Efficient and reliable methods for rounded-interval arithmetic

Abrams, Stephen L.; Cho, Wonjoon; Hu, Chun-Yi; Maekawa, Takashi; Patrikalakis, Nicholas M.; Sherbrooke, Evan C.; Ye, Xiuzi

doi:10.1016/s0010-4485(97)00086-9

Cited by 31 publications

(18 citation statements)

References 9 publications

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“…In this scenario, the algorithm that does not take into account the discreteness of the system often fails with severe consequences. In this section, interval arithmetics (Abrams et al, 1998;Tsuzuki and Shimada, 2003) are explained briefly. Firstly, an interval of real numbers if defined by…”

Section: Interval Arithmeticsmentioning

confidence: 99%

Lung Movement Determination in Temporal Sequences of MR Images Using Hough Transform and Interval Arithmetics

Tavares¹

2009

IFAC Proceedings Volumes

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Since the lung is an organ whose real movement has never been seen, as it is totally dependent on the rib cage and collapses without them, the objective of the present work is to develop a method to study its movement. The visualization of the lung in motion is an actual topic of research in medicine. Computerized Tomography (CT) can obtain spatiotemporal images of the heart by synchronizing with electrocardiographic waves. The field of view (FOV) of the heart is small when compared to the lung's FOV. The lung's movement is not periodic and it is susceptible to variations in the degree of respiration. Compared to CT, Magnetic Resonance (MR) imaging involves longer acquisition times and it is preferable because they do not involve radiation. The breathing is associated to a standard respiratory function, and through 2D image processing, edge detection, Hough transform and interval arithmetics, respiratory functions are obtained and, consequently, the position of the points in time are estimated. A standard respiratory function must be provided as input to the modified Hough transform. The Hough transform uses a discrete quantization space, implemented as an accumulator matrix. An improved Hough transform is proposed by using interval arithmetics in the accumulation phase of the algorithm. The discreteness of the quantization space is considered in the algorithm, and its consequences are minimized. This work showed more consistent results when compared to previous approaches.

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Section: Interval Arithmeticsmentioning

confidence: 99%

Lung Movement Determination in Temporal Sequences of MR Images Using Hough Transform and Interval Arithmetics

Tavares¹

2009

IFAC Proceedings Volumes

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“…Intervals inherently represent uncertainties and errors in technical constructions, measuring, computations, and ranges of fluctuation and variation. In engineering fields, interval analysis has been applied in computer graphics [27,28,29], robust geometry construction and evaluation [30,31,32,33], set-based modeling [34], imprecise structural analysis [35], design optimization [36], finite-element formulation and analysis [37,38], soft constraint solving [39,40], and worst-case tolerance analysis and synthesis [41,42].…”

Section: 3mentioning

confidence: 99%

Semantic Tolerance Modeling With Generalized Intervals

Wang

2008

Journal of Mechanical Design

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“…In engineering fields, methods of interval analysis have been used in computer graphics [41,42,43,44,45], robust geometry construction and evaluation [46,47,48,49,50,51], set-based modeling [52], imprecise structural analysis [53], design optimization [54], finite-element formulation and analysis [55,56,57], soft constraint solving [58,59], and worst-case tolerance analysis and synthesis [60].…”

Section: Interval Analysismentioning

confidence: 99%

Semantic Tolerance Modeling

Wang

2006

Volume 1: 32nd Design Automation Conference, Parts a and B

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A significant amount of research efforts has been given to explore the mathematical basis for 3D dimensional and geometric tolerance representation, analysis, and synthesis. However, engineering semantics is not maintained in these mathematic models. It is hard to interpret calculated numerical results in a meaningful way. In this paper, a new semantic tolerance modeling scheme based on modal interval is introduced to improve interpretability of tolerance modeling. With logical quantifiers, semantic relations between tolerance specifications and implications of tolerance stacking are embedded in the mathematic model. The model captures the semantics of physical property difference between rigid and flexible materials as well as tolerancing intents such as sequence of specification, measurement, and assembly. Compared to traditional methods, the semantic tolerancing allows us to estimate true variation ranges such that feasible and complete solutions can be obtained.

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Efficient and reliable methods for rounded-interval arithmetic

Cited by 31 publications

References 9 publications

Lung Movement Determination in Temporal Sequences of MR Images Using Hough Transform and Interval Arithmetics

Lung Movement Determination in Temporal Sequences of MR Images Using Hough Transform and Interval Arithmetics

Semantic Tolerance Modeling With Generalized Intervals

Semantic Tolerance Modeling

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