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In this paper, we present a new framework for non-rigid structure from motion (NRSFM) that simultaneously addresses three significant challenges: severe occlusion, perspective camera projection, and large non-linear deformation. We introduce a concept called a model graph, which greatly reduces the computational cost of discovering groups of input images that depict consistent 3D shapes. A 3D model is constructed for each input image by traversing the model graph along multiple evolutionary paths. A compressive shape representation is constructed, which (1) consolidates the multiple 3D models for each image reconstructed during model evolution and (2) reduces the number of models needed to represent the input image set. Assuming feature correspondences are known, we demonstrate our algorithm on both real and synthetic data sets that exemplify all three aforementioned challenges.