Automated estimation of the parameters of Gibbs priors to be used in binary tomography

Abstract

Image modeling using Gibbs priors was previously shown, based on experiments, to be e ective in image reconstruction problems. This motivated us to evaluate three methods for estimating the priors. Two of them accurately recover the parameters of the priors; however, all of them are useful for binary tomography. This is demonstrated by two sets of experiments: in one the images are from a Gibbs distribution and in the other they are typical cardiac phantom images. ?

Sequential Binary Image Estimation Algorithms

“…3 and % 131 . 3 , respectively. The mean difference of the FODM over all pairs of training/testing sets was % 090 .…”

“…3 misclassified pixels on average). The Counting Estimation Method is simpler than the Expected Value Estimation Method.…”

“…There exist 512 different (black and white) clique configurations. To simplify the model, we partition the set of clique configurations into six clique configuration types (or types for short): the uniform black configuration, the uniform white configuration, edge configurations, convex white corner configurations, concave white corner configurations and all other clique configurations (see [3] for exact definitions). See Figure 1 for examples of these types.…”

A discrete tomography algorithm for improving the quality of three-dimensional X-ray diffraction grain maps

“…First, the Gibbs potentials were determined from experimental data by the so-called 'heuristic method ' [equation (3)] (Carvalho et al, 1999). In the work of Liao & Herman (2004) two alternative expressions are presented for deriving the potentials by means of counting. Under idealized conditions, these are shown to lead to more accurate potentials and ultimately to superior restorations.…”

A method for reconstructing label images from a few projections, as motivated by electron microscopy

“…We choose Gibbs priors as it has been experimentally demonstrated (Carvalho et al, 1999;Liao and Herman, 2004) that for certain types (all of those that were tested) of Gibbs distributions there are algorithms that recover an unknown image (that is a typical sample from the distribution) when provided with only a few projections of the image and with the values of the parameters of the Gibbs distribution. Some of those Gibbs distributions are such that the typical samples correspond to images that have relatively large Fig.…”