fuzzy art for relatively fast unsupervised image color quantization
DESCRIPTION
Fuzzy ART for Relatively Fast Unsupervised Image Color Quantization. Nicholas S. Shorter [email protected]. Takis Kasparis [email protected]. Research Website: http://www.nshorter.com. School of Electrical Engineering and Computer Science University of Central Florida - PowerPoint PPT PresentationTRANSCRIPT
http://www.nshorter.com 1
Fuzzy ART for Relatively Fast Unsupervised Image Color Quantization
Takis Kasparis
Nicholas S. Shorter
School of Electrical Engineering and Computer ScienceUniversity of Central Florida
Orlando, Florida, 32816 USA
Research Website:http://www.nshorter.com
http://www.nshorter.com 2
Presentation Outline
• Research Objectives
• Fuzzy ART
• Cluster Assignment Methods
• Performance Metrics
• Experiments
• Results Discussion
• Conclusions
http://www.nshorter.com 3
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
http://www.nshorter.com 4
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
http://www.nshorter.com 5
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
http://www.nshorter.com 6
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
http://www.nshorter.com 7
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
http://www.nshorter.com 8
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
http://www.nshorter.com 9
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
http://www.nshorter.com 10
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
http://www.nshorter.com 11
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
http://www.nshorter.com 12
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
http://www.nshorter.com 13
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
10.00
15.00
20.00
25.00
30.00
0.5 0.6 0.7 0.8 0.9
Vigilance Parameter
Ro
ot
Mea
n S
qu
are
Err
or
Single Epoch Three Epochs Convergence
http://www.nshorter.com 14
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
http://www.nshorter.com 15
Lenna and Mandrill Images
• Lenna– Image Dimensions – 512x512– Number of Colors – 148,279
• Mandrill– Image Dimensions – 512x512– Number of Colors – 230,427
http://www.nshorter.com 16
RMSE for Diff Cluster Assignment Methods
RMSE for Diff. Output Methods for Lenna
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
16 32 64 128 256 512
Colors
Ro
ot
Mea
n S
qu
are
Err
or
AVG Med Col Trim AVG
RMSE for Diff. Output Methods for Mandrill
0.00
5.00
10.00
15.00
20.00
25.00
30.00
16 32 64 128 256 512
ColorsR
oo
t M
ean
Sq
uar
e E
rro
r
AVG Med Col Trim AVG
http://www.nshorter.com 17
Original Lenna and Lenna 64 Color
http://www.nshorter.com 18
Original Mandrill and Mandrill 64 Color
http://www.nshorter.com 19
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
http://www.nshorter.com 20
Scene 1 Original
http://www.nshorter.com 21
Scene 1 64 Color
http://www.nshorter.com 22
Scene 2 Original
http://www.nshorter.com 23
Scene 2 64 Color
http://www.nshorter.com 24
Scene 1 Original vs CQ
http://www.nshorter.com 25
Scene 2 Original vs CQ
http://www.nshorter.com 26
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)
http://www.nshorter.com 27
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
http://www.nshorter.com 28
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
http://www.nshorter.com 29
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
http://www.nshorter.com 30
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)
http://www.nshorter.com 31
Acknowledgements
• Harris Cooperation for their Funding
• Fairfield Data Set from Dr. Simon Clode, Dr. Franz Rottensteiner, AAMHatch