On a Neural Network that Performs an Enhanced Nearest-Neighbour Matching |
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Authors: | G Labonté |
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Affiliation: | (1) Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario, Canada, CA |
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Abstract: | We review some of the main methods of solving the image matching problem in Particle-Tracking Velocimetry (PTV). This is
a technique of Experimental Fluid Dynamics for determining the velocity fields of moving fluids. This problem is a two-dimensional
random-points matching problem that condtitutes a prototypal problem, analogous to the one-dimensional matching problem for
Julesz 1] random-dot stereograms. Our study deals with a particular method of solution, namely the neural network algorithm
proposed by Labonté 2,3]. Our interest in this neural network comes from the fact that it has been shown to outperform the
best matching methods in PTV, and the belief that it is actually a method applicable to many other instances of the correspondence
problem. We obtain many new results concerning the nature of this algorithm, the main one of which consists in showing how
this neural network functions as an enhancer for nearest-neighbour particle image matching. We calculate its complexity, and
produce two different types of learning curves for it. We exhibit the fact that the RMS error of the neural network decreases
at least exponentially with the number of cycles of the neural network. The neural network constructs a Self-Organised Map
(SOM), which corresponds to distorting back the two photos until they merge into a single photo. We explain how this distortion
is driven, under the network dynamics, by the few good nearest-neighbours (sometimes as few as 20%) that exist initially.
These are able to pull with them the neighboring images, toward their matching partners. We report the results of measuremnts
that corroborate our analysis of this process.
Received: 22 February 1999, Received in revised form: 22 September 1999, Accepted: 18 October 1999 |
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Keywords: | : Correspondence Displacement field Nearest-neighbour algorithm Particle-Tracking Velocimetry Paricle-Image Velocimetry Self-organised mapping |
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