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# Jan Caha - Visibility Analysis on Uncertain Surfaces

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### Jan Caha - Visibility Analysis on Uncertain Surfaces

1. 1. Visibility Analysis on Uncertain Surfaces Jan Caha InDOG Conference 2013 Department of Geoinformatics Palacký University Olomouc
2. 2. 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
3. 3. Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions Introduction ∙ visibility analysis sometimes also referred as viewshed operation ∙ application in landscape planning, acheology, location of transmitters and receivers, various ecological applications and obviously determinations of ideal locations for viewing towers and hiking trails ∙ uncertainty of the surface is very important because the calculation of visibility is extremely sensitive to any changes of surface InDOG Conference 2013 - 15.10.2013 3/14
4. 4. 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 the uncertainty is caused by lack of knowledge ∙ fuzzy surfaces provide better framework for assessing impact of uncertainty on visibility InDOG Conference 2013 - 15.10.2013 4/14
5. 5. 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 was performed by Peter Fisher ∙ several aspects that determine the process and may vary between implementations: approximation of source and target point and process of inferring elevations from the grid ∙ the most important part of the algorithm is determination of so 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 InDOG Conference 2013 - 15.10.2013 5/14
6. 6. Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions Visibility calculation - Calculation of 𝛼i 1 ∆h αi 0 V Pi ∆d InDOG Conference 2013 - 15.10.2013 6/14
7. 7. Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions Visibility calculation Δh Δd ∙ point Pm on LoS is visible if 𝛼i < 𝛼m for all m < i, otherwise the point Pm is invisible from the viewpoint V ∙ 𝛼i = arctan InDOG Conference 2013 - 15.10.2013 7/14
8. 8. Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions Visibility calculation - LoS 1 0 0 1 2 InDOG Conference 2013 - 15.10.2013 3 4 5 6 7 8 9 10 8/14
9. 9. 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 is not represented by exact number z but by fuzzy number z ˜ ∙ contains uncertainty of the input data and in some cases of uncertainty that arise from the process of interpolation of the dataset ∙ allows creation of derived characteristics such are slope, aspect, profile curvatures and visibility with uncertainty of the surface propagated to it ∙ requires use of fuzzy arithmetic and possibility theory InDOG Conference 2013 - 15.10.2013 9/14
10. 10. 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, Δd remains crisp number 1 ∆hmin αmin ∆hmax αmax 0 V Pi ∆d InDOG Conference 2013 - 15.10.2013 10/14
11. 11. 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 be done in the framework of possibility theory ∙ possibility and necessity of exceedance are used to determine possible 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 InDOG Conference 2013 - 15.10.2013 11/14
12. 12. Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions Visibility on fuzzy surfaces 3 necessary visibility line 2 C E B A 1 possible visibility line D 0 0 1 2 3 4 5 Comparison of possible and necessary visibility of points C, D, E from viewpoint A with respect to the point B InDOG Conference 2013 - 15.10.2013 12/14
13. 13. 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 for fuzzy 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 LoS and also on presentation of case studies InDOG Conference 2013 - 15.10.2013 13/14
14. 14. Department of Geoinformatics, Palacký University Olomouc, geoinformatics.upol.cz Introduction Visibility calculation Fuzzy surfaces Possibilistic visibility Conclusions Thank you for your attention. InDOG Conference 2013 - 15.10.2013 14/14