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Centroid

About: Centroid is a research topic. Over the lifetime, 4110 publications have been published within this topic receiving 53637 citations. The topic is also known as: barycenter (geometry) & geometric center of a plane figure.


Papers
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Journal ArticleDOI
W. Niblack1, Dragutin Petkovic1
01 Apr 1990
TL;DR: A new, high accuracy method is proposed that consists of smoothing the Hough arrayH(ρ, θ) prior to finding its peak location and interpolating about this peak to find a final sub-bucket peak and with results from least squares fitting.
Abstract: The subject of this paper is very high precision parameter estimation using the Hough transform. We identify various problems that adversely affect the accuracy of the Hough transform and propose a new, high accuracy method that consists of smoothing the Hough arrayH(ρ, θ) prior to finding its peak location and interpolating about this peak to find a final sub-bucket peak. We also investigate the effect of the quantizations Δρ and Δθ ofH(ρ, θ) on the final accuracy. We consider in detail the case of finding the parameters of a straight line. Using extensive simulation and a number of experiments on calibrated targets, we compare the accuracy of the method with results from the standard Hough transform method of taking the quantized peak coordinates, with results from taking the centroid about the peak, and with results from least squares fitting. The largest set of simulations cover a range of line lengths and Gaussian zero-mean noise distributions. This noise model is ideally suited to the least squares method, and yet the results from the method compare favorably. Compared to the centroid or to standard Hough estimates, the results are significantly better—for the standard Hough estimates by a factor of 3 to 10. In addition, the simulations show that as Δρ and Δθ are increased (i.e., made coarser), the sub-bucket interpolation maintains a high level of accuracy. Experiments using real images are also described, and in these the new method has errors smaller by a factor of 3 or more compared to the standard Hough estimates.

65 citations

Journal ArticleDOI
TL;DR: The accuracy of sensor node location estimates from self-calibration in sensor networks is considered and the utility of the proposed error decomposition into relative and transformation components is illustrated.
Abstract: This paper considers the accuracy of sensor node location estimates from self-calibration in sensor networks. The total parameter space is shown to have a natural decomposition into relative and centroid transformation components. A linear representation of the transformation parameter space is shown to coincide with the nullspace of the unconstrained Fisher information matrix (FIM). The centroid transformation subspace-which includes representations of rotation, translation, and scaling-is characterized for a number of measurement models including distance, time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA), and angle-difference-of-arrival (ADOA) measurements. The error decomposition may be applied to any localization algorithm in order to better understand its performance characteristics, and it may be applied to the Cramer-Rao bound (CRB) to determine performance limits in the relative and transformation domains. A geometric interpretation of the constrained CRB is provided based on the principal angles between the measurement subspace and the constraint subspace. Examples are presented to illustrate the utility of the proposed error decomposition into relative and transformation components.

65 citations

Journal ArticleDOI
TL;DR: This work evaluated two representative objects in two orientations to determine the influence of the number of two-dimensional cross-sections on the accuracy of the calculations and dramatically decreases data manipulation and computation as compared to the classical mass element summation technique employed for three-dimensional discrete objects.

65 citations

Journal ArticleDOI
Zhou Zhiyong1, Jian Zheng1, Yakang Dai1, Zhe Zhou1, Shi Chen1 
11 Mar 2014-PLOS ONE
TL;DR: This paper proposes a robust non-rigid point set registration algorithm using the Student's-t mixture model and compared it with other state-of-the-art registration algorithms on both 2D and 3D data with noise and outliers, where it showed accurate results and outperformed the other algorithms.
Abstract: The Student's-t mixture model, which is heavily tailed and more robust than the Gaussian mixture model, has recently received great attention on image processing. In this paper, we propose a robust non-rigid point set registration algorithm using the Student's-t mixture model. Specifically, first, we consider the alignment of two point sets as a probability density estimation problem and treat one point set as Student's-t mixture model centroids. Then, we fit the Student's-t mixture model centroids to the other point set which is treated as data. Finally, we get the closed-form solutions of registration parameters, leading to a computationally efficient registration algorithm. The proposed algorithm is especially effective for addressing the non-rigid point set registration problem when significant amounts of noise and outliers are present. Moreover, less registration parameters have to be set manually for our algorithm compared to the popular coherent points drift (CPD) algorithm. We have compared our algorithm with other state-of-the-art registration algorithms on both 2D and 3D data with noise and outliers, where our non-rigid registration algorithm showed accurate results and outperformed the other algorithms.

65 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023492
20221,001
2021184
2020202
2019269
2018271