We present a shape deformation algorithm that unfolds any given 3D shape into a canonical pose that is invariant to non-rigid transformations. Unlike classical approaches, such as least-squares multidimensional scaling, we preserve the geometric details of the input shape in the resulting shape, which in turn leads to a content-based non-rigid shape retrieval application with higher accuracy. Our optimization framework, fed with a triangular or a tetrahedral mesh in 3D, tries to move each vertex as far away from each other as possible subject to finite element regularization constraints. Intu- itively this effort minimizes the bending over the shape while preserving the details. Avoiding geodesic distances in our computation renders the method robust to topological noise. Compared to state-of-the-art approaches, our method is simpler to implement, faster, more accurate in shape retrieval, and less sensitive to topological errors.
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We thank the anonymous reviewers for their constructive com- ments, and Norm Badler, James O'Brien, Tiantian Liu, Mark Pauly and Lifeng Zhu for fruitful discussions. This work was supported by TUBITAK under the project EEEAG-115E471, and the NSF awards IIS-1622360 and IIS-1350330.