In computer vision, a characteristic of the correspondence-based
approach is clear separations between structure and motion computation,
and between 2D and 3D information. Usually, first 2D-based smoothing constraints
are employed to obtain from the image measurements the optical flow field
or correspondence; then this information is used to estimate 3D motion
and, subsequently, structure. The problem with such an approach is that
optical flow or correspondence cannot be computed well on the basis of
image measurements only, and erroneously computed optical flow in the sequel
leads to errors in 3D motion and structure. There are basically two problems;
one arises from the locations of flow discontinuities which are due to
scene elements at different depths or differently moving objects. If we
knew where the discontinuities were, we could, using a multitude of approaches
based on smoothness constraints, estimate flow values for image patches
corresponding to smooth scene patches; but to know the discontinuities
requires solving for motion and structure first (chicken-egg problem).
A second problem arises, which is of a statistical nature: even within
areas of smooth scene patches, optical flow cannot be estimated accurately;
the estimation is biased and depends on the gradient distribution of the
scene texture. This bias is highly pronounced in the pattern designed by
Ouchi
and explained in our recent work. Slight movements of this pattern produce
different movements in the inset and the background. This is an example
where accurate flow is impossible to compute. This correspondence-based
framework has given rise to some applications, especially ones involving
well-structured geometric objects or techniques involving semi-automatic
approaches (for example, use of an operator). This framework is approaching
its limits. Treating an image sequence as a moving cloud of points has
its limitations.
Revised 1999/04/15
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