Active Mean Fields for Probabilistic Image Segmentation: Connections with Chan-Vese and Rudin-Osher-Fatemi Models

TitleActive Mean Fields for Probabilistic Image Segmentation: Connections with Chan-Vese and Rudin-Osher-Fatemi Models
Publication TypeJournal Article
Year of Publication2017
AuthorsNiethammer M, Pohl K  M, Janoos F, Wells, III W  M
JournalArXiv e-prints; accepted to SIAM Journal on Imaging Science
KeywordsComputer Science - Computer Vision and Pattern Recognition

Image segmentation is a fundamental task for extracting semantically meaningful regions from an image. The goal is to assign object labels to each image location. Due to image-noise, shortcomings of algorithms and other ambiguities in the images, there is uncertainty in the assigned labels. In multiple application domains, estimates of this uncertainty are important. For example, object segmentation and uncertainty quantification is essential for many medical application, including tumor segmentation for radiation treatment planning. While a Bayesian characterization of the label posterior provides estimates of segmentation uncertainty, Bayesian approaches can be computationally prohibitive for practical applications. On the other hand, typical optimization based algorithms are computationally very efficient, but only provide maximum a-posteriori solutions and hence no estimates of label uncertainty. In this paper, we propose Active Mean Fields (AMF), a Bayesian technique that uses a mean-field approximation to derive an efficient segmentation and uncertainty quantification algorithm. This model, which allows combining any label-likelihood measure with a boundary length prior, yields a variational formulation that is convex. A specific implementation of that model is the Chan--Vese segmentation model (CV), which formulates the binary segmentation problem through Gaussian likelihoods combined with a boundary-length regularizer. Furthermore, the Euler--Lagrange equations derived from the AMF model are equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image de-noising. Solutions to the AMF model can thus be implemented by directly utilizing highly-efficient ROF solvers on log-likelihood ratio fields. We demonstrate the approach using synthetic data, as well as real medical images (for heart and prostate segmentations), and on standard computer vision test images.