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: It is shown that for two arbitrary trapezoidal fuzzy numbers if the Distance between centroid points and also the distance between left spreads and right spreads go to zero, then two given fuzzy numbers are equal.
Abstract: We propose a new distance measure for the space of all trapezoidal fuzzy numbers using centroid point and left/right spread of trapezoidal fuzzy numbers. Moreover, the metric properties of suggested distance measure are investigated. Indeed, we show that for two arbitrary trapezoidal fuzzy numbers if the distance between centroid points and also the distance between left spreads and right spreads go to zero, then two given fuzzy numbers are equal. Consequently, we complete discussion about the relation between fuzzy number and its centroid which is the firstly discussed by Hadi-Vencheh and Allame (2010). To the best of our knowledge, this is first time in the literature that such metric is applied by centroid point.
16 citations
Patent•
25 Oct 1972
TL;DR: In this paper, the centroid of an area was determined by scanning the area with a television scanner in a rectangular scan, summating voltages derived from the scan and utilizing said voltages to derive the co-ordinates of the Centroid.
Abstract: Apparatus for determining the centroid of an area by scanning the area with a television scanner in a rectangular scan, summating voltages derived from the scan and utilizing said voltages to derive the co-ordinates of the centroid The invention also extends to apparatus for determining the position and orientation of an object utilizing said centroid determining apparatus and performing a rectangular scan and a spiral scan of the object
16 citations
Proceedings Article•
01 Jan 2009TL;DR: A new approach called rolling penetrate descriptor for shape description that combines the advantage of the contour-based and the region-based methods, and provides an unified scheme to handle various shapes is proposed.
Abstract: This paper proposes a new approach called rolling penetrate descriptor for shape description. It combines the advantage of the contour-based and the region-based methods, and provides an unified scheme to handle various shapes. The main process of the proposed method is to use a set of scanning lines that rotate around the shape centroid to collect information. During the rotating process, three feature functions are computed to reveal the inner structures of the candidate shape. The proposed method is very flexible and can be adapted for certain applications, while the scanning process serves as a framework. The rolling penetrate descriptor method is tested on several data sets with variations including common geometrical transform, noise, distortion and occlusion. Experimental results demonstrate that the proposed approach has strong capability in handling a variety of shapes.
16 citations
01 Apr 2007
TL;DR: Formulas for computing the cardinality, fuzziness, variance and skewness of an IT2 FS are derived and these new formulas have closed-form expressions, so they can be computed very fast.
Abstract: Centroid, cardinality, fuzziness, variance and skewness are all important concepts for an interval type-2 fuzzy set (IT2 FS) because they are all measures of uncertainty, i.e. each of them is an interval, and the length of the interval is an indicator of the uncertainty. The centroid of an IT2 FS has been defined by Karnik and Mendel. In this paper, the other four concepts are defined. All definitions use the Mendel-John representation theorem for IT2 FSs. Formulas for computing the cardinality, fuzziness, variance and skewness of an IT2 FS are derived. Unlike the formulas for the centroid of an IT2 FS, which must be computed by iterative Karnik-Mendel algorithms, these new formulas have closed-form expressions, so they can be computed very fast. These definitions are useful not only for measuring the uncertainties of an IT2 FS, but also in measuring the similarity between two IT2 FSs
16 citations
TL;DR: This article presents a regression-based algorithm for the protection of transmission line with means clustering and weighted weighted nearest neighbor and the robustness of the algorithm for different fault parameters such as fault impedance and fault location is validated.
Abstract: This article presents a $k$ -means clustering and weighted $k$ -nearest neighbor ( $k$ -NN) regression-based algorithm for the protection of transmission line. Three-phase current signals of both the terminals are synchronized and sampled with a sampling frequency of 3.84 kHz. Cumulative differential sum (CDS) is computed by subtracting the samples of current cycle from the previous cycle at both the terminals of transmission line. $k$ -means clustering is applied on CDS to compute two centroids using moving window of width, equal to one cycle. Difference between the absolute values of centroids is computed at both the terminals and represented by the centroid difference (CD). The CD of both the terminals is added to compute the fault index. The computed fault index is used to detect and classify the types of faults. The location of the fault is estimated by the weighted $k$ -NN regression method. Various case studies are performed to validate the robustness of the algorithm for different fault parameters such as fault impedance and fault location. The effect of noise is also considered to check the accuracy of the proposed algorithm in the noisy environment.
16 citations