Image Segmentation by Clustering Methods: Cluster Validity

1
Image Segmentation by Clustering MethodsCluster
Validity
Student Sean Hsien Supervisor Dr. Sid Ray
2
Overview

• Aims of the project
• Conventional cluster evaluation
• Turi and Rays modified criterion
• MML and its application in image clustering
• 2 new evaluation criteria
• Test images used
• Data acquisition and results
• Conclusion
• Future work

3
Aims

• To test the suitability of Turi and Rays
  modified criterion on greyscale images
• Test effectiveness of MML for cluster evaluation
  in image clustering
• To compare different methodologies and find a
  general and effective way of cluster evaluation

4
Conventional cluster evaluation

• Many conventional methods measure cluster
  compactness and separability intra/inter
  cluster distances

Inter
Intra
5
Turi and Rays Modified Criterion

• Based on the basic validity criterion of
  intra/inter ratio
• Modifies the basic criterion with a penalty
  function to penalize low numbers of clusters

6
Modified Criterion Formula
7
Minimum Message Length

• Principle of Occams Razor dont make things
  unnecessarily complex
• 2-part message length to balance goodness-of-fit
  and model complexity

8
Application of MML in Image Clustering

• Used Segment Map and Complementary Image to apply
  MML for cluster evaluation
• MsgLen(Segment Map) ? MsgLen(Model)
• MsgLen(Complementary Image) ? MsgLen(DataModel)

9
Segmented (3 clusters)
Original
ComplementaryImage
10
Compression and MML

• Compression with order 1 Hidden Markov Model was
  used increase information content, spatial
  information
• Higher order could not be used large alphabet
  size of images (256 for greyscale images)

11
2 New Evaluation Criteria

• Based on the basic criterion
• Desirable to have a penalty function that adapts
  to the structure of data
• Use entropy to indicate cluster tendency

where H is the entropy of the input image
12
2 New Evaluation Criteria

• Based on the Liu and Yangs criterion
• Their criterion over emphasized goodness-of-fit

2
13
Test Images Used

• No standard cluster evaluation criteria,
  therefore
• Use visual assessment of natural image clustering
• Generate synthetic images (with/out noise) for
  qualitative analysis

14
Synthetic Images

• Generated noiseless synthetic images with 2, 3,
  5, 8, and 15 segments (equally spaced in the
  range 20 235)
• Synthetic images with Gaussian noise generated
  using pgmgauss and noiseless synthetic images as
  input
• Used standard deviation of 2

15
Synthetic Images
16
Natural Images
17
Data acquisition

• Used K-means clustering algorithm
• Criteria implemented Basic and its variations,
  Davies-Bouldin, modified Liu and Yangs, MML
• All criteria performed well with synthetic images
  noiseless and noisy

18
Results Conventional
c25 turiray( 2) 0.316530 turiray( 3)
0.359345 turiray( 4) 0.102838 turiray( 5)
0.065361 turiray( 6) 0.068889 turiray( 7)
0.058784 turiray( 8) 0.450211 turiray( 9)
0.390798 turiray(10) 0.389613 mly( 2)
2.982e03 mly( 3) 3.422e03 mly( 4)
3.497e03 mly( 5) 4.193e03 mly( 6)
3.493e03 mly( 7) 2.684e03 mly( 8)
1.850e03 mly( 9) 1.749e03 mly(10) 1.821e03
c3 turiray( 2) 0.063367 turiray( 3)
0.071938 turiray( 4) 0.050854 turiray( 5)
0.056477 turiray( 6) 0.068687 turiray( 7)
0.058780 turiray( 8) 0.450211 turiray( 9)
0.390798 turiray(10) 0.389613 newb( 2)
0.044778 newb( 3) 0.061415 newb( 4)
0.092113 newb( 5) 0.126146 newb( 6)
0.166693 newb( 7) 0.149928 newb( 8)
1.196244 newb( 9) 1.075060 newb(10) 1.104512
basic( 2) 0.028845 basic( 3) 0.032746 basic(
4) 0.043765 basic( 5) 0.055266 basic( 6)
0.068659 basic( 7) 0.058780 basic( 8)
0.450211 basic( 9) 0.390798 basic(10)
0.389613 db( 2) 0.270230 db( 3) 0.416883 db(
4) 0.429238 db( 5) 0.421306 db( 6)
0.347008 db( 7) 0.244385 db( 8) 0.405561 db(
9) 0.241530 db(10) 0.347501
noisy-gauss-horiz.gif
19
Results MML
clusters( 2) msglen(seg) 0.19093 msglen(comp)
3.49459 total 3.68552 clusters( 3) msglen(seg)
0.28233 msglen(comp) 3.45295 total
3.73529 clusters( 4) msglen(seg) 0.30517
msglen(comp) 3.45555 total 3.76072 clusters(
5) msglen(seg) 0.39653 msglen(comp) 3.41380
total 3.81034 clusters( 6) msglen(seg) 0.41788
msglen(comp) 3.29724 total 3.71512 clusters(
7) msglen(seg) 0.43525 msglen(comp) 3.18079
total 3.61604 clusters( 8) msglen(seg) 0.44872
msglen(comp) 3.06587 total 3.51459 clusters(
9) msglen(seg) 1.36705 msglen(comp) 2.34274
total 3.70980 clusters(10) msglen(seg) 1.37629
msglen(comp) 2.33173 total 3.70802 clusters(11)
msglen(seg) 1.38431 msglen(comp) 2.32193
total 3.70624 clusters(12) msglen(seg) 1.39548
msglen(comp) 2.31049 total 3.70598 clusters(13)
msglen(seg) 1.40537 msglen(comp) 2.29821
total 3.70358 clusters(14) msglen(seg) 1.41076
msglen(comp) 2.29088 total 3.70164 clusters(15)
msglen(seg) 1.41840 msglen(comp) 2.28172
total 3.70012 clusters(16) msglen(seg) 1.96013
msglen(comp) 1.83203 total 3.79216 clusters(17)
msglen(seg) 1.96240 msglen(comp) 1.82792
total 3.79032 clusters(18) msglen(seg) 1.96762
msglen(comp) 1.82374 total 3.79137 clusters(19)
msglen(seg) 1.97606 msglen(comp) 1.80713
total 3.78319 clusters(20) msglen(seg) 1.98245
msglen(comp) 1.79615 total 3.77860
noisy-gauss-horiz.gif
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Results MML (compression)
clusters( 2) msglen(seg) 0.00531 msglen(comp)
3.06629 total 3.07160 clusters( 3) msglen(seg)
0.00714 msglen(comp) 3.08875 total
3.09589 clusters( 4) msglen(seg) 0.00762
msglen(comp) 3.06985 total 3.07747 clusters(
5) msglen(seg) 0.00968 msglen(comp) 3.06624
total 3.07592 clusters( 6) msglen(seg) 0.00984
msglen(comp) 3.06560 total 3.07545 clusters(
7) msglen(seg) 0.00998 msglen(comp) 3.06116
total 3.07114 clusters( 8) msglen(seg)
0.01008 msglen(comp) 3.06354 total
3.07363 clusters( 9) msglen(seg) 0.92816
msglen(comp) 2.33924 total 3.26740 clusters(10)
msglen(seg) 0.93736 msglen(comp) 2.32849
total 3.26585 clusters(11) msglen(seg) 0.94529
msglen(comp) 2.31937 total 3.26466 clusters(12)
msglen(seg) 0.95642 msglen(comp) 2.30817
total 3.26459 clusters(13) msglen(seg) 0.96626
msglen(comp) 2.29637 total 3.26263 clusters(14)
msglen(seg) 0.97159 msglen(comp) 2.28901
total 3.26060 clusters(15) msglen(seg) 0.97918
msglen(comp) 2.28012 total 3.25929 clusters(16)
msglen(seg) 1.52064 msglen(comp) 1.82848
total 3.34912 clusters(17) msglen(seg) 1.52281
msglen(comp) 1.82494 total 3.34775 clusters(18)
msglen(seg) 1.52788 msglen(comp) 1.82088
total 3.34876 clusters(19) msglen(seg) 1.53630
msglen(comp) 1.80525 total 3.34155 clusters(20)
msglen(seg) 1.54260 msglen(comp) 1.79465
total 3.33725
noisy-gauss-horiz.gif
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Results Conventional
c25 turiray( 2) 0.907895 turiray( 3)
2.139840 turiray( 4) 0.581118 turiray( 5)
0.298118 turiray( 6) 0.265575 turiray( 7)
0.370109 turiray( 8) 0.335818 turiray( 9)
0.438576 turiray(10) 0.397709 mly( 2)
2.901e03 mly( 3) 3.556e03 mly( 4)
3.794e03 mly( 5) 4.109e03 mly( 6)
4.343e03 mly( 7) 4.347e03 mly( 8)
4.395e03 mly( 9) 4.407e03 mly(10) 4.482e03
c3 turiray( 2) 0.181754 turiray( 3)
0.428381 turiray( 4) 0.287365 turiray( 5)
0.257597 turiray( 6) 0.264796 turiray( 7)
0.370089 turiray( 8) 0.335818 turiray( 9)
0.438576 turiray(10) 0.397709 newb( 2)
0.116768 newb( 3) 0.322134 newb( 4)
0.450768 newb( 5) 0.492831 newb( 6)
0.546141 newb( 7) 0.797465 newb( 8)
0.750234 newb( 9) 1.010456 newb(10) 0.941168
basic( 2) 0.082735 basic( 3) 0.179645 basic(
4) 0.247505 basic( 5) 0.236679 basic( 6)
0.415174 basic( 7) 0.370433 basic( 8)
0.470955 basic( 9) 0.432289 basic(10)
0.403885 db( 2) 0.180646 db( 3) 0.499035 db(
4) 0.517406 db( 5) 0.527143 db( 6)
0.558590 db( 7) 0.535128 db( 8) 0.533459 db(
9) 0.533248 db(10) 0.516831
pellets.gif
22
Results MML
clusters( 2) msglen(seg) 0.95801 msglen(comp)
4.71527 total 5.67328lt clusters( 3)
msglen(seg) 1.26187 msglen(comp) 4.45021 total
5.71207 clusters( 4) msglen(seg) 1.56033
msglen(comp) 4.14717 total 5.70749 clusters(
5) msglen(seg) 1.74551 msglen(comp) 3.97131
total 5.71682 clusters( 6) msglen(seg) 2.18648
msglen(comp) 3.69497 total 5.88145 clusters(
7) msglen(seg) 2.29761 msglen(comp) 3.51929
total 5.81691 clusters( 8) msglen(seg) 2.57130
msglen(comp) 3.32845 total 5.89975 clusters(
9) msglen(seg) 2.66154 msglen(comp) 3.18891
total 5.85045 clusters(10) msglen(seg) 2.73549
msglen(comp) 3.05961 total 5.79511 clusters(11)
msglen(seg) 2.82671 msglen(comp) 2.95492
total 5.78163 clusters(12) msglen(seg) 2.86433
msglen(comp) 2.87176 total 5.73609 clusters(13)
msglen(seg) 3.07090 msglen(comp) 2.73890
total 5.80980 clusters(14) msglen(seg) 3.13611
msglen(comp) 2.64677 total 5.78288 clusters(15)
msglen(seg) 3.17683 msglen(comp) 2.59758
total 5.77441 clusters(16) msglen(seg) 3.28102
msglen(comp) 2.48295 total 5.76397 clusters(17)
msglen(seg) 3.27395 msglen(comp) 2.44051
total 5.71447 clusters(18) msglen(seg) 3.35924
msglen(comp) 2.33705 total 5.69629 clusters(19)
msglen(seg) 3.37645 msglen(comp) 2.30539
total 5.68183 clusters(20) msglen(seg) 3.37931
msglen(comp) 2.27475 total 5.65406
pellets.gif
23
Results MML (compression)
clusters( 2) msglen(seg) 0.17260 msglen(comp)
3.71461 total 3.88721 clusters( 3)
msglen(seg) 0.35768 msglen(comp) 3.71061 total
4.06829 clusters( 4) msglen(seg) 0.55191
msglen(comp) 3.54044 total 4.09235 clusters(
5) msglen(seg) 0.63344 msglen(comp) 3.44334
total 4.07678 clusters( 6) msglen(seg) 0.89175
msglen(comp) 3.32420 total 4.21595 clusters(
7) msglen(seg) 0.96849 msglen(comp) 3.21083
total 4.17932 clusters( 8) msglen(seg) 1.12851
msglen(comp) 3.08145 total 4.20995 clusters(
9) msglen(seg) 1.18696 msglen(comp) 2.97689
total 4.16385 clusters(10) msglen(seg) 1.24237
msglen(comp) 2.88126 total 4.12363 clusters(11)
msglen(seg) 1.32742 msglen(comp) 2.79415
total 4.12157 clusters(12) msglen(seg) 1.36082
msglen(comp) 2.72628 total 4.08710 clusters(13)
msglen(seg) 1.50673 msglen(comp) 2.61468
total 4.12142 clusters(14) msglen(seg) 1.56604
msglen(comp) 2.54181 total 4.10785 clusters(15)
msglen(seg) 1.57714 msglen(comp) 2.50831
total 4.08545 clusters(16) msglen(seg) 1.67750
msglen(comp) 2.41434 total 4.09184 clusters(17)
msglen(seg) 1.66978 msglen(comp) 2.37438
total 4.04415 clusters(18) msglen(seg) 1.74989
msglen(comp) 2.28008 total 4.02997 clusters(19)
msglen(seg) 1.76311 msglen(comp) 2.25388
total 4.01699 clusters(20) msglen(seg) 1.78389
msglen(comp) 2.22621 total 4.01011
pellets.gif
24
Results Conventional
c25 turiray( 2) 2.874304 turiray( 3)
2.879318 turiray( 4) 0.736279 turiray( 5)
0.334392 turiray( 6) 0.254306 turiray( 7)
0.324880 turiray( 8) 0.310033 turiray( 9)
0.321600 turiray(10) 0.310487 mly( 2)
1.481e04 mly( 3) 1.352e04 mly( 4)
1.404e04 mly( 5) 1.412e04 mly( 6)
1.314e04 mly( 7) 1.419e04 mly( 8)
1.381e04 mly( 9) 1.396e04 mly(10) 1.496e04
c3 turiray( 2) 0.575415 turiray( 3)
0.576419 turiray( 4) 0.364093 turiray( 5)
0.288941 turiray( 6) 0.253560 turiray( 7)
0.324863 turiray( 8) 0.310033 turiray( 9)
0.321600 turiray(10) 0.310487 newb( 2)
0.350492 newb( 3) 0.402999 newb( 4)
0.525229 newb( 5) 0.504717 newb( 6)
0.474983 newb( 7) 0.633218 newb( 8)
0.624511 newb( 9) 0.666288 newb(10) 0.659223
basic( 2) 0.261930 basic( 3) 0.262387 basic(
4) 0.313340 basic( 5) 0.282743 basic( 6)
0.253458 basic( 7) 0.324860 basic( 8)
0.310033 basic( 9) 0.321600 basic(10)
0.310487 db( 2) 0.530825 db( 3) 0.478174 db(
4) 0.504946 db( 5) 0.516538 db( 6)
0.467455 db( 7) 0.511223 db( 8) 0.515691 db(
9) 0.524497 db(10) 0.540517
mug.gif
25
Results MML
clusters( 2) msglen(seg) 0.98611 msglen(comp)
6.90642 total 7.89253 clusters( 3) msglen(seg)
1.57437 msglen(comp) 6.28974 total
7.86412 clusters( 4) msglen(seg) 1.99827
msglen(comp) 5.98868 total 7.98695 clusters(
5) msglen(seg) 2.25854 msglen(comp) 5.65204
total 7.91058 clusters( 6) msglen(seg) 2.54185
msglen(comp) 5.34344 total 7.88530 clusters(
7) msglen(seg) 2.70332 msglen(comp) 5.19988
total 7.90321 clusters( 8) msglen(seg) 2.94302
msglen(comp) 4.99163 total 7.93465 clusters(
9) msglen(seg) 3.11823 msglen(comp) 4.83729
total 7.95552 clusters(10) msglen(seg) 3.22469
msglen(comp) 4.69594 total 7.92063 clusters(11)
msglen(seg) 3.37008 msglen(comp) 4.58589
total 7.95596 clusters(12) msglen(seg) 3.51144
msglen(comp) 4.47807 total 7.98950 clusters(13)
msglen(seg) 3.59381 msglen(comp) 4.35698
total 7.95079 clusters(14) msglen(seg) 3.71670
msglen(comp) 4.21602 total 7.93273 clusters(15)
msglen(seg) 3.79730 msglen(comp) 4.15773
total 7.95503 clusters(16) msglen(seg) 3.88260
msglen(comp) 4.04205 total 7.92465 clusters(17)
msglen(seg) 3.95024 msglen(comp) 3.99753
total 7.94777 clusters(18) msglen(seg) 4.02162
msglen(comp) 3.88601 total 7.90763 clusters(19)
msglen(seg) 4.09562 msglen(comp) 3.82398
total 7.91959 clusters(20) msglen(seg) 4.16334
msglen(comp) 3.74666 total 7.91000
mug.gif
26
Results MML (compression)
clusters( 2) msglen(seg) 0.12909 msglen(comp)
2.96959 total 3.09868 clusters( 3)
msglen(seg) 0.16243 msglen(comp) 2.98889 total
3.15132 clusters( 4) msglen(seg) 0.25227
msglen(comp) 2.99913 total 3.25140 clusters(
5) msglen(seg) 0.30524 msglen(comp) 2.98977
total 3.29501 clusters( 6) msglen(seg) 0.33630
msglen(comp) 2.99446 total 3.33076 clusters(
7) msglen(seg) 0.39964 msglen(comp) 2.99012
total 3.38976 clusters( 8) msglen(seg) 0.44998
msglen(comp) 2.98191 total 3.43189 clusters(
9) msglen(seg) 0.49405 msglen(comp) 2.99139
total 3.48544 clusters(10) msglen(seg) 0.51936
msglen(comp) 2.97123 total 3.49059 clusters(11)
msglen(seg) 0.54632 msglen(comp) 2.96876
total 3.51509 clusters(12) msglen(seg) 0.58417
msglen(comp) 2.94259 total 3.52676 clusters(13)
msglen(seg) 0.63025 msglen(comp) 2.93819
total 3.56844 clusters(14) msglen(seg) 0.65360
msglen(comp) 2.90471 total 3.55831 clusters(15)
msglen(seg) 0.69339 msglen(comp) 2.90487
total 3.59826 clusters(16) msglen(seg) 0.67994
msglen(comp) 2.85176 total 3.53170 clusters(17)
msglen(seg) 0.73236 msglen(comp) 2.86933
total 3.60169 clusters(18) msglen(seg) 0.74546
msglen(comp) 2.82288 total 3.56835 clusters(19)
msglen(seg) 0.75638 msglen(comp) 2.79524
total 3.55162 clusters(20) msglen(seg) 0.79306
msglen(comp) 2.77067 total 3.56373
mug.gif
27
Results Conventional
c25 turiray( 2) 0.956504 turiray( 3)
2.014973 turiray( 4) 0.554248 turiray( 5)
0.369942 turiray( 6) 0.330328 turiray( 7)
0.307985 turiray( 8) 0.310911 turiray( 9)
0.256562 turiray(10) 0.260443 mly( 2)
6.829e03 mly( 3) 8.138e03 mly( 4)
9.085e03 mly( 5) 8.234e03 mly( 6)
8.682e03 mly( 7) 8.373e03 mly( 8)
8.747e03 mly( 9) 8.590e03 mly(10) 8.723e03
c3 turiray( 2) 0.191485 turiray( 3)
0.403383 turiray( 4) 0.274078 turiray( 5)
0.319659 turiray( 6) 0.329359 turiray( 7)
0.307968 turiray( 8) 0.310911 turiray( 9)
0.256562 turiray(10) 0.260443 newb( 2)
0.119222 newb( 3) 0.290656 newb( 4)
0.409370 newb( 5) 0.579920 newb( 6)
0.642219 newb( 7) 0.625935 newb( 8)
0.653949 newb( 9) 0.555670 newb(10) 0.578634
basic( 2) 0.087164 basic( 3) 0.183621 basic(
4) 0.235873 basic( 5) 0.312802 basic( 6)
0.329226 basic( 7) 0.307966 basic( 8)
0.310911 basic( 9) 0.256562 basic(10)
0.260443 db( 2) 0.179285 db( 3) 0.411011 db(
4) 0.535435 db( 5) 0.470768 db( 6)
0.517264 db( 7) 0.473861 db( 8) 0.482182 db(
9) 0.473553 db(10) 0.491428
parts.gif
28
Results MML
clusters( 2) msglen(seg) 0.88872 msglen(comp)
5.94984 total 6.83856 clusters( 3) msglen(seg)
1.21237 msglen(comp) 5.62992 total
6.84229 clusters( 4) msglen(seg) 1.44588
msglen(comp) 5.35543 total 6.80131 clusters(
5) msglen(seg) 1.72351 msglen(comp) 5.23325
total 6.95676 clusters( 6) msglen(seg) 1.95457
msglen(comp) 5.03226 total 6.98683 clusters(
7) msglen(seg) 2.31526 msglen(comp) 4.54948
total 6.86475 clusters( 8) msglen(seg) 2.39908
msglen(comp) 4.43673 total 6.83581 clusters(
9) msglen(seg) 2.45382 msglen(comp) 4.37250
total 6.82632 clusters(10) msglen(seg) 2.55148
msglen(comp) 4.30782 total 6.85930 clusters(11)
msglen(seg) 2.79302 msglen(comp) 4.01336
total 6.80638 clusters(12) msglen(seg) 2.82934
msglen(comp) 3.95794 total 6.78727 clusters(13)
msglen(seg) 2.86755 msglen(comp) 3.90672
total 6.77427 clusters(14) msglen(seg) 2.97670
msglen(comp) 3.82725 total 6.80396 clusters(15)
msglen(seg) 3.03578 msglen(comp) 3.73110
total 6.76689 clusters(16) msglen(seg) 3.06018
msglen(comp) 3.69381 total 6.75399 clusters(17
) msglen(seg) 3.11618 msglen(comp) 3.66694
total 6.78312 clusters(18) msglen(seg) 3.38921
msglen(comp) 3.43204 total 6.82125 clusters(19)
msglen(seg) 3.32197 msglen(comp) 3.44559
total 6.76756 clusters(20) msglen(seg) 3.20507
msglen(comp) 3.58687 total 6.79194
parts.gif
29
Results MML (compression)
clusters( 2) msglen(seg) 0.06853 msglen(comp)
2.65721 total 2.72574 clusters( 3)
msglen(seg) 0.11425 msglen(comp) 2.70317 total
2.81742 clusters( 4) msglen(seg) 0.18939
msglen(comp) 2.72848 total 2.91788 clusters(
5) msglen(seg) 0.24371 msglen(comp) 2.72483
total 2.96855 clusters( 6) msglen(seg) 0.35095
msglen(comp) 2.72645 total 3.07739 clusters(
7) msglen(seg) 0.34635 msglen(comp) 2.71818
total 3.06453 clusters( 8) msglen(seg) 0.37958
msglen(comp) 2.69586 total 3.07543 clusters(
9) msglen(seg) 0.41807 msglen(comp) 2.68056
total 3.09863 clusters(10) msglen(seg) 0.45282
msglen(comp) 2.66514 total 3.11796 clusters(11)
msglen(seg) 0.49602 msglen(comp) 2.64091
total 3.13693 clusters(12) msglen(seg) 0.54413
msglen(comp) 2.62628 total 3.17041 clusters(13)
msglen(seg) 0.57186 msglen(comp) 2.61655
total 3.18841 clusters(14) msglen(seg) 0.63639
msglen(comp) 2.59211 total 3.22850 clusters(15)
msglen(seg) 0.61206 msglen(comp) 2.55553
total 3.16759 clusters(16) msglen(seg) 0.62329
msglen(comp) 2.54859 total 3.17188 clusters(17)
msglen(seg) 0.73997 msglen(comp) 2.53512
total 3.27509 clusters(18) msglen(seg) 0.74119
msglen(comp) 2.50312 total 3.24431 clusters(19)
msglen(seg) 0.70840 msglen(comp) 2.49589
total 3.20428 clusters(20) msglen(seg) 0.82594
msglen(comp) 2.48605 total 3.31199
parts.gif
30
Results Conventional
c25 turiray( 2) 2.874304 turiray( 3)
2.879318 turiray( 4) 0.736279 turiray( 5)
0.334392 turiray( 6) 0.254306 turiray( 7)
0.324880 turiray( 8) 0.310033 turiray( 9)
0.321600 turiray(10) 0.310487 mly( 2)
1.244e04 mly( 3) 2.853e03 mly( 4)
3.162e03 mly( 5) 3.780e03 mly( 6)
3.758e03 mly( 7) 4.277e03 mly( 8)
4.304e03 mly( 9) 4.392e03 mly(10) 4.925e03
c3 turiray( 2) 0.724464 turiray( 3)
0.104224 turiray( 4) 0.076117 turiray( 5)
0.199347 turiray( 6) 0.089837 turiray( 7)
0.154118 turiray( 8) 0.178802 turiray( 9)
0.136754 turiray(10) 0.213157 newb( 2)
0.490037 newb( 3) 0.083985 newb( 4)
0.129173 newb( 5) 0.415182 newb( 6)
0.202609 newb( 7) 0.364373 newb( 8)
0.439475 newb( 9) 0.347419 newb(10) 0.557261
basic( 2) 0.329778 basic( 3) 0.047443 basic(
4) 0.065506 basic( 5) 0.195071 basic( 6)
0.089801 basic( 7) 0.154117 basic( 8)
0.178802 basic( 9) 0.136754 basic(10)
0.213157 db( 2) 0.555344 db( 3) 0.196758 db(
4) 0.349625 db( 5) 0.464390 db( 6)
0.438794 db( 7) 0.460611 db( 8) 0.453797 db(
9) 0.464053 db(10) 0.489775
catscan.gif
31
Results MML
clusters( 2) msglen(seg) 0.30120 msglen(comp)
3.99914 total 4.30034 clusters( 3)
msglen(seg) 1.20186 msglen(comp) 3.51052 total
4.71238 clusters( 4) msglen(seg) 1.42220
msglen(comp) 3.17919 total 4.60139 clusters(
5) msglen(seg) 1.41704 msglen(comp) 3.12083
total 4.53786 clusters( 6) msglen(seg) 1.53307
msglen(comp) 3.29052 total 4.82359 clusters(
7) msglen(seg) 1.69364 msglen(comp) 2.91238
total 4.60602 clusters( 8) msglen(seg) 1.63223
msglen(comp) 2.96074 total 4.59297 clusters(
9) msglen(seg) 1.69393 msglen(comp) 3.11830
total 4.81222 clusters(10) msglen(seg) 2.04556
msglen(comp) 2.53640 total 4.58196 clusters(11)
msglen(seg) 2.07229 msglen(comp) 2.48145
total 4.55375 clusters(12) msglen(seg) 2.09874
msglen(comp) 2.42672 total 4.52546 clusters(13)
msglen(seg) 2.11242 msglen(comp) 2.40013
total 4.51255 clusters(14) msglen(seg) 2.20274
msglen(comp) 2.39125 total 4.59399 clusters(15)
msglen(seg) 2.21187 msglen(comp) 2.37642
total 4.58829 clusters(16) msglen(seg) 2.16486
msglen(comp) 2.31882 total 4.48367 clusters(17)
msglen(seg) 2.24201 msglen(comp) 2.24699
total 4.48900 clusters(18) msglen(seg) 2.25112
msglen(comp) 2.22778 total 4.47890 clusters(19)
msglen(seg) 2.23899 msglen(comp) 2.22521
total 4.46420 clusters(20) msglen(seg) 2.24702
msglen(comp) 2.20647 total 4.45349
catscan.gif
32
Results MML (compression)
clusters( 2) msglen(seg) 0.08553 msglen(comp)
2.09802 total 2.18355 clusters( 3)
msglen(seg) 0.15318 msglen(comp) 2.21724 total
2.37042 clusters( 4) msglen(seg) 0.24786
msglen(comp) 2.18955 total 2.43741 clusters(
5) msglen(seg) 0.23233 msglen(comp) 2.18068
total 2.41302 clusters( 6) msglen(seg) 0.28102
msglen(comp) 2.18363 total 2.46465 clusters(
7) msglen(seg) 0.36099 msglen(comp) 2.13410
total 2.49510 clusters( 8) msglen(seg) 0.33307
msglen(comp) 2.11860 total 2.45168 clusters(
9) msglen(seg) 0.37223 msglen(comp) 2.13415
total 2.50637 clusters(10) msglen(seg) 0.49323
msglen(comp) 2.03049 total 2.52372 clusters(11)
msglen(seg) 0.50914 msglen(comp) 2.00783
total 2.51698 clusters(12) msglen(seg) 0.51731
msglen(comp) 1.98695 total 2.50425 clusters(13)
msglen(seg) 0.52914 msglen(comp) 1.96970
total 2.49884 clusters(14) msglen(seg) 0.58694
msglen(comp) 1.97046 total 2.55741 clusters(15)
msglen(seg) 0.59436 msglen(comp) 1.96224
total 2.55660 clusters(16) msglen(seg) 0.56548
msglen(comp) 1.92448 total 2.48995 clusters(17)
msglen(seg) 0.61131 msglen(comp) 1.89871
total 2.51002 clusters(18) msglen(seg) 0.61896
msglen(comp) 1.89046 total 2.50941 clusters(19)
msglen(seg) 0.61645 msglen(comp) 1.87014
total 2.48659 clusters(20) msglen(seg) 0.62342
msglen(comp) 1.86023 total 2.48365
catscan.gif
33
Results Conventional
c25 turiray( 2) 2.991038 turiray( 3)
3.218748 turiray( 4) 0.604428 turiray( 5)
0.327728 turiray( 6) 0.308129 turiray( 7)
0.278123 turiray( 8) 0.317733 turiray( 9)
0.362598 turiray(10) 0.347851 mly( 2)
1.141e04 mly( 3) 1.215e04 mly( 4)
1.105e04 mly( 5) 1.066e04 mly( 6)
1.138e04 mly( 7) 1.099e04 mly( 8)
1.114e04 mly( 9) 1.154e04 mly(10) 1.140e04
c3 turiray( 2) 0.598784 turiray( 3)
0.644370 turiray( 4) 0.298892 turiray( 5)
0.283182 turiray( 6) 0.307225 turiray( 7)
0.278108 turiray( 8) 0.317733 turiray( 9)
0.362598 turiray(10) 0.347851 newb( 2)
0.366676 newb( 3) 0.453832 newb( 4)
0.434853 newb( 5) 0.499260 newb( 6)
0.581190 newb( 7) 0.547670 newb( 8)
0.646840 newb( 9) 0.759449 newb(10) 0.746818
basic( 2) 0.272568 basic( 3) 0.293319 basic(
4) 0.257228 basic( 5) 0.277108 basic( 6)
0.307102 basic( 7) 0.278106 basic( 8)
0.317733 basic( 9) 0.362598 basic(10)
0.347851 db( 2) 0.546135 db( 3) 0.551879 db(
4) 0.482077 db( 5) 0.470612 db( 6)
0.520555 db( 7) 0.494981 db( 8) 0.500130 db(
9) 0.536775 db(10) 0.520929
lenna_256.gif
34
Results MML
clusters( 2) msglen(seg) 0.97825 msglen(comp)
6.58971 total 7.56796 clusters( 3) msglen(seg)
1.53539 msglen(comp) 6.05819 total
7.59358 clusters( 4) msglen(seg) 1.94567
msglen(comp) 5.61176 total 7.55743 clusters(
5) msglen(seg) 2.28677 msglen(comp) 5.30118
total 7.58794 clusters( 6) msglen(seg) 2.55890
msglen(comp) 5.06692 total 7.62582 clusters(
7) msglen(seg) 2.75194 msglen(comp) 4.82988
total 7.58182 clusters( 8) msglen(seg) 2.96150
msglen(comp) 4.69041 total 7.65190 clusters(
9) msglen(seg) 3.08371 msglen(comp) 4.53207
total 7.61578 clusters(10) msglen(seg) 3.23460
msglen(comp) 4.38479 total 7.61939 clusters(11)
msglen(seg) 3.37332 msglen(comp) 4.26351
total 7.63683 clusters(12) msglen(seg) 3.42829
msglen(comp) 4.23759 total 7.66588 clusters(13)
msglen(seg) 3.55397 msglen(comp) 4.08410
total 7.63807 clusters(14) msglen(seg) 3.65488
msglen(comp) 4.00315 total 7.65803 clusters(15)
msglen(seg) 3.75095 msglen(comp) 3.86644
total 7.61739 clusters(16) msglen(seg) 3.84119
msglen(comp) 3.80109 total 7.64228 clusters(17)
msglen(seg) 3.93254 msglen(comp) 3.68456
total 7.61709 clusters(18) msglen(seg) 4.02986
msglen(comp) 3.60238 total 7.63224 clusters(19)
msglen(seg) 4.09505 msglen(comp) 3.50406
total 7.59911 clusters(20) msglen(seg) 4.14025
msglen(comp) 3.45798 total 7.59823
lenna_256.gif
35
Results MML (compression)
clusters( 2) msglen(seg) 0.37291 msglen(comp)
5.30594 total 5.67885 clusters( 3)
msglen(seg) 0.65112 msglen(comp) 5.26328 total
5.91441 clusters( 4) msglen(seg) 0.83863
msglen(comp) 5.10159 total 5.94022 clusters(
5) msglen(seg) 1.00497 msglen(comp) 4.96102
total 5.96600 clusters( 6) msglen(seg) 1.20067
msglen(comp) 4.81178 total 6.01244 clusters(
7) msglen(seg) 1.29426 msglen(comp) 4.63247
total 5.92672 clusters( 8) msglen(seg) 1.44331
msglen(comp) 4.52951 total 5.97282 clusters(
9) msglen(seg) 1.54799 msglen(comp) 4.41080
total 5.95879 clusters(10) msglen(seg) 1.64780
msglen(comp) 4.29704 total 5.94484 clusters(11)
msglen(seg) 1.74398 msglen(comp) 4.18675
total 5.93073 clusters(12) msglen(seg) 1.80232
msglen(comp) 4.16929 total 5.97161 clusters(13)
msglen(seg) 1.89048 msglen(comp) 4.03754
total 5.92801 clusters(14) msglen(seg) 1.98032
msglen(comp) 3.96456 total 5.94487 clusters(15)
msglen(seg) 2.03033 msglen(comp) 3.83652
total 5.86685 clusters(16) msglen(seg) 2.12481
msglen(comp) 3.77656 total 5.90138 clusters(17)
msglen(seg) 2.18763 msglen(comp) 3.66376
total 5.85139 clusters(18) msglen(seg) 2.27335
msglen(comp) 3.58452 total 5.85787 clusters(19)
msglen(seg) 2.32329 msglen(comp) 3.48818
total 5.81147 clusters(20) msglen(seg) 2.35762
msglen(comp) 3.44664 total 5.80426
lenna_256.gif
36
Conclusion Conventional Methods

• Assumes normally distributed clusters (use of
  Euclidean distance imply spherical clusters)
• Intra approaches 0 as number of segments approach
  number of grey levels in image
• High correlation between intra and inter cluster
  distances

37
Conclusion Turi and Rays Modified Criterion

• The value of c does matter with the evaluation of
  clusters from greyscale images
• For greyscale images, optimum value of c was
  found to be 3

38
Conclusion New Evaluation Methods

• New basic Too much bias towards the low number
  of clusters
• Modified Liu and Yang Found to give same results
  as Davies-Bouldin index with only intra-cluster
  information shows the high correlation between
  intra and inter

39
Conclusion MML

• Makes no assumptions
• MML provides a general way of qualitative cluster
  assessment
• MsgLen(segment map) may decrease with increasing
  K
• Compression seems to bias smaller number of
  clusters
• Markovian compression impractical large
  alphabet size of images (preprocessing)

40
Future Work

• Test MML and new approaches with colour images
  (various colour spaces)
• Use other compression or noise removal techniques
  to improve MML analysis
• Use of different clustering algorithms to form
  other types of cluster distributions
• Explore further adaptive penalty functions

41
Questions?