Volumetric Bias in Segmentation and Reconstruction: Secrets and Solutions

TL;DR

This paper identifies a volumetric bias in standard segmentation and reconstruction methods, demonstrating its artifacts and proposing optimization techniques to remove or control this bias for improved accuracy.

Contribution

It reveals the overlooked volumetric bias in common energy formulations and introduces methods to eliminate or adjust this bias in segmentation and reconstruction tasks.

Findings

Standard likelihood corresponds to a generalized probabilistic K-means energy.

Volumetric bias causes significant artifacts in segmentation and reconstruction.

Proposed techniques effectively remove or control the bias.

Abstract

Many standard optimization methods for segmentation and reconstruction compute ML model estimates for appearance or geometry of segments, e.g. Zhu-Yuille 1996, Torr 1998, Chan-Vese 2001, GrabCut 2004, Delong et al. 2012. 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, which can be expressed 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 many continuous or discrete energy formulations in segmentation, stereo, and other reconstruction problems.