Volumetric Bias in Segmentation and Reconstruction: Secrets and Solutions

Many standard optimization methods for segmentation and reconstruction compute ML model estimates for appearance or geometry of segments, e.g. Zhu-Yuille [23], Torr [20], Chan-Vese [6], GrabCut [18], Delong et al. [8]. We observe that the standard likelihood term in these formu-lations corresponds to a generalized probabilistic K-means energy. In learning it is well known that this energy has a strong bias to clusters of equal size [11], which we express as a penalty for KL divergence from a uniform distribution of cardinalities. However, this volumetric bias has been mostly ignored in computer vision. We demonstrate signif- icant artifacts in standard segmentation and reconstruction methods due to this bias. Moreover, we propose binary and multi-label optimization techniques that either (a) remove this bias or (b) replace it by a KL divergence term for any given target volume distribution. Our general ideas apply to continuous or discrete energy formulations in segmenta- tion, stereo, and other reconstruction problems.