Robust Shape Collection Matching and Correspondence from Shape Differences

Abstract

We propose a method to automatically match two shape collections with a similar shape space structure, e.g. two characters in similar poses, and compute the inter‐maps between the collections. Given the intra‐maps in each collection, we extract the corresponding shape difference operators, and use them to construct an embedding of the shape space of each collection. We then align the two shape spaces, and use the knowledge gained from the alignment to compute the inter‐maps. Unlike existing approaches for collection alignment, our method is applicable to small and large collections alike, and requires no parameter tuning. Furthermore, unlike most approaches for non‐isometric correspondence, our method uses solely the variation within the collection to extract the inter‐maps, and therefore does not require landmarks, descriptors or any additional input. We demonstrate that we achieve high matching accuracy rates, and compute high quality maps on non‐isometric shapes, which compare favorably with automatic state‐of‐the‐art methods for non‐isometric shape correspondence.

DWKS : A Local Descriptor of Deformations Between Meshes and Point Clouds

“…Shape difference operators provide a powerful tool for summarizing the variability within shape collections, which has motivated their use in computing cross-collection shape correspondences. Our work is directly inspired by the excellent results shown in [39,5] where corresponding shape difference operators are matched together to compute cross-collection functional maps. The solving procedure, however, relies on SVD which suffers both from sign ambiguity and possible instability.…”

“…We show that while shape difference operators [35] capture the global difference between shapes, their properties allow pointwise information to be extracted in the form of vertex-wise descriptors. This information can be used either in conjunction with the pipeline of [39,5] in the case of complete shapes, or even directly, in the case of partial shapes 3. Background…”

“…Although originally shape difference operators were introduced for shape analysis, they also have been used for solving cross-collection shape correspondence problems [39,5]. Specifically, given two shape collections {M i } n i=0 and {N i } n i=0 , where deformation between M 0 and M i are similar to deformation between N 0 and N i for any i ∈ {1, .…”

“…Remarkably while 3D shapes often come in the context of a collection, very few methods [39,5] have tried to leverage the commonality of the deformations that exist within the collections to facilitate matching across them, e.g. to disambiguate such symmetries or address partiality.…”

“…In our work, we use shape difference operators [35] that have been used for both analysing deformations within a collection [16] and even shape synthesis [19]. In the context of cross-collection mapping, shape difference operators have been used in [39,5] as global objectives within the functional map framework, which can limit their utility to complete shape matching. Instead, we demonstrate that pointwise spectral descriptors can successfully be extracted from shape difference operators.…”