A New Case for Image Compression Using Logic Function Minimization

Abstract

This paper proposes implements and evaluates an image compression method called YALMIC (Yet Another Logic Minimization Based Image Compression) which depends on logic function minimization. This method considers adjacent pixels of the image as disjointed minterms constructing a logic function and compresses the 24-bit color images through minimizing the function. We compare the compression ratio of the proposed method to those of existing methods and show that YALMIC improves the compression ratio by about 25% on average.

Research of 5-bit boolean functions minimization protocols by combinatorial method

“…-generalized substitution of variables for 4, 8 and 16 blocks: given by the truth table Σ (1,2,3,4,5,7,9,11,12,13,14,15,16,17,18,20,22,26,28,30,31) by the combinatorial method, using the minimization protocols:…”

“…The method of logic-minimizing image compression, which depends on the logical function, is demonstrated in [7]. The minimization process treats adjacent pixels of the image as separate minterms, representing a logical function and compresses 24-bit color images using the function minimization procedure.…”

Minimization of Boolean functions by combinatorial method

“…In contrast to [7][8][9][10][11][12][13][14][15][16], in this paper, the object of solving the problem of minimizing a Boolean function is a combinatorial block-diagram with repetition, which allows to concentrate the minimization principle within the truth table of a given function. The peculiarities of the combinatorial method consist in greater informativeness of the process of solving the problem in comparison with the algebraic method of minimizing the function, due to tabular organization and the introduction of figurative calculus apparatus.…”

“…In [12], the method of logical-minimized image compression, which depends on the logical function, is demonstrated. The minimization process treats neighboring pixels of the image as separate minterms representing a logic function and compresses 24-bit color images using the function minimization procedure.…”

“…No. Using Table 5, let's compose the PDNF of the given 5-bit function from the blocks for which the function receives the value of 1, that is, for the sets 1,4,5,7,9,11,12,13,16,17,18,22,28,31. …”