1. Sub-image Searching Using Genetically-Evolved Wavelet Transforms By Chris Wedge

2. Evolved Transform Coefficients Wavelets capable of lossless compression in a perfect conditions Dr. Frank Moore showed superior coefficients could be evolved in imperfect conditions Very time-intensive

3. Evolution on Sub-images Don Tinsley and Jason Kettell explored evolution with sub-images Similar performance gains but with computation time drastically reduced Noted performance disparity between sub- image and super-image Can disparity be exploited?

4. Where’s Waldo?

5. Search Algorithms Four algorithms used, though basically all the same: iteratively apply transform –Strict repeated transform application Interesting side-effects with quantization –Repeated transform application, but quantize only once –Repeated transform application, only on Y Again, side-effects present –Repeated transform application, only on Y, but quantize only once Search focus placed on developing high- performance transforms

6. Performance Evaluation Two methods of evaluation –Quantitative Compare mean-squared error (MSE) values between sub-image and super-image –“Anecdotal” MSE comparisons may indicate improvement, but searching meant for human consumption

7. Meet The Crew

8. Simple Evolution Evolve versus non-representative sub- image Repeatedly apply resulting transforms using search algorithms

9. Simple Evolution - Parameters 24 total runs –Fixed parameters Daubechies-4 (D4) wavelet used as basis wavelet Population (M) = 5000 Generations (G) = 2500 Multi-resolution (MR) = 1 Sub-image size 32x32 pixels (regular is 512x512) –Variable parameters 4 images 3 quantization (Q) levels: 0, 32, 64 2 threshold (T) levels: 0, 16

10. Simple Evolution - Results 24 runs –1 run each per Q, T, image combination –Mean runtime 63min 57sec, St Dev 0.00144 –MSE reductions over D4 on sub-image Q=64: 3.5%, 15.0%, 8.8%, 16.2%* Q=32: 4.8%, 11.0%, 5.2%, 22.3%* Q=0: –T=16: 7.9%, 6.7%, 1.8%, 12.4%* –T=0: 25.6%, 30.3%, 19.3%, 49.4%* –MSE reductions over D4 on super-image Q=64: 7.9%, -1.3%, 6.8%, 83%* Q=32: 3.9%, 6.7%, 4.6%, 84.1%* Q=0: –T=16: 7.6%, 1.9%, 1.4%, 95.6%* –T=0: 24.9%, 44.8%, 18.9%, 99.6%* –*(lenna, goldhill, monet, and dissimilar, respectively)

11. Simple Evolution - Results 

12. Simple Evolution - Conclusions MSE reduction of sub-image over parent image seems somewhat arbitrary –More runs needed to get a better picture, but want a general method which always works, so little point exploring that T has no effect if it is set to a value less than Q –Not surprising. Should have been obvious before running the tests MSE reduction at Q = 0 is by far the highest –Very surprising! Wavelets theoretically capable of lossless compression. Attributed to imprecision of floating-point arithmetic Dissimilar, the toy image, had some impressive results! Unfortunately, they are far from the desired results, and not exactly realistic

13. Detour! Non-representative sub-image did not perform as well as expected Representative sub-image performance –Revisiting Tinsley’s, Kettell’s work to concretize More runs More fixed parameters (size, etc) –But what is representative? No determination algorithm, criteria mentioned, largely subjective Ended up using miniature versions of the image

14. Detour! - Parameters 63 total runs –Fixed parameters D4 wavelet used as basis wavelet M = 5000 G = 2500 MR = 1 T = 0 Mini-image size 32x32 pixels (regular is 512x512) –Variable parameters 4 images 3 Q levels: 0, 32, 64

15. Detour! - Results Evolution versus single image –60 runs 5 per combination of Q level, image Mean runtime 63min 51sec, St Dev 0.00065 Mean MSE reductions over D4 –Q=64: 5.5% - 8.3% –Q=32: 2.4% - 2.7% –Q=0: 16.7% - 25.1%

16. Detour! - Results Evolution versus all images –3 runs 1 for each Q level –Wanted 5 each, but bugs, time constraints got in the way Mean runtime 250min 57sec, St Dev 0.00212 MSE reduction over D4 –Q=64: 6.4% - 9.5% –Q=32: 3.9% - 5.2% –Q=0: 17.3% - 27.2%

17. Detour! - Results 4.5% improvement

18. Detour! - Conclusions MSE improved over D4 in every run –Excluding Q=0, higher Q values may increase improvement, but need more Q levels tested –Improvement even noticed when transform applied to different images Single-image mean runtime approximately 98% lower than in Dr. Moore’s runs Four-image evolution outperformed single-image evolution, but more runs needed Four-image mean runtime approximately 91% lower than in Dr. Moore’s runs

19. Back to searching… Simple evolution failed to do the trick Want very good performance on desired sub-image Also want very poor performance on the whole But how to do both simultaneously?

20. Co-evolution Alter the GA to use a weighted fitness function –Total fitness = sub-image “goodness” + super-image “badness”. –Can “weight” the importance of each aspect to drive evolution SUBIMAGE_WEIGHT = 50; SUPERIMAGE_WEIGHT = 100; … fitness[M] = (subMSE / minSubImageMSE) * SUBIMAGE_WEIGHT + (maxParentMSE / parentMSE) * SUPERIMAGE_WEIGHT;

21. Co-evolution - Parameters 25 total runs so far –Fixed parameters D4 basis wavelet M = 500 G = 200 MR = 1 T = 0 Sub-image size 32x32 pixels (super is 512x512) –Variable parameters 3 images 3 Q levels: 0, 32, 64 3 weightings used (sub vs super) : 50 vs 100, 100 vs 50, 100 vs 100

22. Co-evolution - Results Mean runtime 242min 26sec, St Dev 0.00149 25 runs –1 for each image, Q level, weight combination* –Results vary wildly! –*Two Monet runs unfinished

23. Co-evolution - Results

24. Co-evolution - Conclusions Does seem to be a slight trend in favor of weights D4 MSEs of sub-image vs super-image is inconsistent Low M, G does not give much time to evolve

25. Finishing Up… Last two Monet co-evolves Co-evolution using mini-images as the super-image –Runtime reduction –Increased G, M

26. That Which Could Not Be Finishing additional four-image mini-image runs In general, more runs More parameter testing explored Unless mini co-evolution proves fruitful, unable to get search working

27. Extensions Forward transforms Variable-length transforms Evolve versus Y, U, V instead of just Y Initially seed coefficients randomly Adapt for distributed / parallel computing

28. Fin Questions?