The paper concerns the problem of thresholding of an integer domain of 1D cyclic histogram (periodic function) resulting in two or more consecutive regions (classes). An optimal solution is searched for in the terms of the statistical criterion well known in the pattern recognition area as Fisher's LDA (Linear Discriminant Analysis) and also successfully applied for image binarization by Otsu (1979). An effective (quadratic complexity) extension of the Otsu's method is also known, which segments the image by respective thresholding of the image intensity histogram into arbitrary number of classes. We propose one more extension of this approach for the case of the cyclic histograms. Similar problem can be brought by the optimal segmentation of color images based on their HSV histogram, and more general in all problems which try to approximate a given periodic function with a predefined number of Gaussians. The paper describes the theoretical basis and the experimental evaluation of the proposed approach.