!""#$%&'()*%+$),' -.,")/)0%1/$2+' - - PowerPoint PPT Presentation

▶
0 1 2 34 5 6 1 7 8 9 0
SMART_READER_LITE
LIVE PREVIEW

!""#$%&'()*%+$),' -.,")/)0%1/$2+' - - PowerPoint PPT Presentation

Sep 29, 2022 171 likes •429 views

!""#$%&'()*%+$),' -.,")/)0%1/$2+' 34'5,6,$1%'7$&&%,'8)/9.:';/%%+' ' !"#$%&'()'#)*+,-)./0. ) Erik Sudderth Brown University Work by J. Kivinen, E. Sudderth, & M. Jordan ICCV 2007: Learning Multiscale

slide-1
SLIDE 1

!""#$%&'()*%+$),'

  • .,")/)0%1/$2+'

34'5,6,$1%'7$&&%,'8)/9.:';/%%+' '

!"#$%&'()'#)*+,-)./0.) Erik Sudderth

Brown University

Work by J. Kivinen, E. Sudderth, & M. Jordan ICCV 2007: Learning Multiscale Representations of Natural Scenes using Dirichlet Processes ICIP 2007: Image Denoising with Nonparametric Hidden Markov Trees

slide-2
SLIDE 2
  • .$+%'<%0.:)#'

=%>#?//$,@' 5,")$,A,@'B'<%+1./)A.,'

C.DE#%:%#'50)@%'!,)#*+$+'

What are the statistical properties of natural images?

slide-3
SLIDE 3

F.)+1' G"%,'F.?,1/*' H1/%%1'

  • )1?/)#'H2%,%'F)1%@./$I)A.,'

J./%+1' ;)##'(?$#&$,@'

How do semantic labels affect these properties?

slide-4
SLIDE 4

K):%#%1'=%2.0".+$A.,+ '

  • ! Bandpass decomposition
  • f images into multiple

scales & orientations

  • ! Multiscale dependencies

captured via latent quadtree structure

slide-5
SLIDE 5

K):%#%1+L'8)/@$,)#'H1)A+A2+ '

Wavelet Coefficient Log Probability Smooth Surfaces Occlusion Boundaries & Texture

slide-6
SLIDE 6

M)?++$),'8$N1?/%'8.&%#+ '

Gaussian Scale Mixture (GSM)

Wainwright & Simoncelli, 2000 Wavelet Coefficient Log Probability Wavelet Coefficient Log Probability

Binary Gaussian Mixture

Computational advantages!

slide-7
SLIDE 7

K):%#%1+L'O.$,1'H1)A+A2+ '

Pairwise Joint Histograms:

Orientation Scale Vertical Horizontal

Pairwise Conditional Histograms:

Orientation Scale Vertical Horizontal

Large magnitude wavelet coefficients!

  • ! Persist across multiple scales
  • ! Cluster at adjacent spatial locations
slide-8
SLIDE 8

!"#"$%!&$'()'** !"#$$#%&*'+,#-(#.'$! /(00$.*$'('!*+-*'12!"$-* #!!(3.4$." %)$!*+!,*5#,$1$"* '+$6'($." !"#"$*'*(&$#-%&* 0(!"-(728+.!

9! :+$6'($."!*4#-3(.#11;*0(!"-(72"$0*#!*4(<"2-$!*+=*"5+*>#2!!(#.!* 9! ?#-@+,*0$&$.0$.'($!*7$"5$$.*/(00$.*!"#"$!*'#&"2-$*&$-!(!"$.'$* +=*(4#3$*'+."+2-!*#'-+!!*1+'#8+.!*#.0*!'#1$!* 9! A#'/*+-($."#8+.*(!*4+0$1$0*(.0$&$.0$."1;*

($,)/*'7$&&%,'8)/9.:';/%%+'

.*%/$!012%3(401516(*(&#/40178891

slide-9
SLIDE 9

P)#$&)A.,'L'50)@%'=%,.$+$,@'

G/$@$,)#1 F.//?"1%&'>*'!&&$A:%' 'KQ$1%'M)?++$),'-.$+%'' RSH-<''T'U34VW'&(X1

slide-10
SLIDE 10

=%,.$+$,@'D$1Q'($,)/*'78;+'

  • .$+*'5,"?1''

=%,.$+%&'RY8')#@./$1Q0X' 9! B!*"5+*!"#"$!*&$-*!'#1$*!26'($."C**D+5*4#.;*(!*$.+23/C1 9! E/+210*!"#"$!*7$*!/#-$0*"/$*!#4$*5#;*=+-*#11*(4#3$!F* +-*=+-*#11*5#,$1$"*0$'+4&+!(8+.!C*

slide-11
SLIDE 11

7$%/)/2Q$2)#'=$/$2Q#%1'S/.2%++'7$&&%,'8)/9.:';/%%+'

(.0$<$!*#&:&#'!*!$"* +=*/(00$.*!"#"$! +7!$-,$0*+!;'%**+=** 5#,$1$"*'+$6'($."! (.).("$*!$"*+=*!"#"$** '*(&$#-%&*0(!"-(728+.! !"#"$%!&$'()'*!"#$$#%&*'+,#-(#.'$!

slide-12
SLIDE 12

:/(10*!"#"$* <=!>1!'?1(@?1ABBCD1

KQ*'')'7$%/)/2Q$2)#'=S'Z'

=*(&$#-%&1,#$'*#)/-%&$1 E+!*(F!1$'('!1G*!H/!&;#!$1 >1+7#1*'1#!!$!* E+ 1 1 1

9! D($-#-'/('#1*GH*&-(+-*#11+5!*2!*"+*1$#-.*#*&+"$.8#11;*(.).("$*!$"*+=* (II!(*(&;!1I(J!*&$*=-+4*.#"2-#1*(4#3$!1 9! D($-#-'/('#1*'+2&1(.3*$.!2-$!F*5("/*/(3/*&-+7#7(1(";F*"/#"*#* '+44+.*!$"*+=*;>#@,*!"#"$!*#-$*-$#'/#71$*=-+4*$#'/*I(*!&'**

KI(*$#'L151+(*#()#@#'L1%G1 '*(&$#-%&1,#$'*#)/-%&$1

slide-13
SLIDE 13

=%,.$+$,@L'5,"?1 '

24.61 dB

slide-14
SLIDE 14

=%,.$+$,@L'($,)/*'78; '

Crouse, Nowak, & Baraniuk, 1998

29.35 dB

slide-15
SLIDE 15

=%,.$+$,@L'7=SE78; '

32.10 dB

slide-16
SLIDE 16

=%,.$+$,@L'C.2)#'MH8 '

Portilla et. al., 2003

31.84 dB

slide-17
SLIDE 17

I-#.!=$-*0$.+(!(.3** #&&-+#'/*-$2!$!*4218!'#1$* /(00$.*!"#"$*&#J$-.!*+=* '1$#.*(4#3$!*=+-*4#@(.3*

  • +72!"*&-$0('8+.!*

A4&(-('#1*K#;$!(#.* #&&-+#'/*$!84#"$!* 4+0$1*&#-#4$"$-!*=-+4* "/$*.+(!;*(4#3$*

Y+A0)A,@'F#%),'50)@%+'

slide-18
SLIDE 18

=%,.$+$,@'Y$,+1%$,'

2%#$L1 7B?MB1,601B?BNO1 PQRSPT=1 <=*(&$G!*D1 AM?9B1,601B?MMC1 6UKSVKT1 AM?W91,601B?MCO1 6TWQ1 AM?C81,601B?MN81 X*#F#&(@1 PQRSPT=11 <Y"I?16(L!$D1 AN?MC1,601B?NMC1

slide-19
SLIDE 19
  • )1?/)#'H2%,%'=%,.$+$,@'

2%#$L1 9?7C1,601B?BWW1 PQRSPT=1 <=*(&$G!*D1 AM?NB1,601B?O8C1 6UKSVKT1 AN?N81,601B?OAM1 6TWQ1 AN?OC1,601B?ON71 X*#F#&(@1 PQRSPT=11 <Y"I?16(L!$D1 AC?AC1,601B?N781

slide-20
SLIDE 20

F.)+1'

9!L(!2#11;**!;%F&#Z!*.#"2-#1*!'$.$*'#"$3+-($!* 9!M''2-#"$1;*4+0$1*"/$*!"#8!8'!*+=*&('/*(@1$;!&!1;('!F%*#!$*

G"%,'F.?,1/*' H1/%%1'

  • )1?/)#'H2%,%'F)1%@./$I)A.,'

V%(@$[*

J./%+1' ;)##'(?$#&$,@'

slide-21
SLIDE 21

7=SE78;'H2%,%'8.&%#'

9! D(00$.*!"#"$!*********3$.$-#"$*,$'"+-!*+=*'1$#.*5#,$1$"*'+$6'($."!********** #"*4218&1$*+-($."#8+.!F*+-*0$.!$*4218!'#1$*EBNI*0$!'-(&"+-!*

slide-22
SLIDE 22

[':%/+?+'>)+%#$,%'7=SE(GJ'

O+.&#-#4$"-('*K#;$!(#.*$<"$.!(+.*+=*PGM*!'$.$*4+0$1!*QN$(%N$(*R*H$-+.#F*STTUV* 5/('/*(3.+-$*!&#8#1*1+'#8+.!*+=*1+'#11;*$<"-#'"$0*(4#3$*=$#"2-$!*

PQRSPT=1 PQRS6X\1

slide-23
SLIDE 23
  • ?0>%/'.\'H1)1%+'
slide-24
SLIDE 24

5,"?1'50)@%' 7=S'7$&&%,' 8)/9.:';/%%' 7=S'()@'.\'J%)1?/%+'

H)0"#%+'@$:%,'8!S'+1)1%+'

slide-25
SLIDE 25

F)1%@./$I$,@'-)1?/)#'H2%,%+'

"#11*72(10(.3* !"-$$"* +&$.*'+2."-;* 4+2."#(.* (.!(0$*'(";* /(3/5#;* =+-$!"* '+#!"* "#11*72(10(.3* !"-$$"* +&$.*'+2."-;* 4+2."#(.* (.!(0$*'(";* /(3/5#;* =+-$!"* '+#!"* "#11*72(10(.3* !"-$$"* +&$.*'+2."-;* 4+2."#(.* (.!(0$*'(";* /(3/5#;* =+-$!"* '+#!"* "#11*72(10(.3* !"-$$"* +&$.*'+2."-;* 4+2."#(.* (.!(0$*'(";* /(3/5#;* =+-$!"* '+#!"*

PQRS6X\1]ON?W1^_1 PQRSPT=1]9B?O1^_1 PQRS6X\1]9A?C1^_1 PQRSPT=1]9M?N1^_1

`(+!@!'1<$GIOD1 Ka\=1