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Fitting discrete polynomial curve and surface to noisy data

Annals of Mathematics and Artificial Intelligence, 2014
The problem of fitting geometric models (line, circles, and planes) leads to many applications in image analysis and computer vision, such as object recognition, shape approximation and image segmentation. One issue of the problem is that of using discrete models when the discrete spaces are discussed. Classically, such models are defined as the result
Fumiki Sekiya, Akihiro Sugimoto
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Uncertainty quantification and estimation of closed curves based on noisy data

Computational Statistics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Luming Chen, Sujit K. Ghosh
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Determining perceptually significant points on noisy boundary curves

Pattern Recognition Letters, 1991
One method of describing the shape of objects in images is to locate points of maximum curvature on object boundaries. These are commonly believed to be the most perceptually significant points on digital curves. However, our work indicates that estimators of point curvature become highly unreliable in the presence of noise.
D. P. Illing, P. T. Fairney
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Curve Reconstruction from Noisy and Unordered Samples

Proceedings of the 3rd International Conference on Pattern Recognition Applications and Methods, 2014
An algorithm for the reconstruction of closed and open curves from clouds of their noisy and unordered samples is presented. Each curve is reconstructed as a polygonal path represented by its vertices, which are determined in an iterative process comprising evolutionary and decimation stages.
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Phase Information and Space Filling Curves in Noisy Motion Estimation

IEEE Transactions on Image Processing, 2009
This correspondence presents a novel approach for translational motion estimation based on the phase of the Fourier transform. It exploits the equality between the averaging of a group of successive frames and the convolution of the reference one with an impulse train function.
Bruni V, De Canditiis D, Vitulano D
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Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves

Biometrics, 2001
Summary.We propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients. The method is applicable when the individual curves are sampled at variable and irregularly spaced points.
Rice, John A., Wu, Colin O.
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Subtractive clustering: A tool for reconstructing noisy curves

2014 International Conference on Signal Processing and Integrated Networks (SPIN), 2014
A new approach for reconstructing noisy curves has been proposed in this paper. Direct use of curve fitting on the noisy data yields very poor results and so some form of smoothing is required to eliminate this noise. Subtractive clustering combined with traditional curve fitting has been used to generate the original curves.
Kavita Khanna, Navin Rajpal
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Smoothing: Computing Curves from Noisy Data

2009
The previous two chapters have introduced the Matlab and R code needed to specify basis function systems and then to define curves by combining these coefficient arrays. For example, we saw how to construct a basis object such as heightbasis to define growth curves and how to combine it with a matrix of coefficients such as heightcoef so as to define ...
J.O Ramsay, Giles Hooker, Spencer Graves
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A numerical procedure for curve fitting of noisy infrared spectra

Analytica Chimica Acta, 1998
A method for the detection of overfitting of noisy spectra is presented. When fitting data that contains random noise, the autocorrelation function (RL) of residuals at lag 1 (R1) approaches zero and then shows a tendency toward more negative values, while the Wald–Wolfowitz test tends to give more positive values, as the data is overfitted.
Carlos E. Alciaturi   +2 more
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Transformations for the Computer Detection of Curves in Noisy Pictures

Computer Graphics and Image Processing, 1975
Abstract Transformations which map noisy feature points originating from the same curve in a picture into dense regions are considered. These transformations are to be followed by clustering to detect curves in the original picture. Properties of the transformations are treated as they relate to this subsequent clustering.
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