Functional Characterization of Intrinsic and Extrinsic Geometry
Name
Solomon_Functional characterization.pdf
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16.12 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Corman, Etienne
Ben-Chen, Mirela
Guibas, Leonidas
Ovsjanikov, Maks
Solomon, Justin
Date Issued
March 2017
Journal
ACM Transactions on Graphics
Publisher
Association for Computing Machinery (ACM)
Citation
Corman, Etienne, et al. “Functional Characterization of Intrinsic and Extrinsic Geometry.” ACM Transactions on Graphics 36, 2 (March 2017): 1–17 © Association for Computing Machinery (ACM)
Version
Author's final manuscript
Abstract
We propose a novel way to capture and characterize distortion between pairs of shapes by extending the recently proposed framework of shape differences built on functional maps. We modify the original definition of shape differences slightly and prove that after this change, the discrete metric is fully encoded in two shape difference operators and can be recovered by solving two linear systems of equations. Then we introduce an extension of the shape difference operators using offset surfaces to capture extrinsic or embedding-dependent distortion, complementing the purely intrinsic nature of the original shape differences. Finally, we demonstrate that a set of four operators is complete, capturing intrinsic and extrinsic structure and fully encoding a shape up to rigid motion in both discrete and continuous settings. We highlight the usefulness of our constructions by showing the complementary nature of our extrinsic shape differences in capturing distortion ignored by previous approaches. We additionally provide examples where we recover local shape structure from the shape difference operators, suggesting shape editing and analysis tools based on manipulating shape differences.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/2999535
