How to maximize the contact perimeter and contact area of shapes composed of cells in the discrete domain

摘要

The contact perimeter of a shape composed of pixels is the number ofjoints between neighboring pixels of the shape, and the contact area of a shapecomposed of voxels (three dimensional cells) is the number of planar jointsbetween neighboring voxels. In this paper, we present the maximal contactperimeter function for shapes composed of pixels, and the maximal contactarea function for voxel-based shapes. Also, we see how each one of thesefunctions induce the definition of the corresponding standard function thatextends the concept of contact perimeter (area) to non discrete squares (cubes),and which is used in the definition of the normalized discrete compactness.