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.

Non-parametric spectrum cartography using adaptive radial basis functions

Abstract: This paper presents a framework for spectrum cartography based on the use of adaptive Gaussian radial basis functions (RBF) centered around a specific number of centroid locations, which are determined, jointly with the other RBF parameters, by the available measurement values at given sensor locations in a specific geographical area. The spectrum map is constructed non-parametrically as no prior knowledge about the transmitters is assumed. The received signal power at each location (over a given bandwidth and time period) is estimated as a weighted contribution from different RBF, in such a way that the both RBF parameters and the weights are jointly optimized using an alternating minimization method with a least squares loss function and a quadratic regularization term. Our method is evaluated through simulations, showing a performance (in terms of normalized MSE) that is comparable to semi-parametric methods, and even superior as the number of sensors or RBF increases.

A robust and outlier-adaptive method for non-rigid point registration

Abstract: In this paper, a flexible probabilistic method is introduced for non-rigid point registration, which is motivated by the pioneering research named Coherent Point Drift (CPD). Being different from CPD, our algorithm is robust and outlier-adaptive, which does not need prior information about data such as the appropriate outlier ratio when the point sets are perturbed by outliers. We consider the registration as the alignment of the data (one point set) to a set of Gaussian Mixture Model centroids (the other point set), and initially formulate it as maximizing the likelihood problem, then the problem is solved under Expectation---Maximization (EM) framework. The outlier ratio is also formulated in EM framework and will be updated during the EM iteration. Moreover, we use the volume of the point set region to determine the uniform distribution for modeling the outliers. The resulting registration algorithm exhibits inherent statistical robustness and has an explicit interpretation. The experiments demonstrate that our algorithm outperforms the state-of-the-art method.

On the Optimum Synthesis of Six-Bar Linkages Using Differential Evolution and the Geometric Centroid of Precision Positions Technique

Abstract: This paper presents the development of a methodology for the synthesis of six-bar dwell mechanisms combining Differential Evolution, an evolutionary optimization scheme, and the Geometric Centroid of Precision Positions technique for defining the initial bounds of the design variables. Two penalty functions are employed one for constraint violation and one for relative accuracy. The results of the initial application of this methodology were also used as “good initial guesses” for improving the desired accuracy level. The developed methodology is applied to the synthesis of six-bar linkages for dwell and dual-dwell mechanisms with prescribed timing and transmission angle constraints. The six-bar mechanism is synthesized using two different approaches: four-bar and extension to six-bar, direct six-bar. Results demonstrating the successful application of the developed methodology and the three approaches are presented.Copyright © 2003 by ASME

Centroid-based methods for calculating quantum reaction rate constants: Centroid sampling versus centroid dynamics

Abstract: A new method was recently introduced for calculating quantum mechanical rate constants from centroid molecular dynamics (CMD) simulations [E. Geva, Q. Shi, and G. A. Voth, J. Chem. Phys. 115, 9209 (2001)]. This new method is based on a formulation of the reaction rate constant in terms of the position-flux correlation function, which can be approximated in a well defined way via CMD. In the present paper, we consider two different approximated versions of this new method, which enhance its computational feasibility. The first approximation is based on propagating initial states which are sampled from the initial centroid distribution, on the classical potential surface. The second approximation is equivalent to a classical-like calculation of the reaction rate constant on the centroid potential, and has two distinct advantages: (1) it bypasses the problem of inefficient sampling which limits the applicability of the full CMD method at very low temperatures; (2) it has a well defined TST limit which is directly related to path-integral quantum transition state theory (PI-QTST). The approximations are tested on a model consisting of a symmetric double-well bilinearly coupled to a harmonic bath. Both approximations are quite successful in reproducing the results obtained via full CMD, and the second approximation is shown to provide a good estimate to the exact high-friction rate constants at very low temperatures.

Surface-based characteristic path generation

Abstract: This document discusses, among other things, systems and methods for efficiently using surface data to calculate a characteristic path of a virtual three-dimensional object. A surface mesh is constructed using segmented volumetric data representing the object. Geodesic distance from a reference point is calculated for each shape element in the surface mesh. The geodesic distance values are used to produce rings. Ring centroids are computed and connected to form the characteristic path, which is optionally pruned and smoothed.