Showing papers on "Centroid published in 1975"
TL;DR: In this article, the authors investigated the problem of translating, rotating, reflecting and scaling configurations to minimize the goodness-of-fit criterion, where Gi is the centroid of the points in p-dimensional space.
Abstract: SupposePi(i) (i = 1, 2, ...,m, j = 1, 2, ...,n) give the locations ofmn points inp-dimensional space. Collectively these may be regarded asm configurations, or scalings, each ofn points inp-dimensions. The problem is investigated of translating, rotating, reflecting and scaling them configurations to minimize the goodness-of-fit criterion Σi=1m Σi=1n Δ2(Pj(i)Gi), whereGi is the centroid of them pointsPi(i) (i = 1, 2, ...,m). The rotated positions of each configuration may be regarded as individual analyses with the centroid configuration representing a consensus, and this relationship with individual scaling analysis is discussed. A computational technique is given, the results of which can be summarized in analysis of variance form. The special casem = 2 corresponds to Classical Procrustes analysis but the choice of criterion that fits each configuration to the common centroid configuration avoids difficulties that arise when one set is fitted to the other, regarded as fixed.
2,852 citations
TL;DR: A comparison is presented of representing skeletal muscles as centroid lines and as straight lines in force analysis of musculoskeletal systems and results are discussed along with the underlying assumptions for the centroid comparison.
152 citations
TL;DR: The nodes in Tare are denoted by small letters (possibly with a subscript) such as u, ur, etc., the edgeq areDenoted by node pairs such as @,q)# an8 the distance (positive numbers) associated with the ‘edp !
52 citations
TL;DR: It is found that the centroid of a normally shaped intensity function of a time-space point process is conditionally normal given the observations, and the resulting filter is nonlinear, but closely related to the continuous-discrete Kalman-Bucy filter.
Abstract: In this correspondence, we examine the problem of estimating the centroid of a normally shaped intensity function of a time-space point process in terms of an observed realization of the point process. The centroid is assumed to move randomly as a projection of a Gauss-Markov process. We find that the centroid is conditionally normal given the observations. Dynamical equations are given for the conditional mean and covariance of the centroid. The resulting filter is nonlinear, but closely related to the continuous-discrete Kalman-Bucy filter. An application to optical position sensing is given.
34 citations
TL;DR: A computer program written in FORTRAN IV is presented which will create a population of desired size with marginally normal score vectors manifesting any desired centroid and covariance matrix.
Abstract: A computer program written in FORTRAN IV is presented which will create a population of desired size with marginally normal score vectors manifesting any desired centroid and covariance matrix. Uses and documentation are provided.
15 citations