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Published 2001 | Accepted Version
Book Section - Chapter Open

Averaged Template Matching Equations


By exploiting an analogy with averaging procedures in fluid dynamics, we present a set of averaged template matching equations. These equations are analogs of the exact template matching equations that retain all the geometric properties associated with the diffeomorphismgrou p, and which are expected to average out small scale features and so should, as in hydrodynamics, be more computationally efficient for resolving the larger scale features. Froma geometric point of view, the new equations may be viewed as coming from a change in norm that is used to measure the distance between images. The results in this paper represent first steps in a longer termpro gram: what is here is only for binary images and an algorithm for numerical computation is not yet operational. Some suggestions for further steps to develop the results given in this paper are suggested.

Additional Information

© 2001 Springer. We would like to thank J. Tilak Ratnanather for bringing the TME to our attention in 1999 and keeping us informed of their work since then. We would also like to thank Steve Shkoller, Antonio Hernandez, Sergey Pekarsky and Banavara Shashikanth for helpful discussions. Comments from the mutual review group in Caltech Computer Science, especially the detailed suggestions from Min Chen were very useful in improving the organization of the paper.

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August 19, 2023
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