The most standard approach to resolve the inherent ambiguities of the non-rigid structure from motion problem is using low-rank models that approximate deforming shapes by a linear combination of rigid basis. These models are typically global, i.e., each shape basis contributes equally to all points of the surface. While this approach has been shown effective to represent smooth deformations, its performance degrades for surfaces composed of various regions, each following a different deformation rule. Piecewise methods attempt to capture this type of behavior by locally modeling surface patches, although they subsequently require enforcing global constraints to assemble back the patches. In this paper we propose an approach that combines the best of global and local models: it locally considers low-rank models but, by construction, does not need to impose global constraints to guarantee local patch continuity. We achieve this by a simple expectation maximization strategy that besides learning global shape bases, it locally adapts their contribution to each specific surface region. Furthermore, as a side contribution, in order to split the surface into different local patches, we propose a novel physically-based mesh segmentation approach that obeys an energy criterion. The complete framework is evaluated in both synthetic and real datasets, and shows an improved performance to competing methods.
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