Extension of the generalized image rectification - catching the infinity cases

This paper addresses the topic of image rectification, a widely used technique in 3D-reconstruction and stereo vision. The most popular algorithm uses a projective transformation to map the epipoles of the images to infinity. This algorithm fails whenever an epipole lies inside an image. To overcome this drawback, a rectification scheme known as polar rectification can be used. This, however, fails whenever an epipole lies at infinity. For autonomous systems exploring their environment, it can happen that successive camera positions constitute cases where we have an image pair with one epipole at infinity and the other inside an image. So neither of the previous algorithms can be applied directly. We present an extension to the polar rectification scheme. This extension allows the rectification of image pairs whose epipoles lie even at such difficult positions. Additionally, we discuss the necessary computation of the orientation of the epipolar geometry in terms of the fundamental matrix directly, avoiding the computation of a line homography as in the original polar rectification process.