2011/02/18 by Thomas Schoenemann, Schoenemann, Thomas, Fredrik Kahl +5
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Artificial Intelligence (cs.AI) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Medical Image Segmentation Techniques #Optimization and Control (math.OC) #cs.AI #cs.CV #math.OC
paper · pdf · doi:10.48550/arxiv.1102.3830
arxiv created 2011/02/18 · openalex publication_date 2011/02/18 · arxiv updated 2011/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present the first method to handle curvature regularity in region-based image segmentation and inpainting that is independent of initialization. To this end we start from a new formulation of length-based optimization schemes, based on surface continuation constraints, and discuss the connections to existing schemes. The formulation is based on a cell complex and considers basic regions and boundary elements. The corresponding optimization problem is cast as an integer linear program. We then show how the method can be extended to include curvature regularity, again cast as an integer linear program. Here, we are considering pairs of boundary elements to reflect curvature. Moreover, a constraint set is derived to ensure that the boundary variables indeed reflect the boundary of the regions described by the region variables. We show that by solving the linear programming relaxation one gets quite close to the global optimum, and that curvature regularity is indeed much better suited in the presence of long and thin objects compared to standard length regularity.