Diffeomorphism Spline Article Swipe
Wei Zeng
,
Muhammad Razib
,
Abdur R. Shahid
·
YOU?
·
· 2015
· Open Access
·
· DOI: https://doi.org/10.3390/axioms4020156
YOU?
·
· 2015
· Open Access
·
· DOI: https://doi.org/10.3390/axioms4020156
Conventional splines offer powerful means for modeling surfaces and volumes in three-dimensional Euclidean space. A one-dimensional quaternion spline has been applied for animation purpose, where the splines are defined to model a one-dimensional submanifold in the three-dimensional Lie group. Given two surfaces, all of the diffeomorphisms between them form an infinite dimensional manifold, the so-called diffeomorphism space. In this work, we propose a novel scheme to model finite dimensional submanifolds in the diffeomorphism space by generalizing conventional splines. According to quasiconformal geometry theorem, each diffeomorphism determines a Beltrami differential on the source surface. Inversely, the diffeomorphism is determined by its Beltrami differential with normalization conditions. Therefore, the diffeomorphism space has one-to-one correspondence to the space of a special differential form. The convex combination of Beltrami differentials is still a Beltrami differential. Therefore, the conventional spline scheme can be generalized to the Beltrami differential space and, consequently, to the diffeomorphism space. Our experiments demonstrate the efficiency and efficacy of diffeomorphism splines. The diffeomorphism spline has many potential applications, such as surface registration, tracking and animation.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/axioms4020156
- OA Status
- gold
- Cited By
- 1
- References
- 39
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- OpenAlex ID
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All OpenAlex metadata
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https://openalex.org/W4244681417Canonical identifier for this work in OpenAlex
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https://doi.org/10.3390/axioms4020156Digital Object Identifier
- Title
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Diffeomorphism SplineWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2015Year of publication
- Publication date
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2015-04-10Full publication date if available
- Authors
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Wei Zeng, Muhammad Razib, Abdur R. ShahidList of authors in order
- Landing page
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https://doi.org/10.3390/axioms4020156Publisher landing page
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YesWhether a free full text is available
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goldOpen access status per OpenAlex
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https://doi.org/10.3390/axioms4020156Direct OA link when available
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Diffeomorphism, Mathematics, Spline (mechanical), Submanifold, Differential geometry, Euclidean space, Pure mathematics, Mathematical analysis, Affine transformation, Physics, ThermodynamicsTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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2017: 1Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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