Blended intrinsic maps
Abstract
This paper describes a fully automatic pipeline for finding an intrinsic map between two non-isometric, genus zero surfaces. Our approach is based on the observation that efficient methods exist to search for nearly isometric maps (e.g., Möbius Voting or Heat Kernel Maps), but no single solution found with these methods provides low-distortion everywhere for pairs of surfaces differing by large deformations. To address this problem, we suggest using a weighted combination of these maps to produce a "blended map." This approach enables algorithms that leverage efficient search procedures, yet can provide the flexibility to handle large deformations. The main challenges of this approach lie in finding a set of candidate maps { m i } and their associated blending weights { b i ( p )} for every point p on the surface. We address these challenges specifically for conformal maps by making the following contributions. First, we provide a way to blend maps, defining the image of p as the weighted geodesic centroid of m i ( p ). Second, we provide a definition for smooth blending weights at every point p that are proportional to the area preservation of m i at p . Third, we solve a global optimization problem that selects candidate maps based both on their area preservation and consistency with other selected maps. During experiments with these methods, we find that our algorithm produces blended maps that align semantic features better than alternative approaches over a variety of data sets.
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[8], [9] can handle near-to approximate isometric deformation.
“[8], [9] that can handle near-to approximateisometric deformation.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [8]
[8] uses the sum of isometric distortion-difference of geodesic distances between the end-points of one correspondence with respect to all the other correspondences.
“[8] uses sum of isometric distortion-difference of geodesic distances between the end-points of one correspondence with respect to all the other correspondences.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [8]
[8] recruited a volunteer to label 10-35 semantically meaningful and consistent feature points for each class of objects in the watertight meshes dataset [114].
“[8] also recruited a volunteer to label 10-35 semantically meaningful and consistent feature points for each class of objects in the watertight meshes dataset [114].”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [8]
For non-rigid shapes, many deformations are only near/approximate isometric, which may lead to matching ambiguities [8].
“For non-rigid shapes, many deformations are only near/approximateisometric, which may lead to matching ambiguities [8].”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [8]
[8] has started in this direction using blended conformal maps.
“[8] has started in this direction using blended conformal maps.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [8]
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- Authors
- Kim, V. G., Lipman, Y., & Funkhouser, T.
- Affiliations
- Princeton University (US)
- ORCID
- Kim, Vladimir G.
- Venue
- ACM Transactions on Graphics
- Published
- 2011-07
- Volume
- 30
- Issue
- 4
- Pages
- 1-12
- ISSN
- 0730-0301 (ISSN-L)
- 1557-7368
- OpenAlex
- W4241422529
- Cited by
- 298
- References
- 27
- Citations by year
- 2026: 13 · 2025: 16 · 2024: 19 · 2023: 16 · 2022: 22 · 2021: 10 · 2020: 21 · 2019: 27 · 2018: 38 · 2017: 27 · 2016: 29 · 2015: 14 · 2014: 16 · 2013: 17 · 2012: 12
- FWCI
- 14.81
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- ACM Transactions on Graphics (publishedVersion)
- Funders
- Air Force Office of Scientific Research (1096101)
- Division of Computer and Network Systems (IIS-0612231CNS-0831374CCF-0702672CCF-0937139)
- Division of Computing and Communication Foundations (IIS-0612231CNS-0831374CCF-0702672CCF-0937139)
- Division of Information and Intelligent Systems (IIS-0612231CNS-0831374CCF-0702672CCF-0937139)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › 3D Shape Modeling and Analysis
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computer Graphics and Visualization Techniques
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computational Geometry and Mesh Generation
- Keywords
- surface registration, genus zero surfaces, conformal mapping, area preservation, global optimization
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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