Trifocal geometry
The trifocal geometry is the extension of the epipolar geometry to three images. If the position of an object point is known in two images, its position in the third image is the intersection of the two epipolar lines. In contrast to the image pair, there is a clear result, provided that the point is not in the trifocal plane (the plane that is formed from the three projection centers) or the three projection centers are on a line. The arrangement in which the 3D point lies on the trifocal plane is called a singular case .
The trifocal tensor
The trifocal tensor t is a tensor that contains the geometric relationships between the three cameras. It consists of three homogeneous 3 × 3 matrices and has 18 degrees of freedom.
Calculation of the trifocal tensor
The three projection matrices P of the cameras can be used to calculate the trifocal sensor . If these with P 1 = [ I | 0 ], P 2 = [ a ij ] and P 3 = [ b ij ] ( I is the identity matrix and 0 is the zero vector ), then the trifocal tensor t is also calculated
Extensions to more than three images
It is possible to expand the geometric relationships to more than three images. In practice, this is only common for four views. The so-called quadrifocal tensor exists here, which describes the relationship of pixels and lines between these views. However, no mathematical relationships were examined for more than four views.
Web links
- The Trifocal Tensor - Detailed explanation of the trifocal geometry (English; PDF file; 178 kB)