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Total Least Square Error Computation in E2: A New Simple, Fast and Robust Algorithm

Published: 28 June 2016 Publication History

Abstract

Many problems, not only in signal processing, image processing, digital imaging, computer vision and visualization, lead to the Least Square Error (LSE) problem or Total (Orthogonal) Least Square Error (TLSE) problem computation. Mostly the LSE is used due to its simplicity for problems leading to f(x, y) = h, resp. f(x, y, z) = h, i.e. to dependences expressible as an explicit function computing "vertical" distances. There are many problems for which the LSE is not convenient and the TSLE is to be used. Those problems usually lead to F(x) = 0, i.e. to dependences expressible as an implicit function computing "orthogonal" distances. Unfortunately, the TLSE is computationally much more expensive.
This paper presents a new, simple, robust and fast algorithm for the total least square error computation in E2.

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  • (2019)A New Simple, Fast and Robust Total Least Square Error Computation in E2: Experimental ComparisonAETA 2018 - Recent Advances in Electrical Engineering and Related Sciences: Theory and Application10.1007/978-3-030-14907-9_32(325-334)Online publication date: 13-Apr-2019
  • (2017)High Dimensional and Large Span Data Least Square Error: Numerical Stability and ConditionalityInternational Journal of Applied Physics and Mathematics10.17706/ijapm.2017.7.3.148-1567:3(148-156)Online publication date: 2017
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cover image ACM Other conferences
CGI '16: Proceedings of the 33rd Computer Graphics International
June 2016
130 pages
ISBN:9781450341233
DOI:10.1145/2949035
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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  • FORTH: Foundation for Research and Technology - Hellas

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 June 2016

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Author Tags

  1. Total least square error
  2. computer vision
  3. digital imaging
  4. image processing
  5. visualization

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  • Short-paper
  • Research
  • Refereed limited

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CGI '16
CGI '16: Computer Graphics International
June 28 - July 1, 2016
Heraklion, Greece

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Overall Acceptance Rate 35 of 159 submissions, 22%

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Cited By

View all
  • (2021) Cooling-Aware Optimization of Edge Server Configuration and Edge Computation Offloading for Wirelessly Powered Devices IEEE Transactions on Vehicular Technology10.1109/TVT.2021.307605770:5(5043-5056)Online publication date: May-2021
  • (2019)A New Simple, Fast and Robust Total Least Square Error Computation in E2: Experimental ComparisonAETA 2018 - Recent Advances in Electrical Engineering and Related Sciences: Theory and Application10.1007/978-3-030-14907-9_32(325-334)Online publication date: 13-Apr-2019
  • (2017)High Dimensional and Large Span Data Least Square Error: Numerical Stability and ConditionalityInternational Journal of Applied Physics and Mathematics10.17706/ijapm.2017.7.3.148-1567:3(148-156)Online publication date: 2017
  • (2017)Adaptive compression of animated meshes by exploiting orthogonal iterationsThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-017-1395-433:6-8(811-821)Online publication date: 1-Jun-2017

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