A Variational Method in Image Recovery
SIAM Journal on Numerical Analysis
Geometric curve flows on parametric manifolds
Journal of Computational Physics
A simple embedding method for solving partial differential equations on surfaces
Journal of Computational Physics
Level Set Equations on Surfaces via the Closest Point Method
Journal of Scientific Computing
Active Contour Based Segmentation of 3D Surfaces
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
IEEE Transactions on Image Processing
Scale Space Analysis and Active Contours for Omnidirectional Images
IEEE Transactions on Image Processing
SIAM Journal on Scientific Computing
Journal of Computational Physics
Real-Time Fluid Effects on Surfaces using the Closest Point Method
Computer Graphics Forum
Journal of Scientific Computing
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We propose a method to detect objects and patterns in textures on general surfaces. Our approach applies the Chan-Vese variational model for active contours without edges to the problem of segmentation of scalar surface data. This leads to gradient descent equations which are level set equations on surfaces. These equations are evolved using the Closest Point Method, which is a recent technique for solving partial differential equations (PDEs) on surfaces. The final algorithm has a particularly simple form: it merely alternates a time step of the usual Chan-Vese model in a small 3D neighborhood of the surface with an interpolation step. We remark that the method can treat very general surfaces since it uses a closest point function to represent the underlying surface. Various experimental results are presented, including segmentation on smooth surfaces, nonsmooth surfaces, open surfaces, and general triangulated surfaces.