1. A character recognition apparatus for discriminating an image into characters and a textured background, comprising: a computer; a memory coupled to the computer; a scanner coupled to the computer and optically scanning the printed image and producing digital data for each of a plurality of pixels to provide a virtual image, and the digital data including pixel densities in a character portion of the virtual image containing the characters and the textured background; said memory including an image memory storing the digital data as a record of the pixel densities in a matrix corresponding to locations of the pixels in the character portion; said memory including a program memory storing a program; said computer running the program and locating, in the virtual image, a learning area A containing only the textured background and a learning area B containing both the textured background and at least a part of the characters; said memory storing a plurality of different discriminant functions that each include the digital pixel density information of a pixel being processed and pixels in the immediate adjacent vicinity of the pixel being processed; said memory storing an identification of the learning area A and the learning area B; said computer running the program and retrieving from said memory at least a part of the stored digital data as digital pixel density information by using the identification; said computer running the program and determining a specific discriminant function by producing output values of the plurality of different discriminant functions that each include the digital pixel density information of a pixel being processed and pixels in the immediate adjacent vicinity of the pixel being processed separately for each of the learning areas A and B, and selecting one of the plurality of different discriminant functions as the specific discriminant function based upon the output values of the one of the plurality of different discriminate functions for learning area A and learning area B best satisfying a criteria when compared to the output values of the others of the plurality of different discriminant functions; said memory storing, under control of the computer, accumulated statistics of the output values of the specific discriminant function for a plurality of different pixels being processed for at least one of the learning areas A and B; said computer running the program and discriminating with the specific discriminant function whether each pixel, of the virtual image, is part of the characters or part of the textured background by comparing an output value of the specific discriminant function for the each pixel as the pixel being processed with the stored accumulated statistics of the output values of the specific discriminant function for a plurality of different pixels of at least one of the learning areas A and B, so that said discriminating discriminates that part of the digital data representing the characters from the virtual image containing the characters and textured background with respect to at least the learning area B; said memory storing the part of the digital data; said computer running the program, and retrieving from said memory and converting the .part of the digital data of the virtual image into digital encoded information providing codes for corresponding discrete ones of the characters; wherein said specific discriminant function produces dispersion values for learning areas A and B that are substantially non-overlapping and mutually exclusive; and wherein the specific discriminant function has a sum of its dispersion values less than or equal to a predetermined value as the criteria and includes iterative steps using Lagrange's method of indeterminate coefficients.