Study Of The Fundamental Matrix Estimation Methods

Understanding of the 3D structure described by 2D images is usually an important goal of computer vision. As the lack of depth information in one 2D image, commonly at least two 2D images are required to describe a 3D scene. A pair of two perspective images of the same scene which is called a binocular system satisfies epipolar geometry. Without calibrating of the camera (the focal length and the principle point are unknown) we use fundamental matrix to describe the epipolar geometry.In order to estimate the epipolar geometry, firstly we need to extract the feature points from the 2D images, then we can obtain pairs of corresponding feature points. As important features of images, corners are widely utilized in the field of computer vision. We introduce some commonly used corner detection methods and then choose the scale invariant feature transform (SIFT) to extract and match the feature points. In experimen-tal section, we design an experiment to investigate its rotation, scaling and translation invariance and its results in binocular system. The experimental results demonstrate its quite encouraging performance.We review the current state of fundamental matrix estimation. Because the meth-ods based on least square are always sensitive to noise, they are inapplicable in actual occasion. Besides, the commonly used robust methods do not analyse the character-istic of the matching points, these methods waste a lot of time in useless computation and their estimation results have larger differences between the ground truth. Aiming at the problems discussed above, we propose an estimation method based on clustering. Firstly we obtain pairs of points which contains inaccurately located points and false matching pairs through the feature detecting and matching step. Secondly we utilize the coordinates of each pair of points to construct the 4D vectors. Then clustering of the vectors is used to eliminate the isolated points and find the center of each cluster. These centers are treated as reliable inliers which suffer less from location error and false matching in estimation of the fundamental matrix. Finally we use RANSAC to these centers to estimate the fundamental matrix.To evaluate the effectiveness of the proposed method, we design an experimen-t which estimates the fundamental matrixes of a pair of actual images and a pair of synthetic images and then we compare the proposed method and some conventional methods. The experimental results shows that by using clustering of the 4D vectors, the mean distance between the points and there corresponding epipolar lines which are com-puted based on the fundamental matrix estimated decreases obviously. Besides, when we compare the estimation results with the ground truth fundamental matrix, the pro-posed method produces the best result. The experimental results show the encouraging performance of the proposed method.