Identification of generalized self-similar principal components of single image for image filtering and pattern decomposition

Scale and resolution are critical parameters in utilization of any maps including remotely sensed imagery. With information techniques such as image processing and GIS software, digital images can be easily visualized at multiple scales. Due to the dimensional property (fractality) of objects on the ground or the dimensional properties (multifractalities) of mixing objects, the changing regularities of image patterns observed at different scales or resolutions can be quantified in terms of self- similarity or generalized self-similarity. A newly developed method is introduced for identifying self-similar principal components from a single image so that self-similar components can be utilized for purposes of image filtering and image decomposing. The self-similarity of principal components introduced in this paper is characterized by power-law relations observed from the frequency distributions of the eigenvalues or eigenvectors calculated from a single image. Different groups of self-similar components can be identified and used for image decomposing. The case study for validation is chosen from a DEM at 30 meter resolution in the Greater Toronto Area,Canada.