Visual Motion Estimation based on Motion Blur Interpretation
Abstract
When the relative velocity between the different objects in a scene
and the camera is relative large -- compared with the camera's
exposure time -- in the resulting image we have a distortion called
motion blur. In the past, a lot of algorithms have been proposed for
estimating the relative velocity from one or, most of the time, 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. This thesis
presents an algorithm that estimates the velocity vector of an image
patch using the motion blur only, in two steps. The information used
for the estimation of the velocity vectors is extracted from the
frequency domain, and the most computationally expensive operation is
the Fast Fourier Transform that transforms the image from the spatial
to the frequency domain. Consequently, the complexity of the algorithm
is bound by this operation into O(n log(n)). 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, and
an error analysis on these results is also presented.