Convex Relaxation Approach to Optimize the Number of Image Models

Post date: Dec 12, 2010 8:6:50 AM

The optimization of image models, e.g. appearances, is of utmost importance in image segmentation, which, combined with the minimum perimeter of segments, leads to the minimum description length (MDL) principle of image partition. On the other hand, it results a challenging problem both in optimization theory and in numerical computation. Previously, only slow and local solvers were available. Recently, Delong et al proposed a comprehensive graph-cut technique to optimize the smoothness of segmentation edges and the total number of segments at the same time. But it is restricted to the constructed image graph which is well-known to generate metric errors in segmentation results. In this study, we show that the total number of image models, which is highly non-convex, can be properly described as the convex infinity norm of the respective labeling functions. With helps of the total-variation function, MDL based image segmentation, consequently, can be formulated as a convex optimization problem and solved by fast convex programming solvers. Sufficient experiments validates the energy function and proves it significant effectiveness in practice.

Related works:

• • Jing Yuan, Egil Bae, Yuri Boykov and Xue-Cheng Tai, A Continuous Max-Flow Approach to Minimal Partitions with Label Cost Prior, International Conference on Scale Space and Variational Methods in Computer Vision (SSVM) 2011

  • Jing Yuan, Yuri Boykov, TV-Based Image Segmentation with Label Cost Prior, British Machine Vision Conference (BMVC) 2010