Abstract

Finding point correspondences plays an important role in automati- cally building statistical shape models from a training set of 3D surfaces. For the point correspondence problem, Davies et al. [1] proposed a minimum-description- length-based objective function to balance the training errors and generalization ability. A recent evaluation study [2] that compares several well-known 3D point correspondence methods for modeling purposes shows that the MDL-based ap- proach [1] is the best method. We adapt the MDL-based objective function for a feature space that can ex- ploit nonlinear properties in point correspondences, and propose an efficient opti- mization method to minimize the objective function directly in the feature space, given that the inner product of any vector pair can be computed in the feature space. We further employ a Mercer kernel [3] to define the feature space im- plicitly. A key aspect of our proposed framework is the generalization of the MDL-based objective function to kernel principal component analysis (KPCA) [4] spaces and the design of a gradient-descent approach to minimize such an ob- jective function. We compare the generalized MDL objective function on KPCA spaces with the original one and evaluate their abilities in terms of reconstruc- tion errors and speci ficity. From our experimental results on different sets of 3D shapes of human body organs, the proposed method performs signi ficantly better than the original method.