Non-independent Randomized Rounding and an Application to Digital Halftoning

How to Color a Checkerboard with a Given Distribution - Matrix Rounding Achieving Low 2×2-Discrepancy

Motivated by a digital halftoning application to convert a continuous-tone image into a binary image, we discusses how to round a [0; 1]-valued matrix into a f0; 1g binary matrix achieving low discrepancy with respect to the family of all 2 2 square submatrices (or regions). A trivial upper bound of the discrepancy is 2 and the known lower bound is 1. In this paper we shall show how to achieve ...

Non-independent randomized rounding and coloring

Backward Diffusion Methods for Digital Halftoning

We examine using discrete backward diffusion to produce digital halftones. The noise introduced by the discrete approximation to backwards diffusion forces the intensity away from uniform values, so that rounding each pixel to black or white can produce a pleasing halftone. We formulate our method by considering the Human Visual System norm and approximating the inverse of the blurring operator...

Combinatorics and Algorithms on Low-Discrepancy Roundings of a Real Sequence

We discuss the problem of computing all the integer sequences obtained by rounding an input sequence of n real numbers such that the discrepancy between the input sequence and each output binary sequence is less than one. The problem arises in the design of digital halftoning methods in computer graphics. We show that the number of such roundings is at most n + 1 if we consider the discrepancy ...

Matrix Rounding and Related Problems with Application to Digital Halftoning

In this paper, we first study the problem of rounding a real-valued matrix into an integer-valued matrix to minimize an Lp-discrepancy measure between them. To define the Lp-discrepancy measure, we introduce a family F of regions (rigid submatrices) of the matrix, and consider a hypergraph defined by the family. The difficulty of the problem depends on the choice of the region family F. We firs...