Translation, scale, and deformationweighted polar active contours

Polar active contours have proven to be a powerful segmentation method for many medical as well as other computer vision applications, such as interactive image segmentation or tracking. Inspired by recent work on Sobolev active contours we derive a Sobolev-type function space for polar curves, which is endowed with a metric that allows us to favor origin translations and scale changes over smooth deformations of the curve. The resulting translation, scale, and deformation weighted polar active contours inherit the coarse-to-fine behavior of Sobolev active contours as well as their robustness to local minima and are thus very useful for many medical applications, such as cross-sectional vessel segmentation, aneurysm analysis, or cell tracking.