Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A fast level set method for propagating interfaces
Journal of Computational Physics
International Journal of Computer Vision
Geodesic Active Contours and Level Sets for the Detection and Tracking of Moving Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
A PDE-based fast local level set method
Journal of Computational Physics
Fundamenta Informaticae - Special issue on mathematical morphology
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Multigrid
Comparing Images Using the Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multigrid anisotropic diffusion
IEEE Transactions on Image Processing
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Shock filter coupled to curvature diffusion for image denoising and sharpening
Image and Vision Computing
On two multigrid algorithms for modeling variational multiphase image segmentation
IEEE Transactions on Image Processing
A parallel multigrid Poisson solver for fluids simulation on large grids
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Heuristically driven front propagation for geodesic paths extraction
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
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Active contour models are among the most popular PDE-based tools in computer vision. In this paper we present a new algorithm for the fast evolution of geodesic active contours and compare it with other established numerical schemes. The new algorithm employs a full time-implicit and unconditionally stable numerical scheme and applies multigrid methods for the efficient solution of the occurring sparse linear system. When we utilize very big time-steps for the numerical evolution of the front, the proposed scheme has increased accuracy and better rotational invariance properties compared with the alternative AOS scheme. This allows for the rapid evolution and convergence of the contour to its final configuration after only very few iterations. Standard pyramidal and/or narrowband techniques can be easily integrated into our algorithm and further accelerate the curve evolution. Experimental results in object boundary detection demonstrate the power of the method.