Topic
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.
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TL;DR: In this paper, it was shown that the bottleneck for a quantum activated process as defined by VCM does not correspond to the classical bottleneck for the case of an asymmetric barrier.
Abstract: The low temperature behavior of the centroid density method of Voth, Chandler, and Miller (VCM) [J. Chem. Phys. 91, 7749 (1989)] is investigated for tunneling through a one‐dimensional barrier. We find that the bottleneck for a quantum activated process as defined by VCM does not correspond to the classical bottleneck for the case of an asymmetric barrier. If the centroid density is constrained to be at the classical bottleneck for an asymmetric barrier, the centroid density method can give transmission coefficients that are too large by as much as five orders of magnitude. We follow a variational procedure, as suggested by VCM, whereby the best transmission coefficient is found by varying the position of the centroid until the minimum value for this transmission coefficient is obtained. This is a procedure that is readily generalizable to multidimensional systems. We present calculations on several test systems which show that this variational procedure greatly enhances the accuracy of the centroid density method compared to when the centroid is constrained to be at the barrier top. Furthermore, the relation of this procedure to the low temperature periodic orbit or ‘‘instanton’’ approach is discussed.
44 citations
TL;DR: This paper casts the multi-view registration into a clustering problem, which can be solved by the extended K-means clustering algorithm, which has tested on some public data sets and compared with the-state-of-art algorithms.
44 citations
TL;DR: By using the centroid mode for fixation detection, a valid fixation is 2.86 times more likely to be identified than by using the start-point mode, which shows a good interpretation speed, accuracy, robustness, and ease of implementation.
Abstract: Fixation-identification algorithms, needed for analyses of eye movements, may typically be separated into three categories, viz. (i) velocity-based algorithms, (ii) area-based algorithms, and (iii) dispersion-based algorithms. Dispersion-based algorithms are commonly used but this application introduces some difficulties, one being optimization. Basically, there are two modes to reach this goal of optimization, viz., the start-point mode and the centroid mode. The aim of the present study was to compare and evaluate these two dispersion-based algorithms. Manual inspections were made of 1,400 fixations in each mode. Odds ratios showed that by using the centroid mode for fixation detection, a valid fixation is 2.86 times more likely to be identified than by using the start-point mode. Moreover, the algorithm based on centroid mode dispersion showed a good interpretation speed, accuracy, robustness, and ease of implementation, as well as adequate parameter settings.
44 citations
Patent•
02 Nov 1987
TL;DR: In this article, a system for monitoring changes in shape of a structure employs a laser source attached to the structure and a set of beam splitters mounted at various locations on the structure.
Abstract: A system for monitoring changes in shape of a structure employs a laser source attached to the structure and a set of beam splitters mounted at various locations on the structure and arranged to route portions of a laser beam produced by the laser source into various video cameras also mounted on the structure. Each video camera includes a photodetector array and produces an output signal indicating the intensity of light detected by each photodetector of the array, thereby indicating the beam intensity distribution in a corresponding plane of interest. The video output signal of each camera is digitized and stored as an intensity data array in the memory of a digital computer. The computer calculates from the intensity data array the position of the centroid of the beam with respect to a reference point on the plane of interest using a least squares fit of the intensity data to a two-dimensional Gaussian intensity distribution. Any deviation of the calculated beam centroid position from the reference point indicates a change in jig shape in the plane of interest. The reference point in each plane of interest is determined by a least squares fit of the computed beam centroids in several planes to a line.
44 citations
TL;DR: In this paper, the effect of projected large-scale structure (LSS), smoothing of mass maps, and shape noise on the weak-lensing peak positions was studied, and the authors concluded that projected LSS, although a major contaminant for weaklensing mass estimates, is not a source of confusion for identifying halo centres.
Abstract: Centroid positions of peaks identified in weak-lensing mass maps often show offsets with respect to other means of identifying halo centres, such as position of the brightest cluster galaxy or X-ray emission centroid. Here we study the effect of projected large-scale structure (LSS), smoothing of mass maps, and shape noise on the weak-lensing peak positions. In addition, we compare the offsets in mass maps to those found in parametric model fits. Using ray-tracing simulations through the Millennium RunN-body simulation, we find that projected LSS does not alter the weak-lensing peak position within the limits of our simulations’ spatial resolution, which exceeds the typical resolution of weak-lensing maps. We conclude that projected LSS, although a major contaminant for weak-lensing mass estimates, is not a source of confusion for identifying halo centres. The typically reported offsets in the literature are caused by a combination of shape noise and smoothing alone. This is true for centroid positions derived both from mass maps and model fits.
44 citations