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Multiresolution Histograms and their Use for Texture Classification. Stathis Hadjidemetriou, Michael Grossberg and Shree Nayar CAVE Lab, Columbia University Partially funded by NSF ITR Award, DARPA/ONR MURI. Q: Is there a fast feature which captures spatial information?. Same Histogram.

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Multiresolution histograms and their use for texture classification

Multiresolution Histograms and their Use for Texture Classification

Stathis Hadjidemetriou, Michael Grossberg and Shree Nayar

CAVE Lab, Columbia University

Partially funded by NSF ITR Award, DARPA/ONR MURI


Fast and simple feature

Q: Is there a fast feature which captures spatial information?

Same Histogram

A: Consider multiple resolutions.

Fast and Simple Feature


Histograms of filtered images
Histograms of Filtered Images information?

Histograms

Histograms

Bin Count

Bin Count

Graylevel

Graylevel

Bin Count

Bin Count

Resolution

s

Graylevel

Graylevel

Bin Count

Bin Count

Graylevel

Graylevel

Bin Count

Bin Count

Graylevel

Graylevel


Analysis of multiresolution histograms

Shape and Texture information?

Properties

Shape and Texture

Images

Multiresolution

Histograms

Difference

Histograms

Analysis of Multiresolution Histograms

Bin Count

Graylevel

?

Bin Count Change

Bin Count

Graylevel

Graylevel

Bin Count

Bin Count Change

Graylevel

Graylevel


Tools for analysizing the histogram
Tools for Analysizing the Histogram information?

  • Shanon Entropy

  • Change in Shanon Entropy: Fisher Information

  • Generalization:

    • Tsallis Entropy/Generalized Fisher Information

Multiresolution Histogram

Resolution

Bin

Filter Dependent Constant


Relating histogram change to image
Relating Histogram Change to Image information?

  • Fisher Information:

    • Measure of image sharpness[Stam, 59, Plastino et al, 97]:

Image Gradient

Image Domain

Image

Edge filter never computed: Implicit


Analysis of multiresolution histograms1

Shape and Texture information?

Images

Shape and Texture

Properties

Multiresolution

Histograms

Fisher

Information

Difference

Histograms

Analysis of Multiresolution Histograms

Bin Count

Graylevel

  • Shape Elongation

  • Shape Boundary

  • Texel Repetition

  • Texel Placement

Bin Count Change

Bin Count

Graylevel

Fisher Information

Graylevel

Resolution s

Bin Count

Bin Count Change

Graylevel

Graylevel


Shape elongation and fisher information
Shape Elongation and Fisher Information information?

  • Gaussian:

  • Pyramid:

St. dev. along axes:

sx, sy.

Sides of base:

rx, ry.

Elongation:

Elongation:

6

5

(analytically)

4

J

3

2

1

2

3

4

5

r


Shape boundary and fisher information

h information?=0.56 h=1.00 h=1.48 h=2.00 h=6.67

(numerically)

Complex boundary

Shape Boundary and Fisher Information

Superquadrics:

6

5

J

4

3

2

0

2

4

6

h


Texel repetition and fisher information
Texel Repetition and Fisher Information information?

Tileing

8

6

4

J

2

0

1

2

3

4

5

6

Tileing p

x 103

8

6

4

J

2

0

1

2

3

4

5

6

Tileing p

(analytically).


Texel placement and fisher information

Randomness information?

(numerically)

Texel Placement and Fisher Information

Stand. dev. of perturbation

x 103

6.6

6.4

6.2

J

6

5.8

0

5

10

15

20

St. Dev (% of Texel Width)

2.9

2.8

2.7

J

2.6

2.5

0

5

10

15

20

Average of 20 trials

St. Dev (% of Texel Width)


Matching algorithm
Matching Algorithm information?

Multiresolution histogram with

Burt-Adelson Pyramid

Cumulative histograms

Compute Feature

Difference histograms between

consecutive resolutions

Concatenate to form feature vector

L1 norm


Histograms bin width
Histograms Bin Width information?

  • Histogram bin width:

  • Subsampling factor in pyramid:


Parameters of multiresolution histogram
Parameters of Multiresolution Histogram information?

  • Histogram smoothing to avoid aliasing:

    • Database images

    • Test images

  • Histogram normalization

    • Image size

    • Histogram size


Databases for matching
Databases for Matching information?

  • Database of Brodatz textures[Brodatz, 66]:

    • 91 images; 7 images

    • Histogram equalized

  • Database of CUReT textures[Dana et al, 99]:

    • 8,046 images; 61 materials

    • Histogram equalized


Database of brodatz textures
Database of Brodatz Textures information?

Samples of equalized images:


Match results for brodatz textures
Match Results for Brodatz Textures information?

Match under Gaussian noise of st.dev. 15 graylevels


Class matching sensitivity brodatz textures

Number of information?

bins

256

128

62

32

16

8

Class Matching Sensitivity: Brodatz Textures

100

80

60

Class matched

40

20

0

0

10

20

30

40

50

60

St dev. of noise sn


Class matching sensitivity brodatz textures1
Class Matching Sensitivity: Brodatz Textures information?

100

95

90

85

80

75

70

65

60

0

10

20

30

40

50

60

St dev. of noise sn

256 Constant

256, Higher Subsampling= 22/3

256, Lower Subsampling = 21/2

smoothing & adaptive bin size


Database of curet textures
Database of Curet Textures information?

Samples of equalized images:


Match results for curet textures
Match Results for Curet Textures information?

Match under Gaussian noise of st.dev. 15 graylevels.


Class matching sensitivity curet textures
Class Matching Sensitivity: CUReT Textures information?

100

90

80

Class matched

70

60

50

0

10

20

30

40

50

St dev. of noise sn

256 Constant

256, Higher Subsampling= 22/3

256, Lower Subsampling = 21/2

Difference norm & Smoothing

  • Match 100 randomly selected images per noise level


Comparison with low level features
Comparison with Low-level Features information?

  • Fourier power spectrum annuli

  • Gabor features

  • Daubechies wavelet features

  • Auto-cooccurrence matrix

  • Markov random field parameters


Comparison with low level features1
Comparison with Low-Level Features information?

  • Fourier power spectrum annuli:

h

z

r1

r2

  • Gabor features

  • Auto-cooccurrence matrix


Comparison with low level features2
Comparison with Low-Level Features information?

  • Wavelet coefficient energies:

Wavelet packets decomposition

Wavelets decomposition

  • Markov random field parameters


Comparison of computation costs
Comparison of Computation Costs information?

decreasing cost

n- number of pixels

l- window width

l- resolution levels



Matching comparison of features brodatz
Matching Comparison of Features: Brodatz information?

  • Brodatz textures database:

100

80

Multiresolution Diff. Histograms

Fourier Power Spectrum

Gabor Features

Wavelet Packets

Cooccurence Matrix

Markov Random Fields

60

Class matched

40

20

0

0

10

20

30

40

50

60

St dev. of noise sn


Matching comparison of features curet
Matching Comparison of Features: CUReT information?

  • Curet textures database:

100

80

Multiresolution Diff. Histograms

Fourier Power Spectrum

Gabor Features

Wavelet Packets

Cooccurence Matrix

Markov Random Fields

60

Class matched

40

r1

20

0

0

10

20

30

40

50

St dev. of noise sn

  • Match 100 randomly selected images per noise level