A"STATISTICAL"MODEL""
OF"THE"MOTION"OF""
PASTELS"UNDER"VIBRATION"
1."Ini8al"problem:"monitoring"damage"induced"by"vibra8ons"
Leila&Sauvage
,
&
TU"DelJ"and"Rijksmuseum,"
l.sauvage@rijksmuseum.nl"
Arash&Sangari
,"
University"of"Wisconsin"Madison"
Dr.&William&Sethares,"
University"of"Wisconsin"
Madison
&
Dr.&Marcias&Mar8nez
,"
TU"DelJ"
Dr.&W.&(Bill)&Wei
,"
Rijksdienst"voor"het"Cultureel"
Erfgoed"
Acknowledgement"
We" would" like" to" thank" Robert" van" Langh," head" of" conserva8on," IdeleSe" van" Leeuwen," head" of" paper" conserva8on," Dionysia" Christoforou," paper" conservator," and" Mar8n"Juergens,"photo"conservator"at"the"Rijksmuseum."This" research"is"currently"funded"by"the"Migelien"Gerritzen"Fond." Unless"men8oned,"all"the"pictures"are"©Rijksmuseum" This"research"is"part"of"a"PhD"dedicated"to"the"predic8on"of"fa8gue"damage"for"18thYcentury"pastel"pain8ngs"subjected"to"vibra8on"loads"during"transport."It"is"the"result"of"a" collabora8on"between"the"Rijksmuseum,"the"University"of"WisconsinYMadison,"the"Rijksdienst"voor"het"Cultureel"Erfgoed"and"the"Technical"University"of"DelJ.""
Pastel"collec8on"in"museum"
Typical(cross, sec.on(of(a(pastel( pain.ng(Transport"
• Complex"and"random"vibra8ons" • Characteriza8on"of"the"loads"?"
J.E.Liotard"Y"Monsieur(Boère" 1746"Y"SKYAY232( Fixa.ve( Support( Medium( Common"fragility:" pastel"medium" poorly"aSached" to"the"support"Failure:"loss"of"medium"
• Need"for"qualita8ve"and"" quan8ta8ve"parameters"for"loss"at" interface"medium/support" x"transports" Two"objec8ves:" • Detec8on"of" changes" • Defini8on"of"a" Just"No8ceable" Difference"(JND)" level"3."Computerized"representa8on"of"a"pastel"par8cle"
2."Changes"due"to"par8cle"moves"
4."Sta8s8cal"analysis"of"the"experiment""
Conclusion"
Frame"0( Frame"1( Frame"2( Frame"3( Frame"4(
Difference"
image"(1Y0)( Difference"image"(2Y1)( Difference"image"(3Y2)( Difference"image"(4Y3)(
A"mockYup"of"pastel"on"paper"was" subjected" to" extreme" vibra8on" loads."Pictures"were"taken"before" (frame" 0)" and" during" fa8gue" tes8ng"(frames"1"to"4)."
""
AJer"image"registra8on"(using"the" SURF" algorithm)," difference" images" were" created" to" facilitate" the" visualisa8on" of" change" from" one"frame"to"another."" To"define"a"JND"level"or"failure"criterion,"percep8on"tests"using"real"mockYups"and" digitally"altered"pastels"will"be"performed"with"conservators."Damage"simula8on" requires"a"computerized"representa8on"of"a"physical"pastel"par8cle,"which"is"an" aggregate"of"pigment"and"filler"grains." "
The" approximate" extent" of" each" par8cle" is" defined" by" joining" together" nearby" pixels" (using" morphological" dila8on)," t r a n s f o r m i n g" t h e" p i x e l" differences" into" connected" areas."
MicroYpicture"of"J.E.Liotard–"Lady(
on(a(sofa(1756Y58"Y"SKYAY240"( Processed"image"showing"probable"digital"“par8cles”(
Using"the"experimentally"derived"sta8s8cs,"it"is"possible"to"recreate/simulate" analogous"par8cle"mo8on.""
• Combine"an"image"processing"technique"called"watershed(segmenta.on"with"
Computa8onal" analysis" offers" new" possibili8es" for" conservators" to" assess" changes" over"8me."In"this"specific"case,"the"design"of"a"sta8s8cal"model"brings"addi8onal"tools" to"understand"a"complex"phenomenon:"fa8gue"failure"of"pastels."The"detec8on"and" quan8fica8on" of" changes" occurring" during" transport" will" help" conservators" assess" damage."Such"sta8s8cal"studies"of"pastel"par8cles"and"the"simula8on"of"damage"to" pastel" pain8ngs" will" be" used" to" inform" the" design" of" perceptual" tests." These" will" provide" a" measure" of" the" cri8cal" amount" of" change" defined" by" conservators" as" a" damage" limit" to" avoid." More" experimental" data" is" needed" to" improve" and" validate" the" simula8ons" presented" here," but" the" preliminary" results" show" already" the" possibili8es"in"monitoring"changes"before"final"failure"is"reached." SEM"picture"of"a"pastel"sample( Binarized"version"of"the" pastel"par8cle."The"red" area"is"the"connected" area( 3"mm" 4"mm"
• Associate" similarly" sized" par8cles" that" are" close" in" the" before/aJer"maps."
• Features"to"look"for"include"count"(size"of"par8cle)"and" centroid"(loca8on)"
• Associate" each" segment" (i.e.," each" nonzero" region" in" the" difference" image)" to" nearest" segment" in" previous" 8me" point."
Tracking&par8cle&moves&
200 400 600 800 1000 0.001 0.002 0.003 0.004 0.005 0.006Distance" moved" follows" (more" or" less)"an"exponen8al"distribu8on."
Distance&moved&
Angle&moved&
-250 -200 -150 -100 -50 50 100 0.01 0.02 0.03 0.04 0.05 0.06• Angle" moved" is" more" or" less" two"bellYcurves"
This" shows" that" vibra8ons" were" done"in"+/Y"180"degrees" 0.2 0.4 0.6 0.8 1.0 0.5 1.0 1.5 2.0 2.5 0.2 0.4 0.6 0.8 1.0 2 4 6 8 0.2 0.4 0.6 0.8 1.0 2 4 6 8 • small"size"par8cles" • medium"size"par8cles" • large"size"par8cles" Rela8onship&between&par8cle&size&and& the&likelihood&of&moving& Percentage"of"moving"par8cles"(yYaxis)"vs"distance" moved"(xYaxis)( Percentage"of"moving"par8cles"(yYaxis)"vs"angle" moved"(xYaxis)( Percentage"of"small"par8cles"(yYaxis)"ploSed" against"a"probability"of"moving"(xYaxis)( Percentage"of"medium"par8cles"(yYaxis)"ploSed" against"a"probability"of"moving"(xYaxis)( Percentage"of"large"par8cles"(yYaxis)"ploSed" against"a"probability"of"moving"(xYaxis)(
Other&observa8ons&
Some8mes" the" par8cles" split" into" two" (or" more)" pieces."Small"par8cles"are"less"likely"to"split."
"If" a" par8cle" of" a" given" size" moved," what" is" the" chance"that"it"moves"again"in"the"next"period?"
5."Simula8on"of"par8cle"mo8on"
the" experimental" par8cle" informa8on" to" divide" a" pastel" into" probable" (digital)"“par8cles.”"
• Simula8ons"show"possible"
future" histories" of" the" object."
