Image segmentation via a Gibbs posterior

Detection of an image boundary when the pixel intensities are measured with noise is an important problem in image segmentation, with numerous applications in medical imaging and engineering. From a statistical point of view, the challenge is that likelihood-based methods require modeling the pixel intensities inside and outside the image boundary, even though these are typically of no practical interest. Since misspecification of the pixel intensity models can negatively affect inference on the image boundary, it would be desirable to avoid this modeling step altogether. Towards this, I present a robust Gibbs approach that constructs a posterior distribution for the image boundary directly, without modeling the pixel intensities. For a suitable prior on the image boundary, the Gibbs posterior concentrates asymptotically at the minimax optimal rate, adaptive to the boundary smoothness. Monte Carlo computation of the Gibbs posterior is straightforward, and simulation experiments show that the corresponding inference is more accurate than that based on existing Bayesian methodology.