An Integral Solution to Surface Evolution PDEs Via Geo-cuts

We introduce a new approach to modelling gradient flows of contours and surfaces. While standard variational methods (e.g. level sets) compute local interface motion in a differential fashion by estimating local contour velocity via energy derivatives, we propose to solve surface evolution PDEs by explicitly estimating integral motion of the whole surface. We formulate an optimization problem directly based on an integral characterization of gradient flow as an infinitesimal move of the (whole) surface giving the largest energy decrease among all moves of equal size. We show that this problem can be efficiently solved using recent advances in algorithms for global hypersurface optimization [4, 2, 11]. In particular, we employ the geo-cuts method [4] that uses ideas from integral geometry to represent continuous surfaces as cuts on discrete graphs. The resulting interface evolution algorithm is validated on some 2D and 3D examples similar to typical demonstrations of level-set methods. ...

• Type: Conference
• Year: 2006
• Where: ECCV
• Authors: Yuri Boykov, Vladimir Kolmogorov, Daniel Cremers, Andrew Delong
• Keywords: Computer Vision, ECCV 2006, Gradient Flows, Integral Motion, Local Interface Motion, Standard L2 Distance, Surface Evolution Pdes