Geodesic
A Reconstruction of Digital Parabolas from Their Least Squares Fit Representation
Yugoslav journal of operations research, Tome 8 (1998) no. 2, p. 273
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It is known that the set of digital parabola segments and the set of their least squares parabola fit are in one-to-one correspondence |8|. This enables constant space representation of a digital parabola segment. One of them is a representation of the form $(x_1, n, \alpha, \beta, \gamma)$ where $x_1$ and $n$ are the x-coordinate of the left endpoint and the number of digital points of the segment, respectively, while $\alpha$, $\beta$ and $\gamma$ are the coefficients of the least squares parabola fit $Y=\alpha X^2+\beta X+\gamma$ for the given parabola segment. This paper gives an $O(n \log^2 n)$ algorithm for recovering a given digital parabola segment from its proposed code.
Classification : 68T10
Keywords: Image processing. pattern analysis, digital shapes. 
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     author = {Nata\v{s}a Sladoje and Jovi\v{s}a \v{Z}uni\'c},
     title = {A {Reconstruction} of {Digital} {Parabolas} from {Their} {Least} {Squares} {Fit} {Representation}},
     journal = {Yugoslav journal of operations research},
     pages = {273 },
     year = {1998},
     volume = {8},
     number = {2},
     zbl = {1009.68137},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_1998_8_2_a7/}
}
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Nataša Sladoje; Joviša Žunić. A Reconstruction of Digital Parabolas from Their Least Squares Fit Representation. Yugoslav journal of operations research, Tome 8 (1998) no. 2, p. 273 . http://geodesic.mathdoc.fr/item/YJOR_1998_8_2_a7/