An estimation of the fundamental matrix using hybrid statistics

Abstract

The fundamental matrix in epipolar constraint represents important information from different viewpoints. This matrix can be estimated using more than seven corresponding keypoints. The maximum-likelihood estimation can correct errors of coordinates of corresponding keypoints, and calculates the fundamental matrix accurately. The accuracy of the fundamental matrix depends on the accuracy of corresponding keypoints; therefore, exact extraction of the corresponding keypoints plays an important role. SIFT (Scale Invariant Feature Transform) represents a feature vector for each keypoint, which is robust against geometrical changes and photometric changes. This property contributes to a high level of discrimination for finding corresponding keypoints. However, SIFT may extract corresponding keypoints with large errors, such as mismatched corresponding keypoints. These corresponding keypoints affect the accuracy of the fundamental matrix. The proposed method eliminates the mismatched corresponding keypoints using not only the statistics of epipolar equation error but also the ratio of the variances of the error before and after the keypoints' elimination. Experimental results demonstrate that the proposed method estimates the fundamental matrix more accurately than conventional methods.