Press "Enter" to skip to content

Using Math to Understand Art | Ingrid Daubechies | TEDxDuke


[Music]

[Applause]

this is the Ghent Altarpiece by Anthony

egg which is an incredibly impressive

picture it was incredibly influential

when it was first painted at the

beginning of the 15th century if you

ever get to againt

in Belgium you should go see it it’s a

politic and when you close it you see on

the middle on the right-hand side

this scene of the Annunciation we’re

behind the Virgin Mary there’s a book a

book that you see here while there’s not

a book there’s a painting of a book

we’re talking about an area of the

painting it’s about 3 inches high and

art historians were wondering whether

Van Eyck who is known to be a great

perfectionist had pushed his

perfectionism so far as to actually

really paint a text I mean a real text

rather than the little vertical and

horizontal marks that might give that

illusion we have the slightest okay so

if you show me a book like that in a

museum I can’t read it because these

medieval give a lettering the literary

format are very hard to read for a non

specialist but specialists couldn’t read

it on this painting either and that’s

because you see all these cracks the

calculator on this painting that’s over

600 years old makes it very hard to

distinguish where you have real letters

which are worn a bit and where the

cracks and so most art historians said

well it’s not a real text come on but I

one of the fields in which I work is

using building mathematical tools for

image analysis and so when I heard of

this I said well maybe we can try to

find algorithms that find these cracks

automatically and then once we’ve marked

them can in paint them and if I had

known how hard a task that was I might

have kept my math but

it turned out it was very challenging

and but we did solve it and became part

of a PhD thesis of a student in

electrical engineering in Brussels and

together with researchers at Kent

we published a paper in which the

solution was published and we went from

the crack Allu on on the right here to

the text on the on the left to the text

on the right and well when I first saw

the results I said well fat lot of good

that has done to us I mean I couldn’t I

couldn’t read anything but specialists

said oh my god look at this and they

could very clearly recognize 12 groups

of words which not only established

beyond a doubt that Vanek really had

painted the text but they found that in

fact they could identify what text it

was a page of a manuscript that had been

copied a few decades earlier in Rouge

and that was a text by Thomas Aquinas on

the Annunciation in an unseen painting

scene so they were absolutely delighted

and there was this was was this made a

very nice article in art history I

wanted to start my story today with that

to tell you that even prior to my main

topic today we had learned how to

recognize and find and in paint cracks

in paintings so my story is about an art

exhibit that is going on right now in

the North Carolina Museum of Art in

Raleigh if you haven’t seen it yet I

recommend it highly

it’s last day’s tomorrow so you don’t

have a lot of time so this was really

something in which we sailed uncharted

waters and let me show you how so it all

started because an altarpiece that dates

back to the 14th century from a small

Church in the maquis region in Italy had

been broken up at in the early 20th

century and sold to collectors three of

those panels are in the North Carolina

Museum of Art collection one is in

Portland three are

in the Metropolitan Museum of Art one is

in Chicago and the very last one well

the very last one is missing art

conservators after they realized and our

curators that these panels belong to the

same altarpiece have looked everywhere

but they haven’t found this panel

they had this dream of bringing all the

panels together here in North Carolina

the other museum said yes yes but you

won’t still have it complete and I

fortunately I happen to know a very

gifted artist but also an art

conservator and art reconstruction

expert shall of the Gospels who they

then commissioned to paint a

reconstruction of this missing painting

she does this mostly for museums for

educational purposes here’s an example

of something she made for a museum in

hotted um so it’s a little bit a portion

of a painting they have that she

reconstructed and for this educational

piece she stopped a quarter in short

with every layer of preparation and so

you see she’s already four months into

working on this panel before she even

starts painting all the different layers

of sizing of gesso and drawing and

gilding and so on so they commissioned a

panel for her for this missing painting

and what you could ask yourself how do I

do that on a painting I mean I don’t

have the panel how do i reconstruct well

the seven panels the seven small panels

that existed reconstructed the followed

episodes mark important episodes of the

life of John the Evangelist as it was

described literally in this medieval

Beth bestseller the golden legend in

which lives of saints are recounted and

we know it’s a best-seller because of

many medieval books we have only may be

part of a copy or something and this of

this we have hundreds so everybody

wanted one so they knew what scene had

to be depicted and then they made a

composition of a scene that borrowed

lots of stylistic elements of the other

panels so as not to invent something

that would not have been appropriate now

if they ever find the ninth panel

it’s not going to look identical to this

but it’s highly likely in this style and

then here you see the buildup of the

panel just like you saw the layers the

you see it being gilded and polished and

then paint is going to come in if my

clicker keeps working and the verdad

show on the faces the different paint

layers and as they get modeled more and

the final result is absolutely fantastic

and you can see that final new panel

with a documentary of how the panel was

made at a museum and you see differences

I mean on old panels where you have this

punch mark that have been knocked into

the gilding they have over all did the

six hundred years since the painting was

made being filled with death they’ve

gradually filled with dirt and they now

show like a dark relief but originally

unless polished on this polished gold

they gave you the reflection since when

and with the candles in the church they

would have given you a sparkling halo

around the head of the saint so you can

all see that on the new panel and so

people they’re the curators and

conservatives were so happy with this

whole experience and how I’d

occasionally it would be and there’s

this glorious new painting but then they

realized that they couldn’t put it next

to the other panels because everybody

would have eyes only for this new one

this new bright shiny one and it would

be the only one that was not authentic

so I then said well I always say that

math can help because what we could do

is we could study the panels and the old

panels and the new panels and we could

on the one hand find Correspondence of

color between the two different types of

panels and change color we could use

that to virtually age the new painting

and in fact when you go to do Z we see

this virtually aged one a printout of

that exposed neck to the other panels

but we could also if we learned all

about that we could rejuvenate the old

panels and that’s what we did

so the crackle ooh well you’ve seen we

can find calculate and we can paint it

in so we did that here you see how we do

indeed find all the red markings is the

automatically found cracks and we once

we did that we can in paint you see an

example here we did that very gradually

with an iterative algorithm that you see

here gradually progressing it was very

important to us to not produce just a

chromel I mean we wanted to use

scholarly grounded methods in order to

make this transition so we never took it

to places where you didn’t have evidence

for how it should have been and if we

didn’t do a perfect job well so be it I

mean but we didn’t we didn’t impose our

vision so here you have the background

of one of those paintings and then the

cracks removed then we could color remap

so here you have the eight authentic

panel the old family and the background

of the ninth new panel and because the

compositions were borrowed from each

other we knew exactly how the pigments

that were new now looked after all their

aging and we could use that in order to

color remapping for these paintings so

we here you see the color remapping for

the old fourteenth century painting on

the left and remapped two new colors on

the right here you see the next one the

new one on the right

coloring mapped to the old version on

the left and then of course to make a

virtual aged version we had to put in

cracks and then we had to add the gold

and that is now what is in in the museum

and I hope some of you get a chance to

see it tomorrow it’s not expensive by

uber to get an Oscar to to SEMA so it’s

absolutely gorgeous to see all those

paintings together you so this whole

effort of the rejuvenation and the aging

was done with the bus connections group

with Under

it’s here Duke and we had a ball and of

course we had a lot of help also from

Charlotte Augustus who gave us advice on

the colors but you see the

reconstruction of that ninth panel was

uncharted waters for the art

conservators and acuities they had never

done something like that and they really

enjoyed experience and then the whole

remapping and and crack removal and so

on was an exhilarating experience also

for us it was no longer a research

project because we had learned to do

that research earlier on the outer piece

of hint but it turned out they were

uncharted waters for the mathematicians

as well because we came up to a new

problem we got to work with platypus

platypus is a software package that we

put together and that saw it’s that’s

that that came that came to life because

of the GC panel because in preparing for

the work on the GC panel I asked to see

the x-rays and when they showed me the

x-rays here you see a detail and the

x-ray I said what’s this nonsense it

looks like it’s behind prison bars I

mean isn’t that annoying to you and the

conservator said no cone says yes it is

annoying and it’s the cradle to cradle

well cradling is something that you see

on many paintings on wood panel here you

see a detail of the other piece of Ghent

it’s also cradled and the cradling is a

hardwood structure of a lava structure

that’s attached to the back of these

panels he spends fortunately about an

inch thick and they would kind of work

and warp with temperature changes and

when collectors bought them from the

churches they preferred something that

was flattered they also in some cases

wanted to remove wood worm damage or

other damage but in many cases it was

just to flatten it and so they made them

much thinner and then gave them

structural in credit in integrity with

this cradle and so this cradle would be

attached to the

back of it with with big fixed numbers

and then sliding members the sliding

members slid probably in the first few

years and then after that the wood had

worked so much that it they were rock

fast but when you x-ray something like

that of course all you see is cradle I

mean and so all the subtle brushwork

that you use the x-rays for or the

subtle details of conservation are

swamped out by that big difference and

so when I heard about this I said well

maybe math can help so and but it was a

very challenging problem because not

only it wasn’t so hard to find the

location of those cradle members and the

first part of our algorithm does that

and it can be assisted if it’s a little

bit difficult by actually by the by the

art conservator but the more interesting

thing is that after you’ve removed that

wood structure you actually still have a

lot of wood grain from that cradle

sitting there as you can see here on the

right and they have been by then we have

become heroes for they are conservators

so they said but you could you could you

please take the wood grain away of the

cradle but we want to keep the wood

grain of the panel I said she really and

I said but maybe we can and it turned

out it was very challenging I mean so

here you have on the left a piece of

Aggie see and on the right the the we

have removed the intensity but the wood

grain is still there and on the Left

wood grain is gone so how did we do that

well we knew of course where the

different cradle members have been and

so we use machine learning techniques to

isolate first of all what wood grain was

and then to find where the different

wood grain what nature was of wood grain

while you only had panel of panel Plus

cradle and so on and then we could

remove it and that was a part of the the

graduate work of one of my graduate

students and we were very proud and so

it’s now used this is for a piece of an

egg here you see a piece of the paddle

in

we actually can compare with because

that was a case where they removed the

the the cradle structure by hand because

it was causing damage to the painting

and you can see that we are actually

much closer to the ground truth with

platypus the name of the software then

with what what what people could do

before so this was done with

collaboration of art conservators art

curators and students and postdocs and

Platypus has learned to leave its cradle

and if everything goes well with the

presentation then we now can see the

movie that is the rejuvenated panel of

the legacy so thank you very much [Applause]

Please follow and like us: