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

Institution:
1Department of Computer Science and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill, NC, USA.
2Center for Health Sciences, SRI International
3Two Sigma Investments, NY, USA.
4Department of Radiology, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA.
Publisher:
Society for Industrial and Applied Mathematics Read More: http://epubs.siam.org/doi/10.1137/16M1058601
Publication Date:
Sep-2017
Journal:
SIAM J. Imaging Sci.
Citation:
SIAM J. Imaging Sci. 2017 Sep; 10(3):1069–1103.
PubMed ID:
29051796
PMCID:
PMC5642306
Keywords:
Segmentation, mean-field approximation, Rudin-Osher-Fatemi model, Chan-Vese model
Appears in Collections:
NAC, NCIGT, SPL
Sponsors:
P41 RR013218/RR/NCRR NIH HHS/United States
P41 EB015902/EB/NIBIB NIH HHS/United States
P41 EB015898/EB/NIBIB NIH HHS/United States
R24 AI067039/AI/NIAID NIH HHS/United States
R01 CA111288/CA/NCI NIH HHS/United States
R01 CA138419/CA/NCI NIH HHS/United States
R01 HL127661/HL/NHLBI NIH HHS/United States
K05 AA017168/AA/NIAAA NIH HHS/United States
Generated Citation:
Niethammer M., Pohl K.M., Janoos F., Wells III W.M. Active Mean Fields for Probabilistic Image Segmentation: Connections with Chan-Vese and Rudin-Osher-Fatemi Models. SIAM J. Imaging Sci. 2017 Sep; 10(3):1069–1103. PMID: 29051796. PMCID: PMC5642306.
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Segmentation is a fundamental task for extracting semantically meaningful regions from an image. The goal of segmentation algorithms is to accurately assign object labels to each image location. However, image noise, shortcomings of algorithms, and image ambiguities cause uncertainty in label assignment. Estimating this uncertainty is important in multiple application domains, such as segmenting tumors from medical images for radiation treatment planning. One way to estimate these uncertainties is through the computation of posteriors of Bayesian models, which is computationally prohibitive for many practical applications. However, most computationally efficient methods fail to estimate label uncertainty. We therefore propose in this paper the active mean fields (AMF) approach, a technique based on Bayesian modeling that uses a mean-field approximation to efficiently compute a segmentation and its corresponding uncertainty. Based on a variational formulation, the resulting convex model combines any label-likelihood measure with a prior on the length of the segmentation boundary. A specific implementation of that model is the Chan-Vese segmentation model, in which the binary segmentation task is defined by a Gaussian likelihood and a prior regularizing the length of the segmentation boundary. Furthermore, the Euler-Lagrange equations derived from the AMF model are equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image denoising. Solutions to the AMF model can thus be implemented by directly utilizing highly efficient ROF solvers on log-likelihood ratio fields. We qualitatively assess the approach on synthetic data as well as on real natural and medical images. For a quantitative evaluation, we apply our approach to the tt icgbench dataset.