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Journal Article

Shape Analysis with Subspace Symmetries


Berner,  Alexander
Computer Graphics, MPI for Informatics, Max Planck Society;


Wand,  Michael
Computer Graphics, MPI for Informatics, Max Planck Society;


Mewes,  Daniel
Computer Graphics, MPI for Informatics, Max Planck Society;


Seidel,  Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

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Berner, A., Wand, M., Mitra, N. J., Mewes, D., & Seidel, H.-P. (2011). Shape Analysis with Subspace Symmetries. Computer Graphics Forum, 30(2), 277-286. doi:10.1111/j.1467-8659.2011.01859.x.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0010-13FA-D
We address the problem of partial symmetry detection, i.e., the identification of building blocks a complex shape is composed of. Previous techniques identify parts that relate to each other by simple rigid mappings, similarity transforms, or, more recently, intrinsic isometries. Our approach generalizes the notion of partial symmetries to more general deformations. We introduce subspace symmetries whereby we characterize similarity by requiring the set of symmetric parts to form a low dimensional shape space. We present an algorithm to discover subspace symmetries based on detecting linearly correlated correspondences among graphs of invariant features. The detected subspace symmetries along with the modeled variations are useful for a variety of applications including shape completion, non-local and non-rigid denoising. We evaluate our technique on various data sets. We show that for models with pronounced surface features, subspace symmetries can be found fully automatically. For complicated cases, a small amount of user input is used to resolve ambiguities. Our technique computes dense correspondences that can subsequently be used in various applications, such as model repair and denoising.