Finite State Two-Dimensional Compressibility

Combining results from [6, 9, 11], a generalized, parametric quantity q(I), measurable on any given individual picture (two dimensional array of data) I, is proved to be a lower bound on the compression ratio attainable for I by any information lossless finite state encoder. Quantity q(I) is shown to be a tight lower bound, asymptotically attainable, and thus an inherent measure of the picture. Different measures of sequence and picture complexity are related to q(I). Other measurable quantities, also serving as tight lower bounds on the attainable compression, are referred to.