Measuring 2-D shape compactness using the contact perimeter

A new perimeter for shapes composed of cells is defined. This perimeter is called the contact perimeter, which corresponds to the sum of the boundaries of neighboring cells of the shape. Also, a relation between the perimeter of the shape and the contact perimeter is presented. The contact perimeter corresponds to the measure of compactness proposed here called discrete compactness. In this case, the term compactness does not refer to point-set topology, but is related to intrinsic properties of objects.