A new methodfor the black-and-white display ofgray-scale images limits cumulative error in binary subdivisions of images and eliminates deficiencies of the ordered dither technique. Using Peano Curves for Bilevel Display of Continuous -Tone Images Ian H. Witten and Radford M. Neal University of Calgary A frequent problem in computer graphics is the pre- sentation of gray-scale images on a bilevel black-and- white display. Many displays-liquid crystal, plasma panel, microfilm, ink on paper, laser phototypesetter- are usually bilevel. But most pictures-whether they originate from a camera, film scanner, or computer sys- tem that generates or processes images-are continuous tone. Therefore, an effective bilevel display method for such continuous tone material is needed. The problem is important for transmission also, particularly with the ad- vent of CCITT standards for bilevel digital facsimile transmission of documents. Although the ordered dither technique is frequently used for such displays, we have found the use of Peano curves to be a superior technique. The conventional screened half-tone process of the print industry generates black dots of a continuously vari- able size on a raster pattern of points. Such a process can easily be digitized by allocating an n x n matrix of raster points for each half-tone dot. This gives an (n2 + 1)-level gray scale at the cost of a factor of n decrease in linear res- olution. The ordered dither technique1 is much more suit- able for digital displays, however, and compares favor- ably with other methods.2 This uses a constant n x n dither matrix (where n is a power of 2) to simulate an (n2 + 1)-level gray scale. The matrix contains the integers from 0 ton2 n 1 in a predetermined pattern. It is replicated enough times to cover the image, then subtracted from it; the result is quantized into two levels according to its sign. But the ordered dither method is deficient in several re- spects: * Repetitive, textured patterns are generated on areas where the input intensity is constant. * The jaggedness of a nearly horizontal (or vertical) line, caused by aliasing of high spatial frequencies, is exacerbated. * Each point is treated independently of its neighbors, so errors may accumulate if the dither matrix cannot accommodate the number of gray levels in the image. * Accurate gray levels cannot be obtained on displays whose points overlap, as in most real-life hard-copy displays.3 * The technique appears to be unsuitable for color dis- plays. Figure 1, drawn with n = 16, illustrates the first two of these shortcomings. One-dimensional display using incremental representation Clearly, a method that incorporates feedback, using the cumulative error accrued at each point, is necessary if the third deficiency listed above is to be overcome. It is easy to devise such an algorithm if one-dimensional displays are considered. The problem is identical to that of obtaining an accurate incremental representation of a continuously varying quantity, such as is used in the digital differential analyzer4 and in delta modulation. 0272-1716/82/0500-0047$00.75 ( 1982 IEEE May 1982 47