On the discretization of parameter domain in Hough transformation

Although the basic principle of Hough transformation can be described accurately in continuous spaces, its application is often conducted in digitized ones. The discretization of both a spatial image and the related transformation parameters will result in positioning errors in the parameter domain that affect the accumulation through which the Hough transformation functions. This makes the discretization of its parameter domain an important issue. Its resolution needs to be carefully selected to assure the effective concentration of the accumulation. In this paper, the effects of the digitization of both the spatial and the parameter domain on the resolution of the latter are analyzed numerically, and a procedure to determine the resolution, and therefore the discretization, of the parameter domain is proposed. Computer simulations show the effect of this consideration, and its importance is also demonstrated by applying successfully the Hough transformation to texture analysis in mammographic image processing with the appropriate digitization of its parameter domain