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

Image Segmentation by Clustering Methods:

Cluster Validity

Student: Sean Hsien

Supervisor: Dr. Sid Ray

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

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

Conventional cluster evaluation Many conventional methods measure

cluster compactness and separability — intra/inter cluster distances

Inter

Intra

Inter

IntraCEF min

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

Modified Criterion Formula

2

2

2

)(

22

1),(

1),(

K

eN

Ncyinter

intrayV

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

)|()( ModelDataMsgLenModelMsgLenMsgLen

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)

Segmented(3 clusters)

ComplementaryImage

Original

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)

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

1)(log

Kyinter

intrayF

H where H is the entropy of the input image

2 New Evaluation Criteria Based on the Liu and Yang’s

criterion Their criterion over emphasized

goodness-of-fit

K

i i

i

N

eKF

1

2

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

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

Synthetic Images

Natural Images

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

Results – Conventionalbasic( 2): 0.028845*basic( 3): 0.032746basic( 4): 0.043765basic( 5): 0.055266basic( 6): 0.068659basic( 7): 0.058780basic( 8): 0.450211basic( 9): 0.390798basic(10): 0.389613

db( 2): 0.270230db( 3): 0.416883db( 4): 0.429238db( 5): 0.421306db( 6): 0.347008db( 7): 0.244385db( 8): 0.405561db( 9): 0.241530*db(10): 0.347501

c=25turiray( 2): 0.316530turiray( 3): 0.359345turiray( 4): 0.102838turiray( 5): 0.065361turiray( 6): 0.068889turiray( 7): 0.058784*turiray( 8): 0.450211turiray( 9): 0.390798turiray(10): 0.389613

mly( 2): 2.982e+03mly( 3): 3.422e+03mly( 4): 3.497e+03mly( 5): 4.193e+03mly( 6): 3.493e+03mly( 7): 2.684e+03mly( 8): 1.850e+03mly( 9): 1.749e+03*mly(10): 1.821e+03

c=3turiray( 2): 0.063367turiray( 3): 0.071938turiray( 4): 0.050854*turiray( 5): 0.056477turiray( 6): 0.068687turiray( 7): 0.058780turiray( 8): 0.450211turiray( 9): 0.390798turiray(10): 0.389613

newb( 2): 0.044778*newb( 3): 0.061415newb( 4): 0.092113newb( 5): 0.126146newb( 6): 0.166693newb( 7): 0.149928newb( 8): 1.196244newb( 9): 1.075060newb(10): 1.104512

noisy-gauss-

horiz.gif

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

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

Results – Conventionalbasic( 2): 0.082735*basic( 3): 0.179645basic( 4): 0.247505basic( 5): 0.236679basic( 6): 0.415174basic( 7): 0.370433basic( 8): 0.470955basic( 9): 0.432289basic(10): 0.403885

db( 2): 0.180646*db( 3): 0.499035db( 4): 0.517406db( 5): 0.527143db( 6): 0.558590db( 7): 0.535128db( 8): 0.533459db( 9): 0.533248db(10): 0.516831

c=25turiray( 2): 0.907895turiray( 3): 2.139840turiray( 4): 0.581118turiray( 5): 0.298118turiray( 6): 0.265575*turiray( 7): 0.370109turiray( 8): 0.335818turiray( 9): 0.438576turiray(10): 0.397709

mly( 2): 2.901e+03*mly( 3): 3.556e+03mly( 4): 3.794e+03mly( 5): 4.109e+03mly( 6): 4.343e+03mly( 7): 4.347e+03mly( 8): 4.395e+03mly( 9): 4.407e+03mly(10): 4.482e+03

c=3turiray( 2): 0.181754*turiray( 3): 0.428381turiray( 4): 0.287365turiray( 5): 0.257597turiray( 6): 0.264796turiray( 7): 0.370089turiray( 8): 0.335818turiray( 9): 0.438576turiray(10): 0.397709

newb( 2): 0.116768*newb( 3): 0.322134newb( 4): 0.450768newb( 5): 0.492831newb( 6): 0.546141newb( 7): 0.797465newb( 8): 0.750234newb( 9): 1.010456newb(10): 0.941168

pellets.gif

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

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

Results – Conventionalbasic( 2): 0.261930basic( 3): 0.262387basic( 4): 0.313340basic( 5): 0.282743basic( 6): 0.253458*basic( 7): 0.324860basic( 8): 0.310033basic( 9): 0.321600basic(10): 0.310487

db( 2): 0.530825db( 3): 0.478174db( 4): 0.504946db( 5): 0.516538db( 6): 0.467455*db( 7): 0.511223db( 8): 0.515691db( 9): 0.524497db(10): 0.540517

c=25turiray( 2): 2.874304turiray( 3): 2.879318turiray( 4): 0.736279turiray( 5): 0.334392turiray( 6): 0.254306*turiray( 7): 0.324880turiray( 8): 0.310033turiray( 9): 0.321600turiray(10): 0.310487

mly( 2): 1.481e+04mly( 3): 1.352e+04mly( 4): 1.404e+04mly( 5): 1.412e+04mly( 6): 1.314e+04*mly( 7): 1.419e+04mly( 8): 1.381e+04mly( 9): 1.396e+04mly(10): 1.496e+04

c=3turiray( 2): 0.575415turiray( 3): 0.576419turiray( 4): 0.364093turiray( 5): 0.288941turiray( 6): 0.253560*turiray( 7): 0.324863turiray( 8): 0.310033turiray( 9): 0.321600turiray(10): 0.310487

newb( 2): 0.350492*newb( 3): 0.402999newb( 4): 0.525229newb( 5): 0.504717newb( 6): 0.474983newb( 7): 0.633218newb( 8): 0.624511newb( 9): 0.666288newb(10): 0.659223

mug.gif

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

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

Results – Conventionalbasic( 2): 0.087164*basic( 3): 0.183621basic( 4): 0.235873basic( 5): 0.312802basic( 6): 0.329226basic( 7): 0.307966basic( 8): 0.310911basic( 9): 0.256562basic(10): 0.260443

db( 2): 0.179285*db( 3): 0.411011db( 4): 0.535435db( 5): 0.470768db( 6): 0.517264db( 7): 0.473861db( 8): 0.482182db( 9): 0.473553db(10): 0.491428

c=25turiray( 2): 0.956504turiray( 3): 2.014973turiray( 4): 0.554248turiray( 5): 0.369942turiray( 6): 0.330328turiray( 7): 0.307985turiray( 8): 0.310911turiray( 9): 0.256562*turiray(10): 0.260443

mly( 2): 6.829e+03*mly( 3): 8.138e+03mly( 4): 9.085e+03mly( 5): 8.234e+03mly( 6): 8.682e+03mly( 7): 8.373e+03mly( 8): 8.747e+03mly( 9): 8.590e+03mly(10): 8.723e+03

c=3turiray( 2): 0.191485*turiray( 3): 0.403383turiray( 4): 0.274078turiray( 5): 0.319659turiray( 6): 0.329359turiray( 7): 0.307968turiray( 8): 0.310911turiray( 9): 0.256562turiray(10): 0.260443

newb( 2): 0.119222*newb( 3): 0.290656newb( 4): 0.409370newb( 5): 0.579920newb( 6): 0.642219newb( 7): 0.625935newb( 8): 0.653949newb( 9): 0.555670newb(10): 0.578634

parts.gif

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

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

Results – Conventionalbasic( 2): 0.329778basic( 3): 0.047443*basic( 4): 0.065506basic( 5): 0.195071basic( 6): 0.089801basic( 7): 0.154117basic( 8): 0.178802basic( 9): 0.136754basic(10): 0.213157

db( 2): 0.555344db( 3): 0.196758*db( 4): 0.349625db( 5): 0.464390db( 6): 0.438794db( 7): 0.460611db( 8): 0.453797db( 9): 0.464053db(10): 0.489775

c=25turiray( 2): 2.874304turiray( 3): 2.879318turiray( 4): 0.736279turiray( 5): 0.334392turiray( 6): 0.254306*turiray( 7): 0.324880turiray( 8): 0.310033turiray( 9): 0.321600turiray(10): 0.310487

mly( 2): 1.244e+04mly( 3): 2.853e+03*mly( 4): 3.162e+03mly( 5): 3.780e+03mly( 6): 3.758e+03mly( 7): 4.277e+03mly( 8): 4.304e+03mly( 9): 4.392e+03mly(10): 4.925e+03

c=3turiray( 2): 0.724464turiray( 3): 0.104224turiray( 4): 0.076117*turiray( 5): 0.199347turiray( 6): 0.089837turiray( 7): 0.154118turiray( 8): 0.178802turiray( 9): 0.136754turiray(10): 0.213157

newb( 2): 0.490037newb( 3): 0.083985*newb( 4): 0.129173newb( 5): 0.415182newb( 6): 0.202609newb( 7): 0.364373newb( 8): 0.439475newb( 9): 0.347419newb(10): 0.557261

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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

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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

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Results – Conventionalbasic( 2): 0.272568basic( 3): 0.293319basic( 4): 0.257228*basic( 5): 0.277108basic( 6): 0.307102basic( 7): 0.278106basic( 8): 0.317733basic( 9): 0.362598basic(10): 0.347851

db( 2): 0.546135db( 3): 0.551879db( 4): 0.482077db( 5): 0.470612*db( 6): 0.520555db( 7): 0.494981db( 8): 0.500130db( 9): 0.536775db(10): 0.520929

c=25turiray( 2): 2.991038turiray( 3): 3.218748turiray( 4): 0.604428turiray( 5): 0.327728turiray( 6): 0.308129turiray( 7): 0.278123*turiray( 8): 0.317733turiray( 9): 0.362598turiray(10): 0.347851

mly( 2): 1.141e+04mly( 3): 1.215e+04mly( 4): 1.105e+04mly( 5): 1.066e+04*mly( 6): 1.138e+04mly( 7): 1.099e+04mly( 8): 1.114e+04mly( 9): 1.154e+04mly(10): 1.140e+04

c=3turiray( 2): 0.598784turiray( 3): 0.644370turiray( 4): 0.298892turiray( 5): 0.283182*turiray( 6): 0.307225turiray( 7): 0.278108turiray( 8): 0.317733turiray( 9): 0.362598turiray(10): 0.347851

newb( 2): 0.366676*newb( 3): 0.453832newb( 4): 0.434853newb( 5): 0.499260newb( 6): 0.581190newb( 7): 0.547670newb( 8): 0.646840newb( 9): 0.759449newb(10): 0.746818

lenna_256.gif

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

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

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

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

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

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

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

Questions?