Modelling of Learning and Perception

Centre of Excellence in Computational Complex Systems Research


Image Segmentation by MCMC Methods

Researchers: Timo Kostiainen and Jouko Lampinen

The goal of this work is to develop computationally efficient techniques for the division of natural colour images into meaningful segments. The results can be applied in further processing of the image, for example in object recognition.

The use of a probabilistic approach and numerical Markov chain Monte Carlo (MCMC) methods have recently produced promising results in image segmentation. The approach is based on defining a statistical texture model for the image. The stochastic MCMC algorithm is a top-down process in which a very large number of proposal samples are generated and their likelihoods are evaluated against the texture model. Evaluation of the proposals is computationally intensive, and the complexity depends on the quality of the proposal samples.

We have developed methods for producing efficient proposal samples to reduce the computational complexity. We do this by taking advantage of bottom-up information that the image probability model provides, as well as cues such as edges. In Figure 1, the advantage that we get is illustrated by comparing the method to the case where no bottom-up information is used.

Figure 1

Figure 1. Efficient proposals vs. random proposals. Left: result of our segmentation method after 179 samples. Center: result of segmentation without bottom-up information in the same processing time (365 samples). Right: evolution of the posterior probabilities in the MCMC chains with (continuous) and without (dashed) bottom-up information.

The results of the MCMC algorithm are in the form of a large number of weighted samples from the posterior distribution. In many statistical analysis problems the distribution can be easily interpreted in terms of descriptive statistics. In the case of image processing, the result is a set of different segmentations of the image, which is awkward for visualization and further processing. Analysis of the posterior distribution is another part of this work.

Example results