A Minimum Description Length Approach to Statistical Shape Modelling

Abstract

Statistical shape models show considerable promise as a basis for segmenting and interpreting images. One of the drawbacks of the approach is, however, the need to establish a set of dense correspondences between examples of similar structures, across a training set of images. Often this is achieved by locating a set of ‘landmarks’ manually on each of the training images, which is time-consuming and subjective for 2D images, and almost impossible for 3D images. This has led to considerable interest in the problem of building a model automatically from a set of training shapes. We extend previous work that has posed this problem as one of optimising a measure of model ‘quality’ with respect to the set of correspondences. We define model ‘quality’ in terms of the information required to code the whole set of training shapes and aim to minimise this description length. We describe a scheme for representing the dense correspondence maps between the training examples and show that a minimum description length model can be obtained by stochastic optimisation. Results are given for several different training sets of 2D boundaries, showing that the automatic method constructs better models than the manual landmarking approach. We also show that the method can be extended straightforwardly to 3D.

Acknowledgements

The authors would like to thank Dr. Alan Brett for his contribution to the ideas for the work in this paper. Tim Cootes is funded under an EPSRC Advanced Fellowship Grant. Rhodri Davies would like to thank the BBSRC and AstraZeneca Pharmaceuticals for their financial support.