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

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

1. Introduction(1/3) Art purpose 3

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

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

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

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

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

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

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

2.1.Color Objects Extraction(5/17) 11

2.1.Color Objects Extraction(6/17) 12

2.1.Color Objects Extraction(7/17) 13

2.1.Color Objects Extraction(8/17) 14

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

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

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

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 , 2009.

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

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

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

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

Image Extraction scheme MERFAEEMMNUMHDAccuracy Pink hat (325×415) DTS on RGB DTS on HSI Proposed Flowers (172×222) DTS on RGB DTS on HSI Proposed Pottery (350×251) DTS on RGB DTS on HSI Proposed Cup set (599×399) DTS on RGB DTS on HSI Proposed Sunflower (768×1024) DTS on RGB DTS on HSI Proposed Color Objects Extraction(17/17) 23 Table 1. Comparisons of extraction results

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 MRA_based Color Transform(1/20) 24

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 MRA_based Color Transform(2/20) 25

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

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

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

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

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

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.

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.

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.

CIELAB L*a*b* MEANSTDMEANSTDMEANSTD Dress chrysanthemum Degree Degree Degree Degree Degree Degree Degree Degree Degree 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)

CIELAB C*H*E* MEANSTDMEANSTDMEANSTD Dress chrysanthemum Degree Degree Degree Degree Degree Degree Degree Degree Degree 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)

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

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

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).

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).

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

2.2. MRA_based Color Transform(18/20) 41 CIELAB L*a*b* MEANSTDMEANSTDMEANSTD Blue dress Blue roses Wool hat Potted plant Amber Carnation CIELAB C*H*E* MEANSTDMEANSTDMEANSTD Blue dress Blue roses Wool hat Potted plant Amber Carnation Table 3. The measurement metrics for the target and source objects in Figures 20,21

2.2. MRA_based Color Transform(19/20) 42 CIELAB L*a*b* MEANSTDMEANSTDMEANSTD Blue roses Wool hat Potted plant Amber Carnation CIELAB C*H*E* MEANSTDMEANSTDMEANSTD Blue roses Wool hat Potted plant Amber Carnation Table 4. The measurement metrics for the color transferred target objects in Figures 20, 21

CIELAB Δ L* Δ L*(%) Δ a* Δ a*(%) Δ b* Δ b*(%) Blue roses Wool hat Potted plant Amber Carnation MRA_based Color Transform(20/20) 43 CIELAB Δ C* Δ C*(%) Δ H* Δ H*(%) ΔEΔE Δ E*(%) Blue roses Wool hat Potted plant Amber Carnation Table 5. The absolute difference in measurement metrics of the transferred target-object from the source object in Figures 20 and 21

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 Thank You Questions and Comments