Abstract: Translational, rotational, and scaling invariant (TRSI)pattern recognition is a third-order problemencountered frequently in real-world applications. Butneither traditional image processing/patternrecognition algorithms nor artificial neural networkshave yet provided satisfactory solutions for thisproblem after years of study. Recent research has shownthat a higher-order neural network (HONN), of orderthree with built-in invariances, can effectivelyachieve TRSI pattern recognition. For an N $MUL Nimage, the memory needed to store the connections isproportional to N$+6$/. This huge memory requirementlimits the HONNs application to large-scale images. Tosolve this problem the authors first adapt edgedetection and log-spiral mapping algorithms topreprocess the image so that the problem is convertedinto a second-order one. This reduces the HONN memoryrequirement to O(N$+4$/). Second, the authors modifiedthe second-order HONN architecture to further reducethe memory size to O(N$+2$/). Synthetic and real imageswith resolution 256 $MUL 256 have been used forsimulation. The training samples are noise free, andthe testing samples are rotated, translated, scaled, ornoise-corrupted versions of the training patterns.Simulation results show that this system can indeedachieve TRSI pattern classification. In addition, itshigh robustness to noise and pattern deformation makesit very useful for real-world applications.!
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