Fleet, D.J., Jepson, A.D., and Jenkin, M.
Phase-based disparity measurement.
CVGIP: Image Understanding, 53(2): 198--210, 1991

The measurement of image disparity is a fundamental precursor to binocular depth estimation. Recently, Jenkin and Jepson (1988) and Sanger (1988) described promising methods based on the output phase behaviour of band-pass Gabor filters. Here we discuss further justification for such techniques based on the stability of band-pass phase behaviour as a function of typical distortions that exist between left and right views. In addition, despite this general stability, we show that phase signals are occasionally very sensitive to spatial position and variations in scale, in which cases incorrect measurements occur. We find that the primary cause for this instability is the existence of singularities in phase signals. With the aid of the local frequency of the filter output (provided by the phase derivative) and the local amplitude information, the regions of phase instability near the singularities are detected so that potentially incorrect measurements can be identified. In addition, we show how the local frequency can be used away from the singularity neighbourhoods to improve the accuracy of the disparity estimates. Some experimental results are reported.
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