Abstract: A process for producing a compressed image of a color picture. The color picture is optically scanned to obtain an array of optical parameters representing the basic colors at each coordinate point of the picture which are then converted into digital values. From such digital values, a selection is made of sets of data values representing a series of elements of the picture having discontinuities therein. A model is formulated for each of the elements having a first component containing all of the discontinuities and a second component representing the differentiable content of the elements. The second component is represented by a Taylor polynomial having a selected polynomial degree of at least 2. A maximum allowable error is then selected. The coefficients of the polynomials of the second component are calculated at selected points of a grid with a grid pitch defined by a specified formula. A compressed color picture is derived from the data values constituting the compressed image.