Optical Flow Estimation using Fourier Mellin Transform

In this paper, we propose a novel method of computing the optical flow using the Fourier Mellin Transform (FMT). Each image in a sequence is divided into a regular grid of patches and the optical flow is estimated by calculating the phase correlation of each pair of co-sited patches using the FMT. By applying the FMT in calculating the phase correlation, we are able to estimate not only the pure translation, as limited in the case of the basic phase correlation techniques, but also the scale and rotation motion of image patches, i.e. full similarity transforms. Moreover, the motion parameters of each patch can be estimated to subpixel accuracy based on a recently proposed algorithm that uses a 2D esinc function in fitting the data from the phase correlation output. We also improve the estimation of the optical flow by presenting a method of smoothing the field by using a vector weighted average filter. Finally, experimental results, using publicly available data sets are presented, demonstrating the accuracy and improvements of our method over previous optical flow methods

Radon-based Structure from Motion Without Correspondences

We present a novel approach for the estimation of 3Dmotion directly from two images using the Radon transform. We assume a similarity function defined on the crossproduct of two images which assigns a weight to all feature pairs. This similarity function is integrated over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to filtering the similarity function with a Dirac function embedding the epipolar constraint. The result of this convolution is a function of the five unknownmotion parameters with maxima at the positions of compatible rigid motions. The breakthrough is in the realization that the Radon transform is a filtering operator: If we assume that images are defined on spheres and the epipolar constraint is a group action of two rotations on two spheres, then the Radon transform is a convolution/correlation integral. We propose a new algorithm to compute this integral from the spherical harmonics of the similarity and Dirac functions. The resulting resolution in the motion space depends on the bandwidth we keep from the spherical transform. The strength of the algorithm is in avoiding a commitment to correspondences, thus being robust to erroneous feature detection, outliers, and multiple motions. The algorithm has been tested in sequences of real omnidirectional images and it outperforms correspondence-based structure from motion