The epipolar geometry is the intrinsic projective geometry between two views, and the fundamental matrix is the algebraic representation of epipolar geometry. Recovery of epipolar geometry is a fundamental problem in computer vision. Its importance is due to the fact that it provides relationships between corresponding point in the two images. In this paper, the problem of automatic robust estimation of the epipolar geometry for wide-baseline image pair is addressed. this problem for wide-baseline image pair is difficult because the putative correspondences include a low percentage of inlier correspondences, and it could become a severe problem when the veridical data are themselves degenerate or near-degenerate. Base on our previous work, a topological clustering(TC) is proposed to apply to fundamental matrix estimating. The TC algorithm has been demonstrated to be able to effectively eliminate the mismatches and reserve the correct matches. This advantage is extremely important to speeds up the performance of the epipolar geometry estimation and avoid the degeneracy. First, a set of match clusters are generated from the initial SIFT matches using topological clustering algorithm. Then, all the valid pairs of clusters are used to generate a series of fundamental matrix estimates and the best estimate is chosen as the solution. Six famous image pairs are used to test the proposed algorithms and the comparison with the related methods has been conducted. The compared experiments emphasize the performance of the proposed CPC algorithms.