On Some Properties of Calibrated Trifocal Tensors
| Autor: | Evgeniy V. Martyushev |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Generalization Computer Vision and Pattern Recognition (cs.CV) Applied Mathematics Degrees of freedom Mathematical analysis Computer Science - Computer Vision and Pattern Recognition 010103 numerical & computational mathematics 02 engineering and technology Condensed Matter Physics 01 natural sciences Quintic function Trifocal tensor Essential matrix Position (vector) Modeling and Simulation Quartic function 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Geometry and Topology Computer Vision and Pattern Recognition 0101 mathematics Algebraic number Mathematics |
| Popis: | In two-view geometry, the essential matrix describes the relative position and orientation of two calibrated images. In three views, a similar role is assigned to the calibrated trifocal tensor. It is a particular case of the (uncalibrated) trifocal tensor and thus it inherits all its properties but, due to the smaller degrees of freedom, satisfies a number of additional algebraic constraints. Some of them are described in this paper. More specifically, we define a new notion --- the trifocal essential matrix. On the one hand, it is a generalization of the ordinary (bifocal) essential matrix, and, on the other hand, it is closely related to the calibrated trifocal tensor. We prove the two necessary and sufficient conditions that characterize the set of trifocal essential matrices. Based on these characterizations, we propose three necessary conditions on a calibrated trifocal tensor. They have a form of 15 quartic and 99 quintic polynomial equations. We show that in the practically significant real case the 15 quartic constraints are also sufficient. 18 pages, 1 figure |
| Databáze: | OpenAIRE |
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