Digital image segmentation using periodic codings is explored with reference to two applications. First, the application of uniform periodic codings, to the problem of segmenting the in-focus regions in an image from the blurred parts, is discussed. The work presented in this part extends a previous investigation on this subject by considering the leakage effects. The method proposed consists of two stages. In each stage, filtering is done in the spatial frequency domain after uniform grating functions are applied to the images in the spatial domain. Then, algorithms for finding the period and phase of a physical grating are explored for a hybrid optical-digital application of the method.

Second, a model for textures as the linear superposition of periodic narrowband components, defined as tones, is proposed. A priori information about the number of the tones, their spatial frequencies, and coefficients is necessary to generate tone and texture indicators. Tone indicators are obtained by filtering the image with complex analytical functions defined by the spatial frequencies of the tones present in the image. A criterion for choosing the dimensions of the filter is also provided. Texture indicators are then generated for each texture in the image by applying the a priori information of the tonal coefficients to the filtered images. Several methods for texture segmentation which employ texture indicators are proposed. Finally, examples which illustrate the characteristics of the method are presented.