Institute of Fundamental Technological Research

The accumulation methods emerged in close relation to the development of the Hough transform (HT). The application of some far reaching generalizations of the HT will be presented. The accumulation principle will be taken as a starting point: Accumulate the relevant data from possibly many, possibly competent sources. This principle is known and widely used in image processing, mainly in the methods related to the HT. The principle is in opposition to the tendency to compress the image data as early in the processing as possible. The accumulation principle is a recommendation to utilize the redundancy in the image data in a specific way and should be applied when the images are difficult to process due to their low quality. The basic data structure is the fuzzy histogram, which is in fact an experimentally obtained approximation of the probability density of the phenomenon of interest. The concepts of a degree of fuzzification and the weakly and strongly fuzzified histograms will be introduced. A number of solutions found with the use of the accumulation principle will be presented. In the examples and tests, biomedical images will be used. Such images are challenging because the objects imaged are irregular and the quality of the images is usually limited in a natural way by the imaging modalities used. The accumulation methods are a good solution to the problem of analysis of such images.

The influence of the scale of a fuzzy membership function used to fuzzify a histogram is analysed. It is shown that for a class of fuzzifying functions it is possible to indicate the limit for fuzzification, at which the mode of the histogram equals the mean of the data accumulated in it. The fuzzification functions for which this appears are: the quadratic function for aperiodic histograms and the cosine square function for periodic ones. The scaled and clipped versions of these functions can be used to control the degree of fuzzification belonging to the interval [0,1]. While the quadratic function is related to the widely known Huber-type clipped mean or the kernel function derived from the Epanechnikov kernel, the clipped cosine square seems to be less known. The indications for using strong or weak fuzzification, according to the value of the fuzzification degree, are justified by examples in two applications: classic Hough transform-based image registration and novel accumulation-based line detection. Typically, the weak fuzzification is recommended. The images used are related to simulation images from teleradiotherapy and to mammographic images.

Fuzzy histogram, Accumulation, Scale, Mode to mean transition, Limit fuzzification, Periodic histogram, Line detection, Mammograms, Image registration