Derivatives of eigenvalues and eigenvectors of matrix functions
SIAM Journal on Matrix Analysis and Applications
Estimating the Jacobian of the Singular Value Decomposition: Theory and Applications
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
An Efficient Method for Constructing Optimal Statistical Shape Models
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
Parameterisation Invariant Statistical Shape Models
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 4 - Volume 04
Measures for Benchmarking of Automatic Correspondence Algorithms
Journal of Mathematical Imaging and Vision
Automatic feature point correspondences and shape analysis with missing data and outliers using MDL
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
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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.