Detection of an image boundary when the pixel intensities are measured withnoise is an important problem in image segmentation, with numerous applicationsin medical imaging and engineering. From a statistical point of view, thechallenge is that likelihood-based methods require modeling the pixelintensities inside and outside the image boundary, even though these aretypically of no practical interest. Since misspecification of the pixelintensity models can negatively affect inference on the image boundary, itwould be desirable to avoid this modeling step altogether. Towards this, wedevelop a robust Gibbs approach that constructs a posterior distribution forthe image boundary directly, without modeling the pixel intensities. We provethat, for a suitable prior on the image boundary, the Gibbs posteriorconcentrates asymptotically at the minimax optimal rate, adaptive to theboundary smoothness. Monte Carlo computation of the Gibbs posterior isstraightforward, and simulation experiments show that the correspondinginference is more accurate than that based on existing Bayesian methodology.
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