Monday, February 26, 2007
Multi-scale shape matching
The cuts problem is the problem of making point correspondences between the following two contours:
In order to solve this cuts problem, one may either allow for points on one contour to be skipped in the correspondence (e.g. in COPAP-lambda), or one may separate the low and high frequencies of each contour, developing a pyramidal shape recognition algorithm which would determine that, at the highest resolution, the two shapes above just aren't very similar, whereas after downsampling or blurring the shapes are extremely similar.
The only question is whether to perform this downsampling in image space, or directly on the contour, e.g. removing the highest-frequency terms in the curvature space around the contour. In support of the former (downsampling in image space) is the following example:
In this case downsampling in curvature space would simply shrink the arms of the shape on the left until just a stump in the center is left, whereas the effect we are looking for is to close the gaps between the arms so that the shape is recognized as a pentagon. This task is clearly better accomplished in image space.
In order to solve this cuts problem, one may either allow for points on one contour to be skipped in the correspondence (e.g. in COPAP-lambda), or one may separate the low and high frequencies of each contour, developing a pyramidal shape recognition algorithm which would determine that, at the highest resolution, the two shapes above just aren't very similar, whereas after downsampling or blurring the shapes are extremely similar.
The only question is whether to perform this downsampling in image space, or directly on the contour, e.g. removing the highest-frequency terms in the curvature space around the contour. In support of the former (downsampling in image space) is the following example:
In this case downsampling in curvature space would simply shrink the arms of the shape on the left until just a stump in the center is left, whereas the effect we are looking for is to close the gaps between the arms so that the shape is recognized as a pentagon. This task is clearly better accomplished in image space.
