Circle discrepancy for checkerboard measures
نویسندگان
چکیده
منابع مشابه
The Discrepancy of a Needle on a Checkerboard, Ii
Consider the plane as a checkerboard, with each unit square colored black or white in an arbitrary manner. In a previous paper we showed that for any such coloring there are straight line segments, of arbitrarily large length, such that the difference of their white length minus their black length, in absolute value, is at least the square root of their length, up to a multiplicative constant. ...
متن کاملThe Discrepancy of a Needle on a Checkerboard
Consider the plane as a checkerboard, with each unit square colored black or white in an arbitrary manner. We show that for any such coloring there are straight line segments, of arbitrarily large length, such that the difference of their white length minus their black length, in absolute value, is at least the square root of their length, up to a multiplicative constant. For the corresponding ...
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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 ...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2012
ISSN: 0019-2082
DOI: 10.1215/ijm/1399395833