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.

Fitting Spheres to Range Data From 3-D Imaging Systems

Abstract: Two error functions used for nonlinear least squares (LS) fitting of spheres to range data from 3-D imaging systems are discussed: the orthogonal error function and the directional error function. Both functions allow unrestricted gradient-based minimization and were tested on more than 40 data sets collected under different experimental conditions (e.g., different sphere diameters, instruments, data density, and data noise). It was found that the orthogonal error function results in two local minima and that the outcome of the optimization depends on the choice of starting point. The centroid of the data points is commonly used as the starting point for the nonlinear LS solution, but the choice of starting point is sensitive to data segmentation and, for some sparse and noisy data sets, can lead to a spurious minimum that does not correspond to the center of a real sphere. The directional error function has only one minimum; therefore, it is not sensitive to the starting point and is more suitable for applications that require fully automated sphere fitting.

A geometric interpretation of weighted normal vectors and its improvements

Abstract: The weighted normal vector method was applied to estimate the curvatures on a surface in the 1990s. However, this estimation method still causes serious problems, such as when two adjacent triangles are of coplanarity. In this paper, our main goals are to provide a geometric interpretation of weighted normal vectors and then give an improvement to handle this problem. In 2004, we pointed out that the normal vector estimation with area weights cannot distinguish the difference between contributions when two different triangles have the same area. To deal with this drawback, we presented the centroid weight to improve the estimation of normal vectors. Here, we give a particular interpretation of centroid weight and extend this idea to introduce a new weight, the gravitational weight.

Automatic Placement to Improve Capacitance Matching Using a Generalized Common-Centroid Layout and Spatial Correlation Optimization

Abstract: In analog designs, the most widely adopted layout practice to improve matching is the symmetrical common-centroid placement. However, this arrangement cannot be obtained in general. In this paper, it is shown that there are asymmetrical placements with a common centroid which are also immune to process gradients and suitable for designs where a symmetrical layout is not possible. In addition, this paper proposes an automated method, based on a standard simulated annealing framework, to arrange fully-integrated capacitors in a layout to improve their matching.

Moment inequalities for equilibrium measures in the plane

Abstract: The equilibrium measure of a compact plane set gives the steady state distribution of charges on the conductor. We show that certain moments of this equilibrium measure, when taken about the electrostatic centroid and depending only on the real coordinate, are extremal for an interval centered at the origin. This has consequences for means of zeros of polynomials, and for means of critical points of Green’s functions. We also study moments depending on the distance from the centroid, such as the electrostatic moment of inertia.

Method and apparatus for encoding a contour of an object expressed in a video signal

Abstract: A method encodes a contour image of an object expressed in a video signal. First, a centroid for the contour of the object is detected by averaging pixel positions on the contour. A set of primary vertices on the contour are determined based on the centroid. Subsequently, a set of secondary vertices on the contour are determined based on the set of primary vertices. The set of primary vertices, the set of secondary vertices and the centroid are encoded to provide a digitally coded contour signal.