Geometry and Context for Semantic Correspondences and Functionality Recognition in Man-Made 3D Shapes

We address the problem of automatic recognition of functional parts of man-made 3D shapes in the presence of significant geometric and topological variations. We observe that under such challenging circumstances, the context of a part within a 3D shape provides important cues for learning the semantics of shapes. We propose to model the context as structural relationships between shape parts and use them, in addition to part geometry, as cues for functionality recognition. We represent a 3D shape as a graph interconnecting parts that share some spatial relationships. We model the context of a shape part as walks in the graph. Similarity between shape parts can then be defined as the similarity between their contexts, which in turn can be efficiently computed using graph kernels. This formulation enables us to: (1) find part-wise semantic correspondences between 3D shapes in a nonsupervised manner and without relying on user-specified textual tags, and (2) design classifiers that learn in a supervised manner the functionality of the shape components. We specifically show that the performance of the proposed context-aware similarity measure in finding part-wise correspondences outperforms geometry-only-based techniques and that contextual analysis is effective in dealing with shapes exhibiting large geometric and topological variations.