Diverse bases for functional spaces for non-rigid shape correspondence

Abstract

Computing meaningful correspondences for shapes undergoing non-rigid deformations is a fundamental task, challenging shape analysis community for many decades. The functional map framework has emerged as a powerful tool in this domain over the past decade due to its computational efficiency. Instead of tackling the combinatorial challenge of matching individual points across shapes, it focuses on constructing a linear mapping between the spaces of functions defined on these shapes. The map between function spaces is specified by a low-dimensional matrix obtained via suitably chosen basis functions that characterize the function space. This mapping can then be converted into a point-to-point correspondence between the shapes. The selection of an appropriate basis is a critical factor influencing the overall effectiveness and precision of the task. This survey explores various bases proposed to represent function spaces comprehensively within the realm of shape correspondence. Further insights into possible future directions are also provided.