Conformal Geometry for Viewpoint Change Representation

Autor: Christophe Saint-Jean, Ghina El Mir, Michel Berthier
Přispěvatelé: Mathématiques, Image et Applications - EA 3165 (MIA), Université de La Rochelle (ULR), El Mir, Ghina
Jazyk: angličtina
Rok vydání: 2014
Předmět:
Pure mathematics
Computer Vision
Scalar (mathematics)
Conformal map
Pinhole Camera
01 natural sciences
Combinatorics
Geometric algebra
[INFO.INFO-CV] Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]
[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]
Horosphere
0103 physical sciences
Minkowski space
Euclidean geometry
Image Representation
[MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG]
0101 mathematics
[MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG]
Mathematics
Applied Mathematics
010102 general mathematics
Perspective Distortions
51B10
51B20
62H35
68T45
[INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]
[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]
Geometric Algebra
Conformal Geometry
Embedding
010307 mathematical physics
Conformal geometry
Perspective Plane
Zdroj: Advances in Applied Clifford Algebras
Advances in Applied Clifford Algebras, Springer Verlag, 2014, 24 (2), pp.443-463
HAL
ISSN: 0188-7009
1661-4909
DOI: 10.1007/s00006-013-0431-3
Popis: International audience; We propose in this paper a new model for image representation based on the conformal geometry and its powerfulness to encode perspective distortions through bases of the Minkowski space ${\RR}^{1,1}$. This approach allows us to describe an image as a scalar valued function defined on a horosphere corresponding to an embedding of the Euclidean plane into ${\RR}^{3,1}$ encoding the latitude angle and the rotation parameter of the camera. This is obtained through a generalization of the conformal model such that it includes representations of perspective planes. In this setting, we describe every viewpoint change as a mapping between two horospheres of the space ${\RR}^{3,1}$, each one of these encoding a perspective plane.
Databáze: OpenAIRE
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