An Epipolar Line from a Single Pixel

Abstract

Computing the epipolar geometry from feature points between cameras with very different viewpoints is often error prone, as an object's appearance can vary greatly between images. For such cases, it has been shown that using motion extracted from video can achieve much better results than using a static image. This paper extends these earlier works based on the scene dynamics.In this paper we propose a new method to compute the epipolar geometry from a video stream, by exploiting the following observation: For a pixel p in Image A, all pixels corresponding to p in Image B are on the same epipolar line. Equivalently, the image of the line going through camera A's center and p is an epipolar line in B. Therefore, when cameras A and B are synchronized, the momentary images of two objects projecting to the same pixel, p, in camera A at times t 1 and t 2 , lie on an epipolar line in camera B. Based on this observation we achieve fast and precise computation of epipolar lines.Calibrating cameras based on our method of finding epipolar lines is much faster and more robust than previous methods.

Separable Four Points Fundamental Matrix

“…His approach was later improved by [6], who directly recovered the epipolar lines required for the computation of the epipolar homography by using the motion-barcode descriptor. Similar approaches were introduced by [14,11] for the computation of the epipolar homography by directly estimating the epipolar lines. However, all of the above methods are only applicable to videos of dynamic scenes.…”

“…The green lines are epipolar lines. Methods based on the computation of the epipolar homography [14,24,6,11,12] are rarely used in practice, due to the requirement for the knowledge of (at least) three corresponding epipolar lines. We show here how to compute the epipolar homography without a-priori knowledge of epipolar lines.…”