Template decomposition and inversion over hexagonally sampled images

The family of real-valued circulant templates on nXm rectangular images is isomorphic to a quotient ring of the ring of real polynomials in two variables. Template decomposition is equivalent to factoring the corresponding polynomial. Template invertibility corresponds to polynomial invertibility in the quotient ring. Factoring and inverting are more difficult for polynomials in two variables than for those in one. Hexagonally sampled images have properties which simplify these operations. Hexagons organize themselves naturally into a hierarchy of snowflake-shaped regions. These tile the plane and consequently yield a simple definition of circulancy. Unlike the circulancy of rectangles in the plane, which yields a toroidal topology, the hexagonal analogue yields the topology of a circle. As a result, circulant templates are mapped isomorphically into a quotient of the ring of polynomials in one variable. These polynomials are products of linear factors over the complex numbers. A polynomial will be invertible in the quotient ring whenever each of its linear factors is invertible. This results in a simple criterion for template invertibility.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.