Steerable Filters and Cepstral Analysis for Optical Flow Calculation from a Single Blurred Image

This paper considers the explicit use of motion blur to compute the Optical Flow. In the past, many algorithms have been proposed for estimating the relative velocity from one or more images. The motion blur is generally considered an extra source of noise and is eliminated, or is assumed nonexistent. Unlike most of these approaches, it is feasible to estimate the Optical Flow map using only the information encoded in the motion blur. An algorithm that estimates the velocity vector of an image patch using the motion blur only is presented; all the required information comes from the frequency domain. The first step consists of using the response of a family of steerable filters applied on the log of the Power Spectrum in order to calculate the orientation of the velocity vector. The second step uses a technique called Cepstral Analysis. More precisely, the log power spectrum is treated as another signal and we examine the Inverse Fourier Transform of it in order to estimate the magnitude of the velocity vector. Experiments have been conducted on artificially blurred images and with real world data.