The possibility of using nonlinear media as a highly parallel computation tool is discussed, specifically for image classification and recognition. Some approaches of this type are known, that are based on stationary dissipative structures which can “measure” scalar products of images. In this paper, we exploit the analogy between binary images and point sets, and use the Hausdorff metrics for comparing the images. It does not require the measure at all, and is based only on the metrics of the space whose subsets we consider. In addition to Hausdorff distance, we suggest a new “nonlinear” version of this distance for comparison of images, called “autowave” distance. This distance can be calculated very easily and yields some additional advantages for pattern recognition (e.g. noise tolerance). The method was illustrated for the problem of machine reading (Optical Character Recognition). It was compared with some famous OCR programs for PC. On a medium quality xerocopy of a journal page, in the same conditions of learning and recognition, the autowave approach resulted in much fewer mistakes. The method can be realized using only one chip with simple uniform connection of the elements. In this case, it yields an increase in computation speed of several orders of magnitude.
A fully nonlinear version of the Yamabe problem and a Harnack type inequality
