Mathematical model and implementation of rational processing

Mora, Higinio; Mora-Pascual, Jerónimo; García‐Chamizo, Juan Manuel; Pont, María Teresa Signes

doi:10.1016/j.cam.2016.05.001

Cited by 7 publications

(2 citation statements)

References 34 publications

(30 reference statements)

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“…Since a comparison operation has similar cost than a subtraction, the whole computational cost is 2n-1 subtractions. Please, note that the absolute values calculation for real numbers implies no computation cost where real numbers are represented with sign-bit [ 40 , 41 ].…”

Section: Distance Operator Methodsmentioning

confidence: 99%

Computational Analysis of Distance Operators for the Iterative Closest Point Algorithm

Mora¹,

Mora-Pascual²,

García-García³

et al. 2016

PLoS ONE

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The Iterative Closest Point (ICP) algorithm is currently one of the most popular methods for rigid registration so that it has become the standard in the Robotics and Computer Vision communities. Many applications take advantage of it to align 2D/3D surfaces due to its popularity and simplicity. Nevertheless, some of its phases present a high computational cost thus rendering impossible some of its applications. In this work, it is proposed an efficient approach for the matching phase of the Iterative Closest Point algorithm. This stage is the main bottleneck of that method so that any efficiency improvement has a great positive impact on the performance of the algorithm. The proposal consists in using low computational cost point-to-point distance metrics instead of classic Euclidean one. The candidates analysed are the Chebyshev and Manhattan distance metrics due to their simpler formulation. The experiments carried out have validated the performance, robustness and quality of the proposal. Different experimental cases and configurations have been set up including a heterogeneous set of 3D figures, several scenarios with partial data and random noise. The results prove that an average speed up of 14% can be obtained while preserving the convergence properties of the algorithm and the quality of the final results.

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Section: Distance Operator Methodsmentioning

confidence: 99%

Computational Analysis of Distance Operators for the Iterative Closest Point Algorithm

Mora¹,

Mora-Pascual²,

García-García³

et al. 2016

PLoS ONE

Self Cite

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“…Bertrand Russell explained "it must have required many ages to discover that a brace of pheasants and a couple of days were both instances of the number two". However, when humans managed to abstract the concepts of number and the different number systems, two different mathematical systems were developed (Mora, Mora-Pascual, García-Chamizo, & Signes-Pont 2017;Nagar, 2018).…”

mentioning

confidence: 99%

Use and Abuse of Calculators: Implications for Mathematics Education

Sánchez

Cáceres

2018

Acta Sci.

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Fostering mathematical understanding and sense for numbers is an objective for current mathematics education. This paper presents a historical vision of the use of numbers and of calculation processes and reflects about the current need of electronic calculators. The coexistence of two different mathematical systems, one based on the Greek axiomatic mathematics and another, the floating point system, used in electronic calculators, can lead to some confusions that which affects the teaching of mathematics, especially in the numerical sense development. The paper also presents common mistakes caused by the missing verification of the results from calculations or lack of awareness about the limitations of calculators. Finally, the implications those elements have on the mathematical education are presented together with some conclusions.

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