New Possibilities with Sobolev Active Contours
International Journal of Computer Vision
New possibilities with Sobolev active contours
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
An SL(2) Invariant Shape Median
Journal of Mathematical Imaging and Vision
New Possibilities in Image Diffusion and Sharpening via High-Order Sobolev Gradient Flows
Journal of Mathematical Imaging and Vision
Image Sharpening via Sobolev Gradient Flows
SIAM Journal on Imaging Sciences
Spaces and manifolds of shapes in computer vision: An overview
Image and Vision Computing
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Recently proposed Sobolev active contours introduced a new paradigm for minimizing energies defined on curves by changing the traditional cost of perturbing a curve and thereby redefining their gradients. Sobolev active contours evolve more globally and are less attracted to certain intermediate local minima than traditional active contours. In this paper we analyze Sobolev active contours in the Fourier domain in order to understand their evolution across different scales. This analysis shows an important and useful behavior of Sobolev contours, namely, that they move successively from coarse to increasingly finer scale motions in a continuous manner. Along with other properties, the previous observation reveals that Sobolev active contours are ideally suited for tracking problems that use active contours. Our purpose in this work is to show how a variety of active contour based tracking methods can be significantly improved merely by evolving the active contours according to the Sobolev method.