Estimation of the fundamental matrix based on complex wavelets

In this paper, an automatic fundamental matrix estimation method based on complex wavelets is presented. The fundamental matrix is considered important because it reflects the intrinsic projective geometry of the scene. It is widely used in computer vision areas, such as camera calibration, object reconstruction, visual navigation, stereo vision etc. In comparison with the Discrete Wavelet Transform (DWT), the dual-tree complex wavelet transform (DT CWT) possesses two key properties for computer vision: shift invariance, which makes it possible to extract stable local features in an image; and good directional selectivity, making it possible to measure image energy accurately in multiple directions. First, a feature detector based on complex wavelets is used to find the points of interest, and then complex-wavelet-based polar matching is used to find putative correspondences. Compared with the classic `Harris corner´ interest point detector, the interest point detector based on DT CWT is a multiscale interest point detector, able to detect different kinds of features, including corners, edges, blobs etc. and the number of interest points can be made scale-dependent. Polar matching is a rotation invariant descriptor derived from the DT CWT coefficients; and scale invariance is induced by adjusting the wavelet levels and sampling radius according to the scale estimated by the detector. A minimum of only 7 correspondence points are needed to compute the fundamental matrix. Preliminary tests on some classic building scene images show that the method works well.