We formulate several problems in early vision as inverse problems. Among the solution methods we review standard regularization theory, discuss its limitations, and present new stochastic (in particular, Bayesian) techniques based on Markov Random Field models for their solution. We derive efficient algorithms and describe parallel implementations on digital parallel SIMD architectures, as well as a new class of parallel hybrid computers that mix digital with analog components.

Probabilistic Solution of Ill-Posed Problems in Computational Vision

A method for modeling images of natural terrain is developed and applied to the segmentation of aerial photographic data. An underlying stochastic structure based on linear filtering concepts provides a means of modeling the terrain in local areas of the image. Superimposed on this is a Markov random field that describes transitions from regions of one terrain type to another. Maximum likelihood and maximum a posteriori estimation are applied to estimate regions of similar terrain. Results of application to digitized aerial photographs are presented and discussed.

An estimation-theoretic approach to terrain image segmentation

A continuous two-dimensional region is partitioned into a fine rectangular array of sites, or ‘pixels', each pixel having a particular '‘colour’ belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that pixels close together tend to have the same or similar colours. In this paper, it is assumed that the local characteristics of the true scene can be represented by a non-degenerate Markov random field. Such information can be combined with the records by Bayes' theorem and the true scene can be estimated according to standard criteria. However, the computational burden is enormous and the reconstruction may reflect undesirable large-scale properties of the random field. Thus, a simple, iterative method of reconstruction is proposed, which does ...

Statistical analysis of dirty pictures

The problem of segmentation of Magnetic Resonance images into regions of uniform tissue density is posed as an optimization problem. A new objective function is defined and the resulting minimization problem is solved using Mean Field Annealing, a new technique which usually finds global minima in non-convex optimization problems, and performs particularly well on images. Noise sensitivity is evaluated by tests on synthetic images, and the technique is then applied to clinical images of a brain and a knee. The technique shows considerable promise as a method of quantitative change monitoring.

Segmentation of Magnetic Resonance Images Using Mean Field Annealing

To segment a whole object from an image is an essential and challenging task in image processing. In this paper, we propose a hybrid segmentation algorithm which combines prior shape information with normalized cut. With the help of shape information, we can utilize normalized cut to correctly segment the target whose boundary may be corrupted by noise or outliers. At the same time, we introduce the use of segmentation results of the normalized cut to guide the shape model, and thus avoid searching the shape space. The proposed method was demonstrated to be effective by our experiments on both synthetic and real data.

https://www.cse.ust.hk/~achung/icip06_cai_wu_chung.pdf

Shape-Based Image Segmentation Using Normalized Cuts

By modelling a picture as a two-state Markov field, MAP estimation techniques are used to develop suboptimal but computationally tractable binary segmentation algorithms.

F. Hansen

Papers

Image segmentation using simple Markov field models