The Best Least-Squares Line Fit

Alciatore, David G.; Miranda, Rick

doi:10.1016/b978-0-12-543457-7.50022-x

Cited by 9 publications

(14 citation statements)

References 4 publications

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“…In image processing, signal processing, digital imaging and computer graphics specialized algorithms should be used in the E 2 case. Such a solution for the E 2 case was published in [3] which is based on a line representation in the polar coordinates. Some specialized algorithms for a circle, resp.…”

Section: Total Least Square Error Approximationmentioning

confidence: 99%

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

Smolik

Skala

Majdisova

2019

Lecture Notes in Electrical Engineering

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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. Usually the standard least square error approximation method is used due to its simplicity, but it is not an optimal solution, as it does not optimize the orthogonal distances, but only the vertical distances. There are many problems for which the LSE is not convenient and the TLSE is to be used. 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 E 2 .

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Section: Total Least Square Error Approximationmentioning

confidence: 99%

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

Smolik

Skala

Majdisova

2019

Lecture Notes in Electrical Engineering

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“…The LSE methods are sensitive to a rotation as they measure vertical distances. Rotational and translation invariance are fundamental requirements especially in geometrically oriented applications [8], [9].…”

Section: International Journal Of Applied Physics and Mathematicsmentioning

confidence: 99%

“…2, is to be used [6], [7] which is computationally more expensive. A simple close solution in E 2 is based on a solution of quadratic equation [8]- [10].…”

Section: Introductionmentioning

confidence: 99%

High Dimensional and Large Span Data Least Square Error: Numerical Stability and Conditionality

Skala¹

2017

IJAPM

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Abstract:The Least Square Error (LSE) is widely used method in many engineering and computational problems solution. The LSE method is simple from the "formulation" point of view, offers a simple solution. However, it might lead to wrong or incorrect conclusions, especially if high dimensional or large span data are to be processed or if some variables have significantly smaller influence than the other does, e.g. inconvenient selection of measuring units. In this paper, we analyze influence of row and column "normalization" inspired by the Gershgorin's theorem. The approach has been experimentally verified on a LSE application for high dimensional and large span data. The proposed approach was tested also on Hilbert's matrix inversion for conditional number change analysis.

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“…These lines are computed, with the Total Least Square (TLS, [58]) method, as the lines best fitting the contour points between the four corners they traverse.…”

Section: The Structure Of Musamentioning

confidence: 99%

MusA: Using Indoor Positioning and Navigation to Enhance Cultural Experiences in a Museum

Rubino

Xhembulla

Martina

et al. 2013

Sensors

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Abstract:In recent years there has been a growing interest in the use of multimedia mobile guides in museum environments. Mobile devices have the capabilities to detect the user context and to provide pieces of information suitable to help visitors discover and follow the logical and emotional connections that develop during the visit. In this scenario, location based services (LBS) currently represent an asset, and the choice of the technology to determine users' position, combined with the definition of methods that can effectively convey information, become key issues in the design process. In this work, we present Museum Assistant (MusA), a general framework for the development of multimedia interactive guides for mobile devices. Its main feature is a vision-based indoor positioning system that allows the provision of several LBS, from way-finding to the contextualized communication of cultural contents, aimed at providing a meaningful exploration of exhibits according to visitors' personal interest and curiosity. Starting from the thorough description of the system architecture, the article presents the implementation of two mobile guides, developed to respectively address adults and children, and discusses the evaluation of the user experience and the visitors' appreciation of these applications.

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The Best Least-Squares Line Fit

Cited by 9 publications

References 4 publications

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

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

High Dimensional and Large Span Data Least Square Error: Numerical Stability and Conditionality

MusA: Using Indoor Positioning and Navigation to Enhance Cultural Experiences in a Museum

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