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 formulations 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 significant 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 segmentation, stereo, and other reconstruction problems.