On a Neural Network that Performs an Enhanced Nearest-Neighbour Matching

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.