Fuzzy ART: Efficient Unsupervised Image Color Quantization for Large Images

1. Fuzzy ART for Relatively Fast Unsupervised Image Color Quantization Nicholas S. Shorter nshorter@mail.ucf.edu Takis Kasparis kasparis@mail.ucf.edu Research Website: http://www.nshorter.com School of Electrical Engineering and Computer Science University of Central Florida Orlando, Florida, 32816 USA 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 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: 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 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): 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 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 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 http://www.nshorter.com

13. RMSE vs. Vigilance Parameter 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 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 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 http://www.nshorter.com