Representing shapes is a significant problem for vision systems that must recognize or classify objects.
Methods to compare two shape contours based on evaluating global
deformations tend to be sensitive to occlusion
and fail to account for local deformations (such as articulations)
since these deformations may change the global appearance of objects
considerably while the entire deformation is concentrated in specific
points.
A class of methods compares objects by deforming one object into
another and evaluating the amount of deformation applied in this
process. Guaranteed methods, typically, use dynamic programming
(time-warping) to register two contours. These are all string
(contour) matching algorithms. The main drawback of these approaches
is that they do not account for region information and for symmetries.
For example, in the following figures, we have a shape contour
A followed by two shapes B and C obtained by
different deformations (stretching) into the first one. Note that the
amount of stretching on each one is exactly the same, namely doubling
the size of two pieces of straight lines. However, because they are
applied in different segments, it causes the third shape to look very
different from the first one. All local string deformation methods
will fail to distinguish the dissimilarity between them and the first
one.