Replacing the Hough calculation of the trigonomeric functions, sine and cos0,by the piece-wise linear Hough function(PLH), the basic cost for the sine , cose and the multiplications is removed. The PLH function is directly introduced from the usual Hough function. The PLH function inherits the basic properties of the usual Hough function from the view point to extract the line patterns from the pattern space. The computing cost of the PLH transform was reduced to about 1/6 of that of the usual

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... ough transform. It was also investigated that an additional property of the PLH transform contributes to reduce the memory cost to about 70 % of the usual Hough transform.