Rough approximation of shapes in pattern recognition

The paper approaches the nature of a feature recognition process through the description of image features in terms of the rough sets. Since the basic condition for representing images must be satisfied by any recognition result, elementary features are defined as equivalence classes of possible occurrences of specific fragments existing in images. The names of the equivalence classes (defined through specific numbers of objects and numbers of background parts covered by a window) constitute the best lower approximation of window contents (i.e., names of recognized features). The best upper approximation is formed by the best lower approximation, its attributes, and parameters, all referenced to the object fragments situated in the window. The rough approximation of shapes is resistant to accidental changes in the width of contours and lines and to small discontinuities and, in general, to possible positions or changes in shape of the same feature. The rough sets are utilized also on the level of image processing for noiseless image quantization.