ABSTRACT
Any given foreground space (set) depicting, for instance, Apollonian space, Koch fractal, porous medium, and any other space like nonnetwork space can be fragmented into simple forms of shapes such as squares, rhombus, octagons, triangles, and circles. A popular power-law relationship between the number and radius provides a noninteger dimension that is scale invariant. In this chapter, morphological shape decomposition (MSD) of various sets (foregrounds) mimicking geomorphologic phenomena has been explained to further compute scale-invariant power-laws that are shape dependent.
