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Shape Analysis with Subspace Symmetries
Author(s) -
Berner Alexander,
Wand Michael,
Mitra Niloy J.,
Mewes Daniel,
Seidel HansPeter
Publication year - 2011
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2011.01859.x
Subject(s) - subspace topology , homogeneous space , invariant (physics) , similarity (geometry) , computer science , mathematics , set (abstract data type) , algorithm , linear subspace , dimensionality reduction , artificial intelligence , pattern recognition (psychology) , pure mathematics , image (mathematics) , geometry , mathematical physics , programming language
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. 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.