On the number of digital convex polygons inscribed into an (m,m)-grid

Binary images of objects are digitized by coloring a pixel cell black if more than half of its area is within the interior of the object. For simplicity, the digitization is often modified by looking only at the center point of a cell to determine its pixel value. The digitized boundary curve consis...

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Bibliographic Details
Published in:IEEE transactions on information theory 1994-09, Vol.40 (5), p.1681-1686
Main Authors: Ivic, A., Koplowitz, J., Zunic, J.
Format: Article
Language:English
Subjects:
Algebra
Applied sciences
Binary system
Codes
Conferences
Decoding
Exact sciences and technology
Geometry
Image processing
Information, signal and communications theory
Mathematics
Signal processing
Telecommunications and information theory
Turning
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Summary:Binary images of objects are digitized by coloring a pixel cell black if more than half of its area is within the interior of the object. For simplicity, the digitization is often modified by looking only at the center point of a cell to determine its pixel value. The digitized boundary curve consists of a sequence of 4-directional links, sometimes called a "crack" code since it follows the cracks or edges of the pixel cells. Of interest here is the entropy of digitized binary objects or planar curves on an m/spl times/m integer grid. Let D(m) denote the number of digital convex polygons which can be inscribed into an integer grid of size m/spl times/m. The asymptotic estimation of log D(m) is of interest in determining the entropy of digitized convex shapes. It is shown that log D(m) is of the order m/sup 2/3/.< >
ISSN:0018-9448
1557-9654
DOI:10.1109/18.333894