Recognition and characterization of digitized curves

Michael Werman; Angela Y. Wu; Robert A. Melter

doi:10.1016/0167-8655(87)90065-1

Recognition and characterization of digitized curves

Michael Werman^*, Angela Y. Wu, Robert A. Melter

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We consider the graphs of functions representable in the form h(x) = Σ_j=1ⁿ a_jf_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.

Original language	English
Pages (from-to)	207-213
Number of pages	7
Journal	Pattern Recognition Letters
Volume	5
Issue number	3
DOIs	https://doi.org/10.1016/0167-8655(87)90065-1
State	Published - Mar 1987
Externally published	Yes

Keywords

Digitized curves

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10.1016/0167-8655(87)90065-1

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title = "Recognition and characterization of digitized curves",

abstract = "We consider the graphs of functions representable in the form h(x) = Σj=1n ajfj(x) where the fj 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.",

keywords = "Digitized curves",

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T1 - Recognition and characterization of digitized curves

AU - Werman, Michael

AU - Wu, Angela Y.

AU - Melter, Robert A.

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N2 - We consider the graphs of functions representable in the form h(x) = Σj=1n ajfj(x) where the fj 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.

AB - We consider the graphs of functions representable in the form h(x) = Σj=1n ajfj(x) where the fj 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.

KW - Digitized curves

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VL - 5

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EP - 213

JO - Pattern Recognition Letters

JF - Pattern Recognition Letters

IS - 3

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Recognition and characterization of digitized curves

Abstract

Keywords

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