1. Process for the production of a compressed image of a static or dynamic color picture, comprising the steps of: (a) optical scanning said picture to form color corresponding to its basic colors including at least one color selected from the group consisting of magenta, cyan and yellow at all of the coordinate points of said picture; (b) transforming said color values into an array of digital values; (c) selecting from said array of digital values, sets of values representing a series of elements of said picture having discontinuities therein; (d) storing said sets of values within a computer or other electronic storage device; (e) for each of said elements of said picture, formulating a model, with said model having a first component incorporating the discontinuities of said element and a second component representing the differentiable content of said element, with said second component defined by Taylor polynomials having multiple coefficients; (f) selecting a maximum allowable error for the model to establish a given precision for the image to be produced; (g) defining a grid for said picture divided into different regions having multiple grid points and a grid pitch h determined by CMh.sup.k+1 .ltoreq..epsilon., wherein C=1/(k+1)! and M is the maximum at each grid point of the absolute value of the derivatives of the grid k+1 of the differential component or components of the model; (h) selecting the degree of Taylor polynomials equal to at least two; (i) using a computer to derive from said models of said elements of said picture, an array of data values constituting a compressed image of said original picture based upon the selection of the degree of said polynomials and the maximum allowable error for said models with the coefficients of said Taylor polynomials computed along grid points for approximating the differentiable component of said models; (j) storing in said computer, the values and parameters defining the first component of said models and the computed coefficients for the Taylor polynomials as the array of data values constituting a compressed image of the original picture; (k) deriving from said array of optical data values corresponding for each of the identifiable coordinate points; and (l) generating from said optical values, a color picture which is the compressed image of said original picture.