Abstract

We develop a distance metric for clustering and classification algo- rithms which is invariant to affine transformations and includes priors on the transformation parameters. Such clustering requirements are generic to a number of problems in computer vision. We extend existing techniques for affine-invariant clustering, and show that the new distance metric outperforms existing approximations to af?ne invariant distance computation, particularly under large transformations. In addition, we incorporate prior probabilities on the transformation parameters. This further regularizes the solution, mitigating a rare but serious tendency of the existing solutions to diverge. For the particular special case of corresponding point sets we demonstrate that the affine invariant measure we introduced may be obtained in closed form. As an application of these ideas we demonstrate that the faces of the principal cast of a feature film can be generated automatically using clustering with appropriate invariance. This is a very demanding test as it involves detecting and clustering over tens of thousands of images with the variances including changes in viewpoint, lighting, scale and expression.