The quickhull algorithm for convex hulls

Barber, C. Bradford; Dobkin, David P.; Huhdanpaa, Hannu

doi:10.1145/235815.235821

Cited by 4,429 publications

(2,761 citation statements)

References 30 publications

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“…It is a set of lines connecting each point to its natural neighbors. It is based on the convex hull algorithm in (Barber et al, 1996). From this triangulation, an enclosing triangle is obtained for each point in the uniform grid.…”

Section: Methodsmentioning

confidence: 99%

A comparative study on interpolation methods for controlled cardiac CT

Bharkhada

Zeng

et al. 2007

Int J Imaging Syst Tech

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Bai et al. recently proposed to acquire random fanbeam/cone-beam projections with a linear/planar detector from a circular scanning locus for controlled cardiac computed tomography (CT). After specifying a uniform acquisition geometry required by FBP (filtration-backprojection), we rebin the random fan-beam/cone-beam data via nearest-neighbor, quadrilateral and triangle-based linear interpolation methods. The fan-beam and parallel-beam FBP algorithms are employed for rebinned fan-beam projections. The FDK (Feldkamp-Davis-Kress) and t-FDK (tent-FDK) methods are employed for rebinned cone-beam data. Also, nonuniform weighting fanbeam/FDK methods are used to reconstruct without rebinning. As a benchmark, the images are reconstructed using uniform weighting fan-beam/FDK method from data collected at the specified uniform grid. To evaluate the different methods, effects of increasing the number of projections and adding Poisson noise are studied. The root mean square error (RMSE) is used to quantify the image quality by numerical tests with the cardiac phantom. Our results show that it is helpful to perform data interpolation for improvements of the image quality in controlled cardiac CT from random projections. Our simulations indicate that triangular interpolation gives the most satisfactory result for improved image quality whereas quadrilateral interpolation gives the best noise performance.

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Section: Methodsmentioning

confidence: 99%

A comparative study on interpolation methods for controlled cardiac CT

Bharkhada

Zeng

et al. 2007

Int J Imaging Syst Tech

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“…Each possible set of distributions defines a family of iso-performance lines, and for a given family, the optimal methods are those that lie on the "most-northwest" isoperformance line. Thus, a classifier is optimal for some conditions if and only if it lies on the northwest boundary (i.e., above the line y = x) of the convex hull (Barber, Dobkin, & Huhdanpaa, 1996) of the set of points in ROC space. 2 We discuss this in detail in Section 3.…”

Section: The Roc Convex Hull Methodsmentioning

confidence: 99%

“…3 2. Find the convex hull of the set of points representing the predictive behavior of all classifiers of interest, for example by using the QuickHull algorithm (Barber et al, 1996). 3.…”

Section: Given: E: List Of Tuples I P Wherementioning

confidence: 99%

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2001

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Abstract. In real-world environments it usually is difficult to specify target operating conditions precisely, for example, target misclassification costs. This uncertainty makes building robust classification systems problematic. We show that it is possible to build a hybrid classifier that will perform at least as well as the best available classifier for any target conditions. In some cases, the performance of the hybrid actually can surpass that of the best known classifier. This robust performance extends across a wide variety of comparison frameworks, including the optimization of metrics such as accuracy, expected cost, lift, precision, recall, and workforce utilization. The hybrid also is efficient to build, to store, and to update. The hybrid is based on a method for the comparison of classifier performance that is robust to imprecise class distributions and misclassification costs. The ROC convex hull (ROCCH) method combines techniques from ROC analysis, decision analysis and computational geometry, and adapts them to the particulars of analyzing learned classifiers. The method is efficient and incremental, minimizes the management of classifier performance data, and allows for clear visual comparisons and sensitivity analyses. Finally, we point to empirical evidence that a robust hybrid classifier indeed is needed for many real-world problems.

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“…To solve Eq. (3) the "PETSc" suite (Balay et al (2011(Balay et al ( , 2010(Balay et al ( , 1997) with an LU decomposition is used, the convex hull is calculated using "qhull" (Barber et al (1996)), and the cell cycle model is provided by "Chaste" (Mirams et al (2013); Pitt-Francis et al (2009)). …”

Section: Initial Conditions and Implementationmentioning

confidence: 99%