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.

Median-Based Classifiers for High-Dimensional Data

Abstract: Conventional distance-based classifiers use standard Euclidean distance, and so can suffer from excessive volatility if vector components have heavy-tailed distributions. This difficulty can be alleviated by replacing the L2 distance by its L1 counterpart. For example, the L1 version of the popular centroid classifier would allocate a new data value to the population to whose centroid it was closest in L1 terms. However, this approach can lead to inconsistency, because the centroid is defined using L2, rather than L1 distance. In particular, by mixing L1 and L2 approaches, we produce a classifier that can seriously misidentify data in cases where the means and medians of marginal distributions take different values. These difficulties motivate replacing centroids by medians. However, in the very-high-dimensional settings commonly encountered today, this can be problematic if we attempt to work with a conventional spatial median. Therefore, we suggest using componentwise medians to construct a robust class...

PolyDepth: Real-time Penetration Depth Computation using Iterative Contact-Space Projection

Abstract: We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find an initial collision-free configuration using several methods such as centroid difference, maximally clear configuration, motion coherence, random configuration, and sampling-based search. We project this configuration on to a local contact space using a variant of continuous collision detection algorithm and construct a linear convex cone around the projected configuration. We then formulate a new projection of the in-collision configuration onto the convex cone as a Linear Complementarity Problem (LCP), which we solve using a type of Gauss-Seidel iterative algorithm. We repeat this procedure until a locally optimal PD is obtained. Our algorithm can process complicated models consisting of tens of thousands triangles at interactive rates.

Estimator for the random error in subpixel target location and its use in the bundle adjustment

Abstract: A CCD camera and frame store provide image data that are affected by a number of imperfect processes. However, most of these can be quantified or estimated. For instance, the quantization process of allocating integer values from 0 to 255 for the intensity level of each pixel has well-known statistical properties. This paper discusses how these can lead to an estimate of the precision of location of target image centroids. Two centroid algorithms are analyzed. The theory is tested against experimental and simulated data.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Performance Analysis And Size Optimization Of Focal Planes For Point-Source Tracking Algorithm Applications

Abstract: A number of applications require the precise tracking or position estimation of an object unresolved in the system optics. This paper evaluates several one-dimensional interpolation algorithms (odd N-point centroids, N = 3, 5, 7, 9, and three-point and five-point quadratic curve fits) designed to make these estimates to subpixel accuracy. Analytic, Monte Carlo, and experimental results are presented. The tracking sensor examined was a scanning linear array of infrared detectors assumed to be background-limited. The detector size and physical spacing were varied parametrically, with realistic fabrication constraints, to determine the relative performance and to obtain the optimum configuration. The optics blur spot was assumed Gaussian. The sources of error considered to affect the algorithm performance were the systematic algorithm bias, the random noise, and the postcalibration residual detector responsivity nonuniformities. Track accuracy improves with signal-to-noise ratio (SNR), until limited by algorithm inaccuracies or focal-plane nonuniformity. Among the algorithms tested, the three-point centroid performs best, provided that systematic algorithm bias is corrected. An experimental infrared tracking focal plane, used in a tracker simulation, closely confirmed the analysis. With the three-point algorithms, an experimental accuracy to smaller than 1/100 a detector (<1/250 a blur spot) was obtained at high signal-to-noise ratios.