Abstract
As a binarization threshold selection method to utilize fully edge information, a method has been proposed to select the threshold so that the edge and boundary are as close to each other as possible. In such a method, the binarization actually is performed for various threshold values, and the degree of coincidence is calculated. Consequently, a very large processing time is required. The degree of coincidence is defined as the ratio between the number of boundary points in the edge region to the total number of boundary points in the image.
The authors have devised a method which can determine with a high speed the number of boundary points for each threshold without actually performing the binarization. In this method, the result of applying shrink filtering after binarization is the same as that of applying the binarization with the same threshold after applying the minimum filtering.
By utilizing this property, it is shown that the difference of the cumulative histograms between the original image and the result of processing by the minimum filter is the same as the number of boundary points for the threshold. Furthermore, the following property is shown by extending the method. The degree of coincidence between the edge and the boundary is defined as a twoβvariable function of the threshold of edge detection and the threshold of binarization. Then it is shown that the degree of coincidence between the two can be calculated for any threshold without actually detecting the edges and boundaries.
By utilizing this property, not only the threshold for binarization of the original image but also the threshold for the differentiated image to detect the edge can be determined simultaneously in an optimal way without necessitating a large amount of computation.