fuzzy art for relatively fast unsupervised image color quantization

http://www.nshorter.com 1

Fuzzy ART for Relatively Fast Unsupervised Image Color Quantization

Takis Kasparis

[email protected]

Nicholas S. Shorter

[email protected]

School of Electrical Engineering and Computer ScienceUniversity of Central Florida

Orlando, Florida, 32816 USA

Research Website:http://www.nshorter.com

mailto:[email protected]

mailto:[email protected]

http://www.nshorter.com/


Presentation Outline

• Research Objectives

• Fuzzy ART

• Cluster Assignment Methods

• Performance Metrics

• Experiments

• Results Discussion

• Conclusions


Research Objectives

• Investigate use of Fuzzy ART (FA) efficient for Color Quantization (CQ) of large color (1600x2000 pixels and greater) images

• Use FA CQ as a preprocessing step for JSEG Color Image Segmentation

• Use JSEG Image Segmentation (w/ other methods) for Building Detection in Aerial Images


Color Quantization

• Reducing Number of Colors in Image– Typically used as a preprocessing technique to

image processing applications

• Color Quantized Image should be as similar to the Original as possible

• FA chosen to cluster RGB color component values


Fuzzy Adaptive Resonance Theory• Unsupervised Learning, Clustering Algorithm• Three User Defined Parameters:

– Vigilance Parameter ρ [0,1]• Closer to 0 results in less clusters created• Closer to 1 results in more clusters created

– Learning Rate β [0,1]• Slow Learning β < 1

– Input patterns update clusters (grow to eventually include input)• Fast Learning β = 1

– Upon presentation of input, cluster immediately updated to contain input

– Choice Parameter α (0,∞)• Affects bottom up input calculations


Input Image Presentation to FA

• Define Input Image as matrix with RxC cells each containing 3 components – RGB– – Where and

• Input then reorganized as a single array:– where( ) ( )ary k i j inI I( ) ( )ary k i j inI I( ) ( )ary k i j inI I

, , ,( , ) ( , ), ( , ) ( , ){ }in r in g in bi j I i j I i j I i jinI

1,2,...,i R 1,2,...,j C

1,2,...,k R C


Complement Coding for FA

• Input values normalized between 0 and 1:– (for red color)

• Complement of a:–

• Complement Encoded Input:–

,( ) ( ) 255r ary ra k I k

( ) 1 ( )ca k a k

, , , , ,( ) ( ) ( ) ( ) ( ) ( ) ( )c c cr g b r g bk a k a k a k a k a k a kX , , , , ,( ) ( ) ( ) ( ) ( ) ( ) ( )c c cr g b r g bk a k a k a k a k a k a kX

( ) 1 ( )ca k a k

, , , , ,( ) ( ) ( ) ( ) ( ) ( ) ( )c c cr g b r g bk a k a k a k a k a k a kX

,( ) ( ) 255r ary ra k I k

( ) 1 ( )ca k a k

, , , , ,( ) ( ) ( ) ( ) ( ) ( ) ( )c c cr g b r g bk a k a k a k a k a k a kX


Fuzzy ART Classification

• Fuzzy ART groups pixels with similar RGB values into the same cluster (with CL total clusters)

• Pixels belonging to cluster p are labeled – – – Where

, , ,, , , , ,( ) ( ) ( ) ( ) ( ) ( ) ( )p p p p c p c p c

r g b r g bk a k a k a k a k a k a kpX

1,2,..., Lp C


Cluster Assignment

• Average– The Red, Blue and Green color components,

for all pixels in cluster p, are averaged together:

• (for red color)

– Output for pixel at position (i,j):•

,

1,p p

r in rpp

A I i jN

, , ,p p pr g bi j A A AO


Cluster Assignment

• Median– Calculate median of red, green and blue color

components in single cluster p– Output at position (i,j) is pixel cluster’s median

•

• Trimmed Average– Sort individual color components in cluster P in

ascending order – Calculate mid 1/3 average (of each color

component)– Represent Output as Trimmed Average

•

, , ,p p pr g bi j M M MO

, , ,p p pr g bi j TA TA TAO


Performance Metrics

• Algorithm Execution Time (Machine Specific)• Processor - AMD 3700, 2.2 GHz (Single Core)

• Ram - 2GB of DDR400

– RMSE Between Original and CQ Image• MSE for red color comp. defined as follows:

• Taking average and square root of MSEr, MSEg, and MSEb

2

,1 1

1, ( , )

R C

r r in ri j

MSE O i j I i jR C

1

3 r g bRMSE MSE MSE MSE


Experiments

• Three sets of experiments conducted at incremental values of vigilance parameter– First set – Forced Stop after Single Epoch

• and (one shot learning)

– Second Set – Forced Stop after Three Epochs• and

– Third Set – Algorithm ran until convergence• and • Convergence: no new classes created

1 0.0001

0.8 0.1

0.8 0.01 0.8 0.01 0.8

0.1

0.01 0.8

0.8 0.1

0.01 0.8

1

0.8 0.1

0.01 0.8

0.0001 1

0.8 0.1

0.01 0.8


RMSE vs. Vigilance Parameter

RMSE vs. Vig. for Epochs for Mandrill

0.00

5.00

10.00

15.00

20.00

25.00

30.00

0.5 0.6 0.7 0.8 0.9

Vigilance ParameterR

oo

t M

ean

Sq

uar

e E

rro

r

Single Epoch Three Epochs Convergence

RMSE vs. Vig. for Epochs for Lenna

0.00

5.00

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30.00

0.5 0.6 0.7 0.8 0.9

Vigilance Parameter

Ro

ot

Mea

n S

qu

are

Err

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Single Epoch Three Epochs Convergence


Experiments cont.

• Six Additional Sets of Experiments– 3 Cluster Assignment Methods Tested on

Mandrill– 3 Cluster Assignment Methods Tested on

Lenna– Vigilance parameter fine tuned so resulted CQ

Image had 16, 32, 64, 128, 256 and 512 colors


Lenna and Mandrill Images

• Lenna– Image Dimensions – 512x512– Number of Colors – 148,279

• Mandrill– Image Dimensions – 512x512– Number of Colors – 230,427


RMSE for Diff Cluster Assignment Methods

RMSE for Diff. Output Methods for Lenna

0.00

2.00

4.00

6.00

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12.00

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16.00

18.00

16 32 64 128 256 512

Colors

Ro

ot

Mea

n S

qu

are

Err

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AVG Med Col Trim AVG

RMSE for Diff. Output Methods for Mandrill

0.00

5.00

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16 32 64 128 256 512

ColorsR

oo

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ean

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rro

r

AVG Med Col Trim AVG


Original Lenna and Lenna 64 Color


Original Mandrill and Mandrill 64 Color


Experiments with Natural Scenes

• Images depict commercial and residential buildings in Fairfield, Australia

• Images have 15cm pixel resolution• Scene 1

– Image Dimensions - 1510x1973 Pixels– Number of Colors – 698,843

• Scene 2– Image Dimensions – 1595x1878– Number of Colors – 519,513


Scene 1 Original


Scene 1 64 Color


Scene 2 Original


Scene 2 64 Color


Scene 1 Original vs CQ


Scene 2 Original vs CQ


Execution Times For Images• 256 Colors

– Lenna Image 22 Seconds– Mandrill Image 23 Seconds– Natural Scene 1* 295 Seconds (~4.9 minutes)– Natural Scene 2* 259 Seconds (~4.3 minutes)

• 512 Colors– Lenna Image 40 Seconds– Mandrill Image 42 Seconds– Natural Scene 1* 583 Seconds (~9.7 minutes)– Natural Scene 2* 576 Seconds (~9.6 minutes)

*Recall Images are ~1500x~1900 Pixels (10 times more the number of pixels than Lenna and Mandril)


Discussion of Results

• Lenna looks better because it originally has 80,000 colors less than Mandrill

• Letting FA execute for more than 1 epoch– does not yield significant decrease in RMSE for vig >

0.5 (more than 16 CQ colors)

– Recommend One Shot Stable Learning and only input list presentation

• Averaging output method yielded best RMSE and lowest execution time– When compared to Median and Trimmed Average


Conclusions

• Algorithm Advantages– Proposed FA CQ (one shot stable learning) completes

execution after only single input presentation• The methods proposed in (Ashutosh et. al, 2007) require

multiple input presentations

• Method proposed in (El-Mihoub et. al, 2006) runs until stop criteria is met

• Algorithm Disadvantages– Quick execution comes at a cost of an increase in

RMSE

– Cannot directly specify number of quantized colors


Comparing RMSE

• El-Mihoub et. al, 2006– RMSE for Lenna 16 Color Quantization

• Ashutosh et. al, 2007– RMSE for Lenna at 32, 64, 128 and 256

Colors 32 64 128 256FACQ RMSE 20.91 16.72 13.29 10.34MFOCPN RMSE 13.7 10.3 8.5 6

Popalg Medct FA CQ Octree Neuqu SAHGARMSE 19.7 16.5 15.6 10.8 10.4 9.7


Future Work

• Using FA CQ as preprocessor to JSEG– Using JSEG to segment aerial images

containing buildings– Using segmented images as low level features

for automatic building detection

• Explore use of additional features to account for pixel’s location and context in image (in addition to RGB value)


Acknowledgements

• Harris Cooperation for their Funding

• Fairfield Data Set from Dr. Simon Clode, Dr. Franz Rottensteiner, AAMHatch

fuzzy art for relatively fast unsupervised image color quantization

Documents

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