Shape correspondence for cel animation based on a shape association graph and spectral matching

We present an effective spectral matching method based on a shape association graph for finding region correspondences between two cel animation keyframes. We formulate the correspondence problem as an adapted quadratic assignment problem, which comprehensively considers both the intrinsic geometric and topology of regions to find the globally optimal correspondence. To simultaneously represent the geometric and topological similarities between regions, we propose a shape association graph (SAG), whose node attributes indicate the geometric distance between regions, and whose edge attributes indicate the topological distance between combined region pairs. We convert topological distance to geometric distance between geometric objects with topological features of the pairs, and introduce Kendall shape space to calculate the intrinsic geometric distance. By utilizing the spectral properties of the affinity matrix induced by the SAG, our approach can efficiently extract globally optimal region correspondences, even if shapes have inconsistent topology and severe deformation. It is also robust to shapes undergoing similarity transformations, and compatible with parallel computing techniques.