Shape Correspondence through Landmark Sliding

Mainly motivated by statistical shape analysis, this paper presents a novel landmark-based method for accurate shape correspondence, where the general goal is to align multiple shape instances by identifying a set of corresponded landmark points along those shapes. Different from previous methods, we consider both global shape deformation and local geometric features in defining the shape-correspondence cost function to achieve a consistency between the landmark correspondence and the underlying shape correspondence. According to this cost function, we develop a novel landmark-sliding algorithm to achieve optimal landmark-based shape correspondence. The proposed method is able to correspond various 2D shapes, like closed-curve shapes, open-curve shapes, selfcrossing shapes, and multiple-curve shapes. We also discuss other related practical issues, including landmark initialization and regularization parameter selection. The proposed method has been tested on various biological shapes arising from medical image analysis and validated in constructing statistical shape models.