In this paper, we present characteristic pattern as means to match shapes. The characteristic pattern is a group of convex sets that can uniquely describe the shape with respect to a pre- selected set of basic patterns or structuring elements. Each convex subset of a given shape is a union of convex sets each derived from consecutive dilation of one of structuring elements. A shape can be distinguished from others by inspecting the non-zero measure on the resultant sets of openings with a set of pre-selected elements: structuring elements and the numbers of consecutive openings. A transformation from weakly-connected sets to strongly-connected sets is introduced.
"Characteristic pattern matching based on morphology", Proc. SPIE 1606, Visual Communications and Image Processing '91: Image Processing, (1 November 1991); doi: 10.1117/12.50361; https://doi.org/10.1117/12.50361