of detailed structure from noisy data and can handle topological changes, such as splitting and merging of curves. The method is also capable of recovering shapes with holes in a seamless fashion. The paper discusses the application of the level set method to shape recovery, including various speed functions and approaches to the problem, such as the effect of global speed laws, narrow band formulations, reinitialization, and stopping criteria. The method is shown to be effective in recovering shapes from images, including complex structures like arterial trees and shapes with holes. The approach is also extended to three dimensions, demonstrating its versatility in handling a wide range of shape modeling tasks.
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