Light, Matter, and Geometry The Cornerstones of Appearance Modelling

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Light, Matter, and Geometry
The Cornerstones of Appearance Modelling
Frisvad, Jeppe Revall
Publication date:
2008
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Frisvad, J. R. (2008). Light, Matter, and Geometry: The Cornerstones of Appearance Modelling. DTU Compute
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Light, Matter, and Geometry
The Cornerstones of Appearance Modelling
Jeppe Eliot Revall Frisvad
Kongens Lyngby 2008
IMM-PHD-2008-188
Technical University of Denmark
Informatics and Mathematical Modelling
Building 321, DK-2800 Kongens Lyngby, Denmark
Phone [phone], Fax [phone]
[email protected]
www.imm.dtu.dk
IMM-PHD: ISSN 0909-3192
Abstract
This thesis is about physically-based modelling of the appearance of materials.
Whenamaterialisgraphicallyrendered,itsappearanceiscomputedbyconsid-
ering the interaction of light and matter at a macroscopic level. In particular,
theshapeandthemacroscopicopticalpropertiesofthematerialdeterminehow
itwillinteractwithincidentillumination. Inthisthesisthemacroscopicoptical
properties are connected to the microscopic physical theories of light and mat-
ter. This enables prediction of the macroscopic optical properties of materials,
and, consequently, also prediction of appearance based on the contents and the
physical conditions of the materials.
Physically-based appearance models have many potential input and output pa-
rameters. There are many choices that must be made: How many material
components to include in the model, how many physical conditions to take into
account,whethertheshapeofthematerialshouldbecoupledtotheappearance
model or not, etc. A generalised concept of shape and geometry is presented to
provide a framework for handling these many degrees of freedom. Constraints
betweeninputandoutputparametersaremodelledasmultidimensionalshapes.
Thisgivestheopportunitytousetheappearancemodelsnotonlyforprediction,
but also for analysis of the contents and the physical conditions of a material
given information about its macroscopic optical properties. Since it is possible
to measure these properties using camera technology, the presented framework
enables analysis of material contents and conditions using camera technology.
Three detailed appearance models are presented as to exemplify the applica-
bility of the theory: (1) A model which finds the appearance of water given
temperature, salinity, and mineral and algal contents of the water; (2) a model
which finds the appearance of ice given temperature, salinity, density, and min-
eral and algal contents of the ice; and (3) a model which finds the appearance
of milk given fat and protein contents of the milk.
ii
Resum´e
Denneafhandlingomhandlerfysiskbaseretmodelleringafmaterialersudseende.
N˚aretmaterialebliverfremstilletgrafisk,beregnesdetsudseendevedatoverveje
vekselvirkningen mellem lys og substans p˚a et makroskopisk niveau. Mere
præcist bestemmer materialets form og dets makroskopiske optiske egenskaber,
hvordan det vil vekselvirke med indfaldende belysning. I denne afhandling kop-
les de makroskopiske optiske egenskaber til de mikroskopiske fysiske teorier for
lys og substans. Dette muliggører forudsigelse af materialers makroskopiske
optiske egenskaber, og derfor ogs˚a forudsigelse af deres udseende v.h.a. materi-
alernes indhold og deres fysiske tilstande.
Fysisk baserede modeller for udseende har mange potentielle input og output
parametre. Derermangevalg,somm˚agøres: Hvormangematerialekomponen-
ter der skal inkluderes i modellen, hvor mange fysiske tilstande der skal tages
højde for, om materialets form skal koples til modellen for udseendet eller ej,
o.s.v. Etgenereliseretkonceptm.h.t.formoggeometripræsenteresforatgiveet
system til behandling af disse mange frihedsgrader. Bindinger mellem et mate-
rialesinputogoutputparametremodelleressomenmultidimensionelform. Det
givermulighedforatbrugemodellerforudseendeikkekuntilforudsigelse,men
ogs˚a til analyse af et materiales indhold og dets fysiske tilstande givet informa-
tion om dets makroskopiske optiske egenskaber. Da det er muligt at m˚ale disse
egenskaber ved brug af kamerateknologi, muliggører det præsenterede system
ogs˚a analyse af materialeindhold og tilstande ved brug af kamerateknologi.
Der præsenteres tre detaljerede modeller for udseende for at give eksempler p˚a
teoriens anvendelsesmuligheder: (1) En model til at finde vands udseende givet
vandets temperatur, dets saltindhold og dets indhold af mineraler og alger; (2)
enmodeltilatfindeis’udseendegivetisenstemperatur,saltindhold,massefylde
ogdensindholdafmineralerogalger;og(3)enmodeltilatfindemælksudseende
givet mælkens protein- og fedtindhold.
iv
Preface
Study without thinking, and you are blind; think without studying, and you are
in danger.
Confusius (552 B.C. – 479 B.C.), from the Analects (2:16)
This thesis was written out of curiosity and fascination with nature. It was
prepared at the department of Informatics and Mathematical Modelling of the
Technical University of Denmark in partial fulfillment of the requirements for
acquiring the Ph.D. degree in mathematical modelling.
The subject of the thesis is appearance modelling which is a subject within the
branchofcomputergraphicsknownasrealisticimagesynthesis. Thestudentof
realisticimagesynthesisisprivilegedinbeingallowedtoinvestigatethereasons
forallvisualaspectsofnature. Indeedallvisualaspectsareinteresting,andthe
main objective is to capture their appearance correctly. It seems that this ob-
jective is most sensibly attained by physical models. However, the gap between
thephysicist’sunderstandingofnatureatthemicroscopiclevelofquantumpar-
ticles and the modelling of appearance is wide. It is the aim of this thesis to
buildabridgeoverthegap,orperhapsjusttolaythefoundationforthebridge.
This is done in three parts: One part concerning light, one concerning matter,
and one concerning geometry. A part on each of the three cornerstones of ap-
pearance modelling. Finally, there is a fourth part in which appearance models
are developed based on the theory provided in the first three parts.
Itisunusualforathesistospreadoversuchalargevarietyoftheoriesasyouwill
find in this one. The usual approach would be to focus as narrowly as possible
on the perfection of a single technique. The reason for the unusual approach
is the gap and the missing bridge. If there had been a book closing the gap,
or providing the bridge, this thesis would have been entirely different. As it is,
vi
there is no such book. So instead of building a house with no foundation, this
thesis became an attempt on laying the foundation itself.
Ingraphicswewouldliketobeabletomodeltheappearanceofasmanydifferent
materials as possible. Therefore the theory has been kept as general and as
flexible as possible throughout the thesis. It is in the effort to do so that the
main contributions of the thesis appear. This makes it difficult to split the
thesis in a part on background theory and a part on contributions. Instead, the
introduction contains a relatively detailed overview of the thesis in which the
contributions are pointed out.
Thereaderisassumedtohavesomegraduate-levelmathematicalunderstanding
and some general knowledge about graphics, in particular ray tracing.
The project was advised by Associate Professor Niels Jørgen Christensen and
Professor Peter Falster who are both with the department of Informatics and
Mathematical Modelling of the Technical University of Denmark. The project
has been funded by a Ph.D. scholarship from the Technical University of Den-
mark. Part of the work presented in this thesis has been published, or is to
appear. Details on these publications are provided in the Acknowledgements.
Thehumanmindisafantasticimageprocessor. Whenweobservenature,weare
able to draw conclusions based on subtle details. Especially if we know what
to look for. Mathematical models which describe the appearance of nature
have the ability to teach us what to look for. They can tell us the visual
consequenceofchangingthecontentsofamaterial,orchangingthetemperature,
or changing other properties. In this way, appearance models make observation
of nature more instructive, but also more spectacular. Let us build the bridge
and construct more models.
Lundtofte, November 2007
Jeppe Revall Frisvad
Acknowledgements
FirstandforemostthankstoMonicaforherloveandsupport,andforhercoping
withmyabsenceatmanylonglatehours. Alsotomyparents,SvenandFelicia,
for their everlasting support, and for teaching me to choose my education out
of interest.
To my brother Rasmus, thanks for our shared effort in learning about graphics
during our Master’s studies, and to him, and to Ulrik Lund Olsen, thanks for
many good suggestions as to improvements of this thesis.
Thanks to my Ph.D. advisers Niels Jørgen Christensen and Peter Falster for
their help in getting a Ph.D. scholarship for me, for their unfailing support
throughout my studies, and for their mild guidance such that I was always able
to pursue my own ideas.
A special thanks to Andreas Bærentzen for his open door policy, and for our
numerous discussions on many aspects of the work presented in this thesis (I
hope that I did not take too much of your time).
Iwouldliketothanktheadvisersofmyexternalstays. HenrikWannJensenfor
suggesting that we write a SIGGRAPH paper based on my work, and for the
great help and hospitality given to me by him and his family during my stay in
San Diego in January 2007. Geoff Wyvill for sharing his profound knowledge
about noise and geometry, and for welcoming my three months visit at the
University of Otago, New Zealand, in 2006.
Thanks also to Gert L. Møller for taking an interest in my work, and for co-
authoring some of the first papers published during this project.
Other people who have had a positive influence on my work, and who I would