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An algorithm for affine transformation of binary images stored in pxy tables by run format

The algorithm for an affine transformation (such as magnification, reduction, or rotation of a binary image) using a run format and a combination of a skew transformation and a transposition has been known. A transposition using this conventional algorithm requires a relatively large amount of computation time, although its skewing operation is simple and fast. 
 
 
 
This paper proposes an efficient method of transposition of an image represented by a run format, and its applications to an affine transformation (e.g., rotation, magnification, and reduction of an image). The proposed method uses a simple run data format “pxy tables,” in which the start coordinate of black and white runs are stored alternatively in a one-dimensional array. An experimental comparison of the proposed method with a conventional method shows that the computation time per run of the former is constant, while that of the latter increases with the length of the black runs. In other words, the computation time of an affine transformation of a binary image by using the proposed method is approximately proportional to the number of runs alone.