Methods for Generating Blue-Noise Dither Matrices for Digital Halftoning Kevin E. Spaulding, Rodney L. Miller and Jay Schildkraut Eastman Kodak Company Imaging Research and Advanced Development, Rochester, New York 14650 E-mail:
[email protected] Abstract the input value and compared to a fixed threshold, in- stead of using the dither value itself as the threshold. It Blue-noise dither halftoning methods have been found can easily be shown that these two implementations are to produce images with pleasing visual characteristics. mathematically equivalent, however, in some cases, the Results similar to those generated with error-diffusion second approach may be more computationally efficient. algorithms can be obtained using an image processing algorithm that is computationally much simpler to imple- ment. This paper reviews and compares the various tech- I(x,y) niques that have been used to design blue-noise dither matrices. In particular, a series of visual cost function O(x,y) Compare based methods, a several techniques that involve design- x (column #) xd ing the dither matrices by analyzing the spatial dot dis- mod Mx tribution are discussed. Ways to extend the basic dither matrix d(xd, yd) y (row #) yd blue-noise dither techniques to multilevel and color out- mod My put devices are also described, including recent advances in the design of jointly optimized color blue-noise dither Figure 1. Flow diagram for basic ordered-dither algorithm. matrices. 1 Introduction I(x,y) O(x,y) Threshold Many printing devices are binary in nature, and are there- fore incapable of producing continuous tone images. x (column #) xd Digital halftoning techniques are used to create the ap- mod Mx dither matrix pearance of intermediate tone levels by controlling the d(xd, yd) y (row #) yd spatial distribution of the binary pixel values.