Algebraic constrainst within three camera model and applications

The aim of the thesis is to describe Trifocal geometry devoted to three-camera model. One of the most properties of Trifocal geometry is about Trifocal matrices. Like Fundamental matrix in the case of two-camera model that defines a relationship between two image points of a space point, it does the correspondence line in the third image as long as there are two corresphonce lines in the first and second image.

The thesis also shows some limits of Fundamental matrix when it is used to describe the constrains of points and lines in the case of three cameras. This leads us to use Trifocal matrices to describe the constraints. We focus on Grassmann-Cayley algebra to introduce a new entity, Trifocal tensor that governs those line correspondences.

Scientific side

The study of algebra constraints in the three-camera model leads us to the development in processing images. From the orginnal information of images, we can sunthesize them to create a new image with more information. Or when we want to reconstruct 3D objects of an image, we can solve the problem by using Trifocal matrices.