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A new binary code for pattern recognition by parallel computation

In most pattern recognition schemes, common geometric transformations such as rotation, translation, and perspectivity require computations whose complexity and execution time increase rapidly with increasing grid resolution (number of grid cells). A new code which embodies such transformations as simple, locally applied algorithms (such as rewriting substrings of code as single digits) has been found. By applying these algorithms to the code, the problem of recognizing straight lines on the quadratic lattice has been completely solved. Recognition is achieved by applying a sequence of affine transformations to reduce lines to standard position. This corresponds to reducing a code string to a single digit. The recognition algorithms are parallel (applied simultaneously to entire code string) and are independent of the number of cells in the grid and the slope and position of the line relative to the grid. They are based on some interesting connections between the new code and continued fractions, Farey series, and affine transformations.