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

Abstract

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.