Aligning Shapes by Minimising the Description Length

Abstract

When building shape models, it is first necessary to filter out the similarity transformations from the original configurations. This is normally done using Procrustes analysis, that is minimising the sum of squared distances between the corresponding landmarks under similarity transformations. In this article we propose to align shapes using the Minimum Description Length (MDL) criterion. Previously MDL has been used to locate correspondences. We show that the Procrustes alignment with respect to rotation is not optimal.The MDL based algorithm is compared with Procrustes on a number of data sets. It is concluded that there is improvement in generalisation when using Minimum Description Length. With a synthetic example it is shown that the Procrustes alignment can fail significantly where the proposed method does not.The Description Length is minimised using Gauss-Newton. In order to do this the derivative of the description length with respect to rotation is derived.

Statistical shape models for 3D medical image segmentation: A review

“…It should be pointed out that GPA is not resistant to outlier points, and there have been some experiments of replacing the Euclidean distance metric in the scheme with the L 1 or L 1 norm (see Larsen and Eiriksson, 2001). Moreover, Ericsson and Karlsson (2005) proposed aligning the rotation of all training shapes using Minimum Description Length optimization, similar to the population-based optimization of correspondences (more on this topic in Section 4.5).…”