Recognition and characterization of digitized curves

We consider the graphs of functions representable in the form h( x) = Σ j=1 n a j f j ( x) where the f j constitute a linearly independent set of functions over R. These graphs are digitized by the set of lattice points ( i, ⌊ h( i)⌋). An algorithm is presented to determine if a given set of lattice...

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Bibliographic Details
Published inPattern recognition letters Vol. 5; no. 3; pp. 207 - 213
Main Authors Werman, Michael, Wu, Angela Y., Melter, Robert A.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.03.1987
Elsevier
Subjects
Applied sciences
Artificial intelligence
Computer science; control theory; systems
Digitized curves
Exact sciences and technology
Pattern recognition. Digital image processing. Computational geometry
Digitized curves
Reconstruction
Graph
Digitizing
Pattern recognition
Line (geometry)
Polynome
Algorithm
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Summary:We consider the graphs of functions representable in the form h( x) = Σ j=1 n a j f j ( x) where the f j constitute a linearly independent set of functions over R. These graphs are digitized by the set of lattice points ( i, ⌊ h( i)⌋). An algorithm is presented to determine if a given set of lattice points is part of such a digitization. We also study the digitization of polynomials. An important tool used is the set of differences of the y-coordinates (digital derivatives). For example, if h( x) is a polynomial of degree n, then its n-th digital derivative is cyclic and its ( n + 1)st digital derivative has a bound which depends only on n.
ISSN:0167-8655
1872-7344
DOI:10.1016/0167-8655(87)90065-1