3D Statistical Shape Models Using Direct Optimisation of Description Length

We describe an automatic method for building optimal 3D statistical shape models from sets of training shapes. Although shape models show considerable promise as a basis for segmenting and interpreting images, a major drawback of the approach is the need to establish a dense correspondence across a training set of example shapes. It is important to establish the correct correspondence, otherwise poor models can result. In 2D, this can be achieved using manual ‘landmarks’, but in 3D this becomes impractical. We show it is possible to establish correspondences automatically, by casting the correspondence problem as one of finding the ‘optimal’ parameterisation of each shape in the training set. We describe an explicit representation of surface parameterisation, that ensures the resulting correspondences are legal, and show how this representation can be manipulated to minimise the description length of the training set using the model. This results in compact models with good generalisation properties. Results are reported for two sets of biomedical shapes, showing significant improvement in model properties compared to those obtained using a uniform surface parameterisation.