Sparse Finite Elements for Geodesic Contours with Level-Sets

Level-set methods have been shown to be an effective way to solve optimisation problems that involve closed curves. They are well known for their capacity to deal with flexible topology and do not require manual initialisation. Computational complexity has previously been addressed by using banded algorithms which restrict computation to the vicinity of the zero set of the level-set function. So far, such schemes have used finite difference representations which suffer from limited accuracy and require re-initialisation procedures to stabilise the evolution. This paper shows how banded computation can be achieved using finite elements. We give details of the novel representation and show how to build the signed distance constraint into the presented numerical scheme. We apply the algorithm to the geodesic contour problem (including the automatic detection of nested contours) and demonstrate its performance on a variety of images. The resulting algorithm has several advantages which are...

• Type: Conference
• Year: 2004
• Where: ECCV
• Authors: Martin Weber, Andrew Blake, Roberto Cipolla
• Keywords: Computer Vision, ECCV 2004, Finite Difference Representations, Finite Elements, Geodesic Contour Problem, Maximum Sparsity, Nested Contours