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Image Segmentation by Clustering Methods: Cluster Validity Student: Sean Hsien Supervisor: Dr. Sid Ray.

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Presentation on theme: "Image Segmentation by Clustering Methods: Cluster Validity Student: Sean Hsien Supervisor: Dr. Sid Ray."— Presentation transcript:

1 Image Segmentation by Clustering Methods: Cluster Validity Student: Sean Hsien Supervisor: Dr. Sid Ray

2 Overview  Aims of the project  Conventional cluster evaluation  Turi and Ray’s 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 Ray’s 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  Based on the basic validity criterion of intra/inter ratio  Modifies the basic criterion with a penalty function to penalize low numbers of clusters Turi and Ray’s Modified Criterion

6 Modified Criterion Formula

7 Minimum Message Length  Principle of Occam’s Razor: don’t 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(Data|Model)

9 Segmented (3 clusters) Complementary Image Original

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 Yang’s 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 Yang’s, MML  All criteria performed well with synthetic images – noiseless and noisy

18 Results – Conventional 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 c=25 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): 2.982e+03 mly( 3): 3.422e+03 mly( 4): 3.497e+03 mly( 5): 4.193e+03 mly( 6): 3.493e+03 mly( 7): 2.684e+03 mly( 8): 1.850e+03 mly( 9): 1.749e+03* mly(10): 1.821e+03 c=3 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 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

20 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

21 Results – Conventional 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 c=25 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): 2.901e+03* mly( 3): 3.556e+03 mly( 4): 3.794e+03 mly( 5): 4.109e+03 mly( 6): 4.343e+03 mly( 7): 4.347e+03 mly( 8): 4.395e+03 mly( 9): 4.407e+03 mly(10): 4.482e+03 c=3 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 pellets.gif

22 Results – MML #clusters( 2) msglen(seg): 0.95801 msglen(comp): 4.71527 total: 5.67328< #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 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 c=25 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): 1.481e+04 mly( 3): 1.352e+04 mly( 4): 1.404e+04 mly( 5): 1.412e+04 mly( 6): 1.314e+04* mly( 7): 1.419e+04 mly( 8): 1.381e+04 mly( 9): 1.396e+04 mly(10): 1.496e+04 c=3 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 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 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 c=25 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): 6.829e+03* mly( 3): 8.138e+03 mly( 4): 9.085e+03 mly( 5): 8.234e+03 mly( 6): 8.682e+03 mly( 7): 8.373e+03 mly( 8): 8.747e+03 mly( 9): 8.590e+03 mly(10): 8.723e+03 c=3 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 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 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 c=25 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): 1.244e+04 mly( 3): 2.853e+03* mly( 4): 3.162e+03 mly( 5): 3.780e+03 mly( 6): 3.758e+03 mly( 7): 4.277e+03 mly( 8): 4.304e+03 mly( 9): 4.392e+03 mly(10): 4.925e+03 c=3 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 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 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 c=25 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): 1.141e+04 mly( 3): 1.215e+04 mly( 4): 1.105e+04 mly( 5): 1.066e+04* mly( 6): 1.138e+04 mly( 7): 1.099e+04 mly( 8): 1.114e+04 mly( 9): 1.154e+04 mly(10): 1.140e+04 c=3 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 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  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 Conclusion – Conventional Methods

37  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 Conclusion – Turi and Ray’s Modified Criterion

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  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) Conclusion – MML

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?


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