Shape cognition and representation play an important role in spatial analysis because shape contains some characteristics of geographic phenomena that can be mined to discover hidden geographic principles. As a difficult cognition problem, the shape representation problem in GIS field has the properties of abstraction, indetermination and symbolization. How to use a model to represent shape cognition in our mental world and how to use a single number to compute the shape measure are interesting questions. In the image processing domain, there a...