Prof. Alejo Hausner Profile

Prof. Alejo Hausner

at Univ of New Hampshire

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SPIE Journal Paper | 1 April 2008

Hierarchical graph color dither

Alejo Hausner

JEI, Vol. 17, Issue 02, 023001, (April 2008) https://doi.org/10.1117/12.10.1117/1.2916703

KEYWORDS: Matrices, Halftones, Radon, Diffusion, Raster graphics, Quantization, Binary data, Printing, Image processing, Eye

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Suppose a dispersed-dot dither matrix is treated as a collection of numbers, each number having a position in space; when the numbers are visited in increasing order, what is the distance in space between pairs of consecutive numbers visited? In Bayer’s matrices, this distance is always large. We hypothesize that this large consecutive distance is important for good dispersed-dot threshold matrices. To study the hypothesis, matrices that have this quality were generated by solving a more general problem: given an arbitrary set of points on the plane, sort them into a list where consecutive points are far apart. Our solution colors the nearestneighbor graph, hierarchically. The method does reproduce Bayer’s dispersed-dot dither matrices under some settings and, furthermore, can produce matrices of arbitrary dimensions. Multiple similar matrices can be created to minimize repetitive artifacts that plague Bayer dither while retaining its parallelizability. The method can also be used for halftoning with points on a hexagonal grid, or even randomly placed points. It can also be applied to artistic dithering, which creates a dither matrix from a motif image. Unlike in the artistic dither method of Ostromoukhov and Hersch, the motif image can be arbitrary and need not be specially constructed.

Proceedings Article | 16 January 2006 Paper

Graph-order dithering

Alejo Hausner

Proceedings Volume 6058, 605810 (2006) https://doi.org/10.1117/12.643518

KEYWORDS: Matrices, Binary data, Diffusion, Halftones, Eye, Printing, Image processing, Visualization, Color reproduction, Computer science

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This paper presents a generalization of dispersed-dot dithering. While existing methods such as Bayer's assume that color dots are arranged in a square matrix, this method works with arbitrarily-placed color points. To create a good dither pattern for arbitrarily-placed points, they must be ordered so that consecutive pairs are maximally separated. In this paper, the ordering is obtained by hierarchically coloring the vertices of the points' adjacency graph. Each level in the coloring hierarchy adds a color digit to each graph vertex's label, and sorting the resulting multi-digit labels produces the desired consecutive-point separation. The method can reproduce Bayer's dispersed-dot dither matrices, but can also produce many similar matrices. Multiple matrices can be used to minimize repetitive artifacts that plague Bayer dither, while retaining its parallelizability. The method can also be applied to artistic dithering: given a repeatable motif image, its pixels can be grouped into subsets, one for each gray level, and each subset ordered. Concatenating the subsets yields a dither matrix that reproduces a motif while displaying an overall image. Unlike in previous artistic dither methods, the motif image can be arbitrary, and need not be specially constructed.

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