1. An Multiple Regression Analysis Based Color Transform Between Objects Speaker ： Chen-Chung Liu 1

2. Outline Introduction The proposed algorithm ◦ Color Objects Extraction Algorithm Using Multiple Thresholds (COEMT) ◦ Color Transform Using Multiple Regression Analysis (MRA) Conclusions 2

3. 1. Introduction(1/3) Art purpose 3

4. 1. Introduction (2/3) Image analysis (details increasing) 4

5. 1. Introduction (3/3) Image analysis (image simplify) 5

6. The proposed algorithm 6 Figure 1. The flow chart of the proposed color transformation algorithm.

7. 2.1.Color Objects Extraction(1/17) Figure 2. Color objects extraction algorithm flow chart. 7

8. Figure 3. Pixels values distribution on different planes. Figure 3. Pixels values distribution on different planes. 2.1.Color Objects Extraction (2/17) 8

9. 2.1.Color Objects Extraction (3/17) Figure 4. Intensity versus RGB and saturation versus RGB. 9

10. 2.1.Color Objects Extraction (4/17) Figure 5. The flow chart of EOAFF on HSI domain. 10

11. 2.1.Color Objects Extraction(5/17) 11

12. 2.1.Color Objects Extraction(6/17) 12

13. 2.1.Color Objects Extraction(7/17) 13

14. 2.1.Color Objects Extraction(8/17) 14

15. Filter’s thresholds of hue, saturation, and intensity 2.1.Color Objects Extraction(9/17) 15

16. 2.1.Color Objects Extraction(10/17) Figure 6. An example of the proposed adaptive forecasting filter‘s working. 16

17. 2.1.Color Objects Extraction(11/17) Figure 7. An example of the proposed scheme. 17 original image union result CS result BSE result

18. 2.1.Color Objects Extraction(12/17) 18 Figure 8. Test image: Pink hat. original image with seeds DTS in RGBDTS in HSI proposed scheme C. C. Liu and G. N. Hu, Color Objects Extraction Scheme Using Dynamic Thresholds (DTS), 2009 Workshop on Consumer Electronics (WCE2009), pp. 1130-1138, 2009.

19. 2.1.Color Objects Extraction(13/17) 19 Figure 9. Test image: Flowers. original image with seeds DTS in RGBDTS in HSI proposed scheme

20. 2.1.Color Objects Extraction(14/17) 20 Figure 10. Test image: Pottery. original image with seedsDTS in RGB DTS in HSIproposed scheme

21. 2.1.Color Objects Extraction(15/17) 21 Figure 11. Test image: Cup set. original image with seedsDTS in RGB DTS in HSIproposed scheme

22. 2.1.Color Objects Extraction(16/17) 22 Figure 12. Test image: Sun flower. original image with seeds DTS in RGB DTS in HSIproposed scheme

23. Image Extraction scheme MERFAEEMMNUMHDAccuracy Pink hat (325×415) DTS on RGB0.03550.25490.83190.86964.40610.9645 DTS on HSI0.00790.05370.09750.86290.6960.9921 Proposed0.00790.03970.09490.86150.06250.9921 Flowers (172×222) DTS on RGB0.37260.85860.95564.427211.73710.6274 DTS on HSI0.05140.11190.18351.12900.18480.9486 Proposed0.01860.00850.06640.63150.03720.9814 Pottery (350×251) DTS on RGB0.31400.83050.90121.558816.19600.6860 DTS on HSI0.08410.22670.49830.95220.49270.9159 Proposed0.01600.02630.04610.67200.03720.9840 Cup set (599×399) DTS on RGB0.06210.14900.65421.23890.53220.9379 DTS on HSI0.02860.06770.18740.75660.24940.9714 Proposed0.00660.00590.04170.62140.01240.9934 Sunflower (768×1024) DTS on RGB0.37160.83230.97841.159795.45960.6284 DTS on HSI0.37950.81810.96501.149293.87530.6205 Proposed0.04340.08620.48410.54300.01210.9566 2.1.Color Objects Extraction(17/17) 23 Table 1. Comparisons of extraction results

24. Multiple Regression Analysis (1/5) For data of ordered pairs We want to predict y from x by finding a function that fits the data as closely as possible. 2.2. MRA_based Color Transform(1/20) 24

25. Multiple Regression Analysis (2/5) MRA is used to find a polynomial function of degree, as the predicting function, that has the minimum of the sum of squares of the errors(SSE) between the predicted values of y and the observed values for all of the n data points. 2.2. MRA_based Color Transform(2/20) 25

26. Multiple Regression Analysis (3/5) The values of,,,…,and that minimize are obtained by setting the first partial derivatives,,…, and equal to zero. 2.2. MRA_based Color Transform(3/20) 26

27. Multiple Regression Analysis (4/5) Solving the resulting simultaneous linear system of the so-called normal equations: 2.2. MRA_based Color Transform(4/20) 27

28. Multiple Regression Analysis (5/5) The matrix form solution be where 2.2. MRA_based Color Transform(5/20) 28

29. 2.2. MRA_based Color Transform(6/20) 29 Figure 13. Target object.

30. 2.2. MRA_based Color Transform(7/20) 30 Figure 14. Source object.

31. Best fitting functions 2.2. MRA_based Color Transform(8/20) 31 RedGreenBlue Figure 15. The curves of degree1, 5, and 9 best fitting functions.

32. 2.2. MRA_based Color Transform(9/20) 32 Figure 16. The color transfer results corresponding to the variation in the degree of best fitting polynomials.

33. 2.2. MRA_based Color Transform(10/20) 33 L*a*b* Figure 17. The box-plots of L*, a*, and b* for the target, source, and color transferred objects in Figure 11.

34. CIELAB L*a*b* MEANSTDMEANSTDMEANSTD Dress150.430451.46917106.42368.978589117.77095.477925 chrysanthemum215.671139.28094124.72227.944162200.105726.23079 Degree 1217.829231.33225123.69168.801648195.963128.19823 Degree 2220.721536.31317125.550210.58648196.376930.15897 Degree 3220.22735.17295127.664910.90815196.602929.94967 Degree 4220.203433.89269126.890611.99645196.317130.07789 Degree 5220.272733.9665126.950811.82427196.553629.75918 Degree 6220.278133.79962126.995111.82259196.376630.00075 Degree 7220.398833.6955127.098511.97724196.568129.82683 Degree 8221.886730.26971126.462911.09722197.157729.23962 Degree 9222.843729.33692125.709711.85683193.991329.53413 2.2. MRA_based Color Transform(11/20) 34 Table 2. The measurement metrics for the target, source and color transferred objects in Figure 17 (1/2)

35. CIELAB C*H*E* MEANSTDMEANSTDMEANSTD Dress 158.7859.69240142.040981.432582221.787137.35482 chrysanthemum 236.502420.3878732.303294.79458321.949227.47353 Degree 1 232.656321.089332.711535.441701320.265620.85404 Degree 2 234.177722.5643533.088835.885266323.778123.50912 Degree 3 235.451723.0103833.469085.704993324.393321.74743 Degree 4 234.875322.8860233.350775.926351323.891420.56034 Degree 5 235.065122.7958433.319845.809531324.087920.39675 Degree 6 234.962522.889233.361955.875098323.999920.49778 Degree 7 235.160722.9257633.347575.816235324.225420.37048 Degree 8 235.195922.9131533.12055.521752325.013518.92759 Degree 9232.150723.5463733.389385.610419323.509717.60135 2.2. MRA_based Color Transform(12/20) 35 Table 2. The measurement metrics for the target, source and color transferred objects in Figure 17 (2/2)

36. The target RGB color image is a girl in a blue dress (350×350 pixels). The source color images with different sizes. 2.2. MRA_based Color Transform(13/20) 36 ImageSize (pixel) Blue Roses528×458 Wool Hat450×377 Potted Plant750×1000 Amber399×354 Carnation Flower640×480

37. The extraction procedure lasted between 3 and 25 seconds, and the color transferring procedure lasted about 0.03 seconds. 2.2. MRA_based Color Transform(14/20) 37

38. 2.2. MRA_based Color Transform(15/20) 38 Figure 20. Examples of color transferring between objects with the proposed multiple regression analysis algorithm (1/2).

39. 2.2. MRA_based Color Transform(16/20) 39 Figure 21. Examples of color transferring between objects with the proposed multiple regression analysis algorithm (2/2).

40. Performance measures function: 2.2. MRA_based Color Transform(17/20) 40

41. 2.2. MRA_based Color Transform(18/20) 41 CIELAB L*a*b* MEANSTDMEANSTDMEANSTD Blue dress150.430451.46917106.42368.978589117.77095.477925 Blue roses144.574341.92839134.401713.1304274.827816.13991 Wool hat156.117740.65138106.235613.22336162.011222.88793 Potted plant145.215937.9356399.255799.785787171.883414.54883 Amber145.216336.49202108.842721.26773173.322914.33429 Carnation147.322940.41436150.093433.074180.1815419.15783 CIELAB C*H*E* MEANSTDMEANSTDMEANSTD Blue dress158.7859.69240142.040981.432582221.787137.35482 Blue roses154.98878.62681460.804936.876357214.632526.2399 Wool hat195.139912.3608533.65047.001189252.306824.4726 Potted plant199.03659.35587230.146594.365411248.277624.25018 Amber205.627616.2058732.01845.473507253.651925.00947 Carnation171.544631.4717761.455527.181401229.262934.55282 Table 3. The measurement metrics for the target and source objects in Figures 20,21

42. 2.2. MRA_based Color Transform(19/20) 42 CIELAB L*a*b* MEANSTDMEANSTDMEANSTD Blue roses163.318555.63949128.507417.0255790.4183731.5838 Wool hat188.812639.31711126.217512.73377130.383311.19284 Potted plant162.481453.23631102.419123.91867162.492421.23415 Amber168.295352.25107142.565116.45696164.56621.28246 Carnation169.981447.76056185.628633.01946102.968516.23654 CIELAB C*H*E* MEANSTDMEANSTDMEANSTD Blue roses160.051818.9847655.3171510.59851231.989343.89292 Wool hat181.843512.2898344.024493.452397264.100625.78697 Potted plant194.418810.8495232.271668.746327257.289330.86813 Amber218.257622.2291240.981294.046821280.646420.53054 Carnation214.366121.4830960.225788.366982277.923118.64821 Table 4. The measurement metrics for the color transferred target objects in Figures 20, 21

43. CIELAB Δ L* Δ L*(%) Δ a* Δ a*(%) Δ b* Δ b*(%) Blue roses18.7442211.477095.894274.58671515.5905717.2427 Wool hat32.6948717.3160519.9818815.8313131.6279124.25764 Potted plant17.2655410.626163.1632663.0885529.3910595.779385 Amber23.0789813.7133833.722423.654048.7568625.321186 Carnation22.658513.3299935.535219.1431722.7869522.13002 2.2. MRA_based Color Transform(20/20) 43 CIELAB Δ C* Δ C*(%) Δ H* Δ H*(%) ΔEΔE Δ E*(%) Blue roses5.0631213.1634265.4877789.92057317.356847.481743 Wool hat13.296397.31199510.3740923.5643511.793754.46563 Potted plant4.6176752.3751172.1250716.5849449.0117273.502566 Amber12.630075.7867738.96289121.8706926.994459.618671 Carnation42.8215219.975881.2297372.04187848.6602117.50852 Table 5. The absolute difference in measurement metrics of the transferred target-object from the source object in Figures 20 and 21

44. Simple, effective and accurate in color transferring between objects. Details of target object can be changed by the color complexity of source object. Time consumption is independent of the number of bins selected and the degree of regression. Dynamic ranges of colors of objects don’t have any restriction. Conclusions 44

45. 45 Thank You Questions and Comments