A characterization of digital disks by discrete moments
Abstract

 the number of points of the digital disk

 the sum of xcoordinates of the points of digital disk

 the sum of ycoordinates of the points of digital disk, is proved.
The efficiency of the reconstruction of the original disk from the proposed code is analysed. It is shown that the errors in estimating the radius of the disk, and the coordinates of its center, tend to zero while the radius of the disk tends to infinity. More precisely, if a disk, having the radius equal to r, is digitized and proposed coding scheme is applied, then the radius and the center position of the original disk can be reconstructed (from the obtained code) with relative errors bounded by \(\mathcal{O}\left( {\tfrac{1}{{r \cdot \sqrt[3]{r}}}} \right)\), and absolute errors bounded by \(\mathcal{O}\left( {\tfrac{1}{{\sqrt[3]{r}}}} \right)\).
The numerical data strongly confirm the theoretical results. The illustration by several experimental results is given.
Key words
pattern analysis low level processing and coding shape representationPreview
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