jan caha - visibility analysis on uncertain surfaces
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Visibility Analysis on UncertainSurfaces
Jan Caha
InDOG Conference 2013
Department of GeoinformaticsPalacký University Olomouc
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Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz
Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions
Table of Contents
1 Introduction
2 Visibility calculation
3 Fuzzy surfaces
4 Possibilistic visibility
5 Conclusions
InDOG Conference 2013 - 15.10.2013 2/14
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Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz
Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions
Introduction
∙ visibility analysis sometimes also referred as viewshedoperation
∙ application in landscape planning, acheology, location oftransmitters and receivers, various ecological applications andobviously determinations of ideal locations for viewing towersand hiking trails
∙ uncertainty of the surface is very important because thecalculation of visibility is extremely sensitive to any changesof surface
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Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz
Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions
Surfaces with uncertainty
∙ surfaces always contain some amount of uncertainty∙ uncertainty can have various sources∙ usually modelled by statistics and consequences on visibility
are estimated by employing Monte Carlo method∙ such model captures only relatively specific type of
uncertainty, and is not well suited for situations where theuncertainty is caused by lack of knowledge
∙ fuzzy surfaces provide better framework for assessing impactof uncertainty on visibility
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Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz
Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions
Visibility calculation
∙ most of the research on visibility calculation in GIS wasperformed by Peter Fisher
∙ several aspects that determine the process and may varybetween implementations: approximation of source andtarget point and process of inferring elevations from thegrid
∙ the most important part of the algorithm is determination ofso called Line of Sight (LoS)
∙ the line is formed by points Pi = {1, 2, . . . , n}∙ each point Pi has and elevation e and distance d from the
viewpoint V∙ the important is an angle 𝛼i , by their comparison visible
points can be identified
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Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz
Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions
Visibility calculation - Calculation of 𝛼i
V Pi
0
1
∆d
∆hαi
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Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz
Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions
Visibility calculation
∙ 𝛼i = arctan ΔhΔd
∙ point Pm on LoS is visible if 𝛼i < 𝛼m for all m < i , otherwisethe point Pm is invisible from the viewpoint V
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Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz
Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions
Visibility calculation - LoS
0 1 2 3 4 5 6 7 8 9 100
1
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Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz
Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions
Fuzzy surfaces
∙ fuzzy surface is surface in which value at the position x , y isnot represented by exact number z but by fuzzy number z̃
∙ contains uncertainty of the input data and in some cases ofuncertainty that arise from the process of interpolation ofthe dataset
∙ allows creation of derived characteristics such are slope,aspect, profile curvatures and visibility with uncertainty ofthe surface propagated to it
∙ requires use of fuzzy arithmetic and possibility theory
InDOG Conference 2013 - 15.10.2013 9/14
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Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz
Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions
Visibility on fuzzy surfaces
∙ the ΔH will not be a crisp number but a fuzzy number, Δdremains crisp number
∆d
∆hmin ∆hmaxαmin
αmax
V Pi
0
1
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Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz
Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions
Visibility on fuzzy surfaces
∙ comparison of fuzzy 𝛼i to determine visibility needs to bedone in the framework of possibility theory
∙ possibility and necessity of exceedance are used to determinepossible and necessary visible parts of the LoS
∙ there are several possible outcomes:∙ Πi = 𝒩i = 0 → invisible∙ Πi = 𝒩i = 1 → visible∙ Πi > 0 and 𝒩i = 0 → possibly visible but not necessary∙ Πi = 1 and 𝒩i > 0 → possibly and necessary visible but not
absolutely sure
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Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz
Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions
Visibility on fuzzy surfaces
0 1 2 3 4 50
1
2
3
A B
C
D
E
necessary visibility line
possible visibility line
Comparison of possible and necessary visibility of points C, D, E from viewpoint Awith respect to the point B
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Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz
Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions
Conclusions
∙ concept is extension of the classic viewshed operation forfuzzy surfaces
∙ Monte Carlo is not necessary correct solution∙ proposed way to handle vagueness and lack of knowledge
about the surface∙ obtaining two values - possibility and necessity of visibility
instead of just probability of visibility offers more information∙ future work should focus on comparison of visibility calculated
using proposed approach and classic statistic methods on LoSand also on presentation of case studies
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Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz
Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions
Thank you for your attention.
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