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Conformal Geometry for Viewpoint Change Representation
| Content Provider | Hyper Articles en Ligne (HAL) |
|---|---|
| Author | Mir, Ghina El Saint-Jean, Christophe Berthier, Michel |
| Abstract | 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. |
| File Format | |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Computer Vision Pinhole Camera Conformal Geometry Image Representation Perspective Distortions Geometric Algebra Perspective Plane info math Computer Science [cs] Computer Vision and Pattern Recognition [cs.CV] Mathematics [math] Metric Geometry [math.MG] General Mathematics [math.GM] |
| Content Type | Text |
| Resource Type | Article |
