Robust Structure‐Based Shape Correspondence

Abstract

We present a robust method to find region‐level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the shapes, and devise an adapted graph‐matching technique, from which we infer correspondences between shape regions. The simplified shape graphs are designed to primarily capture the overall structure of the shapes, without reflecting precise information about the geometry of each region, which enables us to find correspondences between shapes that might have significant geometric differences. Moreover, due to the special care we take to ensure the robustness of each part of our pipeline, our method can find correspondences between shapes with different representations, such as triangular meshes and point clouds. We demonstrate that the region‐wise matching that we obtain can be used to find correspondences between feature points, reveal the intrinsic self‐similarities of each shape and even construct point‐to‐point maps across shapes. Our method is both time and space efficient, leading to a pipeline that is significantly faster than comparable approaches. We demonstrate the performance of our approach through an extensive quantitative and qualitative evaluation on several benchmarks where we achieve comparable or superior performance to existing methods.

Multi-kernel Diffusion CNNs for Graph-Based Learning on Point Clouds

“…The 15 labels correspond to the head, thorax, abdomen, left hand, left lower arm, left upper arm, left foot, left lower leg, left upper leg, right hand, right lower arm, right upper arm, right foot, right lower leg and right upper leg. The semantic segmentation on the FAUST dataset was also investigated in [27], but only up to intrinsic symmetry (e.g. no distinction between right and left foot).…”

Consistent segment-wise matching with multi-layer graphs

“…It is an important problem as it helps with higher-level and hierarchical understanding in geometry analysis Zhu et al (2017). It further impacts many downstream applications, like defining better similarity measures between 3D models Kleiman et al (2015); Shapira et al (2010); Kleiman and Ovsjanikov (2017), functionality analysis van Kaick et al (2013a), surface registration Huang et al (2008) and structure-aware analysis Mitra et al (2013).…”

“…Many of them combine topological and geometrical information to help solve the segment-wise matching problem. Kleiman et al (2015); Kleiman and Ovsjanikov (2017) both take input shape segments and build a component graph to capture the topological relationship of segments. Together with geometric similarity of segments, they adapt the spectral technique Leordeanu and Hebert (2005) for matching.…”

“…Together with geometric similarity of segments, they adapt the spectral technique Leordeanu and Hebert (2005) for matching. SHED (Shape Editing Distance) Kleiman et al (2015) innovates to consider one-to-many matching whilst Kleiman and Ovsjanikov (2017) focuses on robust matching of non-isometrically deformed segments and disambiguating symmetric segments. Alhashim et al (2015) also takes pre-defined shape segments as input and builds a component graph to represent their topology.…”

“…We observe two problems for the methods in existing literature. First, most of these techniques rely on input with consistent segmentation Kleiman et al (2015); Kleiman and Ovsjanikov (2017); Alhashim et al (2015); Zhu et al (2017). When the input segmentation is inconsistent (over-/imperfectly segmented), they often lead to incorrect correspondences.…”