Calculating ellipse overlap areas

Hughes, Gary B.; Chraibi, Mohcine

doi:10.1007/s00791-013-0214-3

Cited by 45 publications

(21 citation statements)

References 15 publications

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“…We make use of a method developed by Hughes & Chraibi (2012). Its output are the number of intersection points and the intersection area of a considered pair of ellipses.…”

Section: Association Between Gaussian Clumpsmentioning

confidence: 99%

Spatially associated clump populations in Rosette from CO and dust maps

Veltchev

Ossenkopf-Okada

Stanchev

et al. 2017

Monthly Notices of the Royal Astronomical Society

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Spatial association of clumps from different tracers turns out to be a valuable tool to determine the physical properties of molecular clouds. It provides a reliable estimate for the X-factors, serves to trace the density of clumps seen in column densities only and allows to measure the velocity dispersion of clumps identified in dust emission. We study the spatial association between clump populations, extracted by use of the Gaussclumps technique from 12 CO (1 − 0), 13 CO (1 − 0) line maps and Herschel dust-emission maps of the star-forming region Rosette, and analyse their physical properties. All CO clumps that overlap with another CO or dust counterpart are found to be gravitationally bound and located in the massive star-forming filaments of the molecular cloud. They obey a single mass-size relation M cl ∝ R γ cl with γ ≃ 3 (implying constant mean density) and display virtually no velocity-size relation. We interpret their population as low-density structures formed through compression by converging flows and still not evolved under the influence of self-gravity. The high-mass parts of their clump mass functions are fitted by a power law dN cl /d log M cl ∝ M Γ cl and display a nearly Salpeter slope Γ ∼ −1.3. On the other hand, clumps extracted from the dust-emission map exhibit a shallower mass-size relation with γ = 2.5 and mass functions with very steep slopes Γ ∼ −2.3 even if associated with CO clumps. They trace density peaks of the associated CO clumps at scales of a few tenths of pc where no single density scaling law should be expected.

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“…We make use of a method developed by Hughes & Chraibi (2012). Its output are the number of intersection points and the intersection area of a considered pair of ellipses.…”

Section: Association Between Gaussian Clumpsmentioning

confidence: 99%

Spatially associated clump populations in Rosette from CO and dust maps

Veltchev

Ossenkopf-Okada

Stanchev

et al. 2017

Monthly Notices of the Royal Astronomical Society

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“…In order to evaluate the results of our constrained ellipse fitting approach compared to existing methods, we determine an accuracy measure which is based on the joint (overlap) area of the original underlying ellipse and the fitted ellipse [14]. The accuracy measure m depicts the similarity of the fitted ellipse with the original ellipse from a practical point of view.…”

Section: Resultsmentioning

confidence: 99%

Constrained Ellipse Fitting with Center on a Line

2015

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Fitting an ellipse to given data points is a common optimization task in computer vision problems. However, the possibility of incorporating the prior constraint "the ellipse's center is located on a given line" into the optimization algorithm has not been examined so far. This problem arises, for example, by fitting an ellipse to data points representing the path of the image positions of an adhesion inside a rotating vessel whose position of the rotational axis in the image is known. Our new method makes use of a constrained algebraic cost function with the incorporated "ellipse center on given line"-prior condition in a global convergent onedimensional optimization approach. Further advantages of the algorithm are computational efficiency and numerical stability.

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“…Similarly, polynomial root solving is required for calculating the shortest distance between circles in R 3 or the overlap area of ellipses in R 2 , [19]. It is a well investigated problem, whose solution is crucial to many robotic applications from proximity queries, to imaging [20], and path planning [19].…”

Section: Roots Of Polynomialsmentioning

confidence: 99%

Efficient Proximity Queries for Continuum Robots on Parallel Computing Hardware

Leibrandt

Yang

2017

IEEE Robot. Autom. Lett.

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Abstract-Surgical manipulators are increasingly capable of approaching deep seated pathologies through convoluted pathways due to advances in the field of continuum robotics. This class of robots can be, in most cases, accurately modelled as a chain of cylindrical shapes. In order to safely and seamlessly telemanipulate these robots, which have complex non-intuitive kinematics, haptic guidance schemes have been developed that rely on accurate proximity queries (PQ) to calculate the distance between the continuum robot and the anatomy. This paper introduces an approach to accurately model continuum robots using cylindrical shaped segments with spherical or flat caps and then efficiently calculate the shortest distance to a triangle mesh. Implementations of efficient, analytical narrow phase PQ calculations for simple and complex geometrical primitives suitable for parallel computing hardware are presented together with experimental validation which show improved performance suitable for real-time robotic applications. An in silico experiment comparing various root-finding algorithms, which are commonly used in PQ calculation or other optimization tasks are compared to assess their suitability when executed on different hardware. The implications of these experimental results are discussed, in particular with regards to the selection of a suitable proximity query algorithm depending on the available parallel computing hardware. Finally, an outlook of future improvements for dense dynamic anatomies is presented.

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Calculating ellipse overlap areas

Cited by 45 publications

References 15 publications

Spatially associated clump populations in Rosette from CO and dust maps

Spatially associated clump populations in Rosette from CO and dust maps

Constrained Ellipse Fitting with Center on a Line

Efficient Proximity Queries for Continuum Robots on Parallel Computing Hardware

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