jan caha - visibility analysis on uncertain surfaces

Visibility Analysis on UncertainSurfaces

Jan Caha

InDOG Conference 2013

Department of GeoinformaticsPalacký University Olomouc

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

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

InDOG Conference 2013 - 15.10.2013 3/14

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

InDOG Conference 2013 - 15.10.2013 4/14

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

InDOG Conference 2013 - 15.10.2013 5/14

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

InDOG Conference 2013 - 15.10.2013 6/14

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

InDOG Conference 2013 - 15.10.2013 7/14

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

InDOG Conference 2013 - 15.10.2013 8/14

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

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

InDOG Conference 2013 - 15.10.2013 10/14

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

InDOG Conference 2013 - 15.10.2013 11/14

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

InDOG Conference 2013 - 15.10.2013 12/14

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

InDOG Conference 2013 - 15.10.2013 13/14

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