PSIVT '09 Proceedings of the 3rd Pacific Rim Symposium on Advances in Image and Video Technology
New Possibilities with Sobolev Active Contours
International Journal of Computer Vision
On the role of exponential splines in image interpolation
IEEE Transactions on Image Processing
A stochastic model-based approach to image and texture interpolation
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
A fully implicit framework for Sobolev active contours and surfaces
DAGM'11 Proceedings of the 33rd international conference on Pattern recognition
SIAM Journal on Imaging Sciences
Multiple object tracking via prediction and filtering with a sobolev-type metric on curves
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part I
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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, and it is based on a well-structured Riemannian metric. In this paper, we analyze Sobolev active contours using scale-space analysis in order to understand their evolution across different scales. This analysis shows an extremely important and useful behavior of Sobolev contours, namely, that they move successively from coarse to increasingly finer scale motions in a continuous manner. This property illustrates that one justification for using the Sobolev technique is for applications where coarse-scale deformations are preferred over fine scale deformations. Along with other properties to be discussed, the coarse-to-fine observation reveals that Sobolev active contours are, in particular, ideally suited for tracking algorithms that use active contours. We will also justify our assertion that the Sobolev metric should be used over the traditional metric for active contours in tracking problems by experimentally showing how a variety of active contour based tracking methods can be significantly improved merely by evolving the active contour according to the Sobolev method.