Unsupervised joint deconvolution and segmentation method for textured images: a Bayesian approach and an advanced sampling algorithm

Abstract

The paper tackles the problem of joint deconvolution and segmentation of textured images. The images are composed of regions containing a patch of texture that belongs to a set of K possible classes. Each class is described by a Gaussian random field with parametric power spectral density whose parameters are unknown. The class labels are modelled by a Potts field driven by a granularity coefficient that is also unknown. The method relies on a hierarchical model and a Bayesian strategy to jointly estimate the labels, the K textured images in addition to hyperparameters: the signal and the noise levels as well as the texture parameters and the granularity coefficient. The capability to estimate the latter is an important feature of the paper. The estimates are designed in an optimal manner as a risk minimizer that yields the marginal posterior maximizer for the labels and the posterior mean for the rest of the unknowns. They are computed based on a convergent procedure from samples of the posterior obtained through an advanced MCMC algorithm: Perturbation-Optimization step and Fisher Metropolis-Hastings step within a Gibbs loop. Various numerical evaluations provide encouraging results despite the strong difficulty of the problem.

Hyperparameter selection for Discrete Mumford–Shah

“…A first class of methods relying on hierarchical Bayesian approaches and has been widely used, both in signal and image processing [19,27,37,45]. The drawbacks of Bayesian methods are that they rapidly become computationally heavy as the model for observed data gets more complicated, and their computational cost increases with the number of hyperparameters to be tuned.…”

Parameter-free and fast nonlinear piecewise filtering. Application to experimental physics

“…The two main techniques used in MCMC are Metropolis-Hastings, which relies on accept/reject mechanism and Gibbs sampler, which simplifies the high dimensional problem by successively simulating from different smaller dimensional components. The main limitation of these techniques is to be computationally intensive for solving large size inverse problems (see a contrario [34,52]). We should also refer to some specific configurations where a closed form expression is available such as for the Ising model in 1D and 2D but which is not adapted for general inverse problem solving considered in this work.…”

“…When one wants to estimate jointly the maximum of a posteriori and its hyperparameters, Bayesian hierarchical inference frameworks are particularly adapted and received considerable interest for addressing change-point detection or piecewise denoising problems [20,21,42] or texture segmentation [52]. However, to the best of our knowledge, for the proposed unified 1D-2D framework considered in this work, such a general efficient strategy has not yet been designed.…”

Hyperparameter selection for Discrete Mumford-Shah

“…A first class of methods relying on hierarchical Bayesian approaches and has been widely used, both in signal and image processing [4,14,27,41]. The drawbacks of Bayesian methods are that they rapidly become computationally heavy as the model for observed data gets more complicated, and their computational cost increases with the number of hyperparameters to be tuned.…”