Abstract: The computation of cross ratio by use of image coordinates will cause computational breakdown or deterioration of accuracy, and the N-vector formula for computing cross ratio is established if the points and lines on the image plane are represented in terms of N-vectors. The N-vector computational methods of a pure translation motion focus of expansion are constructed on the basis of the above study. The formula only needs the images of a space point at three different moments or its N-vector, N-rate and N-acceleration. The experimental result shows that this algorithm is more reliable.

Key words: computer application, focus of expansion, cross ratio invariance, vector