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A shape descriptor has been developed which can describe a shape independent of its translation, rotation, and scaling. The description is in the form of a matrix and it is obtained by a polar quantization of a shape. The quantization process takes into consideration not only a shape's outer geometry but its inner geometry as well. The descriptor is information preserving and if the quantization parameters are selected properly, it is possible to reconstruct an original shape from its description. In this technique, shape discrimination is possible by a simple EXCLUSIVE-OR operation on shape descriptions.