Better Flow Estimation from Color Images
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Research Article Better Flow Estimation from Color Images 2 ¨ Hui Ji1 and Cornelia Fermuller 1 Department 2 Computer
of Mathematics, National University of Singapore, Singapore 117543 Vision Laboratory, Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742-3275, USA
Received 1 October 2006; Accepted 20 March 2007 Recommended by Nicola Mastronardi One of the difficulties in estimating optical flow is bias. Correcting the bias using the classical techniques is very difficult. The reason is that knowledge of the error statistics is required, which usually cannot be obtained because of lack of data. In this paper, we present an approach which utilizes color information. Color images do not provide more geometric information than monochromatic images to the estimation of optic flow. They do, however, contain additional statistical information. By utilizing the technique of instrumental variables, bias from multiple noise sources can be robustly corrected without computing the parameters of the noise distribution. Experiments on synthesized and real data demonstrate the efficiency of the algorithm. Copyright © 2007 H. Ji and C. Ferm¨uller. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Optical flow estimation is a heavily studied problem in computer vision. It is well known that the problem is difficult because of the discontinuities in the scene. However, even at the locations of smooth scene patches, the flow cannot be estimated very accurately because of statistical difficulties. In this paper, we consider gradient-based approaches to optical flow estimation. The estimation is based on the basic constraint of constant brightness at an image point over a small time interval. This can be expressed as follows [1]:
where x denotes the parameter vector characterizing the optical flow, and A and b are the measurements. For example, for the model of constant flow in a spatial neighborhood, assuming we combine n image brightness constraint equations, b is the n-dimensional A becomes the n × 2 matrix (Ixi , I yi ), vector (−Iti ), and x is just the two-dimensional optical flow u = (ux , u y ). If the model assumes the flow to be a polynomial function in the image coordinates, then the flow components ux and u y are linear with respect to some k × 1 parameter vector x. In other words,
Ix ux + I y u y + It = 0,
x, ux = fi
1.
INTRODUCTION
t
(1)
where Ix , I y , It denote the spatial and temporal derivatives of the image intensity function I, and u = (ux , u y ) denotes the velocity vector at an image point. This equation, known as the brightness consistency constraint, only gives one component of the optical flow vector u = (ux , u y ). To obtain the second component, further assumptions on the optical flow need to be imposed. Common nonparametric constraints are obtained by assuming that the flow field is smoot
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