Study of the Computational Methods of Collineation Based on Invariance of Cross Ratio

Cross ratio is an essential invariant with respect to projective transformations.To discover intrinsic properties of a scene by using the computation of cross ratio invariance has been one of the most hot research areas in computer vision fields.The computation by using image coordinates will cause computational breakdown or deterioration of accuracy,and the computation by using homogeneous coordinates will increase computation.The N-vector formalism for computing cross ratio is proposed from the perspective of computational processes in this paper if a point and a line on the image plane are represented in terms of N-vectors.One application of the formalism on the basis of study is presented: The procedures for computing collineation matrix that maps four arbitrarily given image points in general position to four arbitrarily given image points in general position based on projective invariance of cross ratio are constructed.The result of example shows that this algorithm is more utility and reliable than traditional algorithms.