Shades of Gray and Colour Constancy

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1 Shades of Gray and Colour Constancy IS&T/SID Twelfth Color Imaging Conference , 2004 Graham D. Finlayson and Elisabetta Trezzi Presented by Jung-Min Sung School of Electrical Engineering and Comuter Science Kyungook ational Univ.

2 Proosed method Max-RGB & Gray-World Abstract Instantiations of Minkowski norm Otimal illuminant estimate L 6 norm: Working best overall 2/19

3 Introduction Categories of color constancy Reresenting an image by illuminant invariant descritors Color constancy methods Physical-based algorithm Statistic-based algorithm Max-RGB, Gray-World, Gray-Edge Gamut constrained algorithm Probability-based algorithm Markov Random Field, Conditional Random Field Learning-based algorithm 3/19

4 Problem of Max-RGB & Gray-World Two extremes in the Minkoswki family norm Mean(L 1 ) and Maximum(L ) Assuming the otimal illuminant estimate is between L 1 and L 4/19

5 Background Modeling a color signal Assuming illuminance E λ is uniform over a scene A Lambertian surface illuminated by a sectral distribution C λ = E λ S λ (1) where E λ : Sectral distribution S λ : Lambertian surface C λ : Color signal 5/19

Sensitivity function An image reresented by three -dimensional vector

6 Intensity on three sensors (R, G, B) E λ R λ G λ B λ R G B = E λ S λ R λ dλ = E λ S λ G λ dλ = E λ S λ B λ dλ S λ Sensor resonse curve Or Sensitivity function An image reresented by three -dimensional vector Given image I I:image R = [R 1, R 2,, R ] T G = [G 1, G 2,, G ] T B = [B 1, B 2,, B ] T 6/19

7 One ixel intensity over the image R i = E λ S i λ R λ dλ G i = E λ S i λ G λ dλ (3) B i = E λ S i λ B λ dλ I:image Position: i 7/19

8 Conventional algorithms Max-RGB Assuming that at least a white atch exist in an image max R i = E λ R λ dλ i 1,2,, = R e max G i = E λ G λ dλ i 1,2,, = G e (7) max i 1,2,, B i = E λ B λ dλ = B e I:image 1 8/19

9 Gray-world Assuming that a scene average is grey μ S λ = S i λ = k S i λ I:image μ R = E λ S i λ μ G = E λ S i λ μ B = E λ S i λ R λ dλ G λ dλ B λ dλ = kk e = kk e = kk e (6) 9/19

10 Minkowski family norm Minkowski norm Definition of -norm for X = X 1, X 2,, X T 1/ X = X i (8) Examle of 2 norm Equal to Euclidean distance X 2 = X i 2 1/2 = X X X 2 10/19

11 Mean of -norm Mean of -norm for X = X 1, X 2,, X T μ X = X 1/ = X 1 + X X (11) Proerty of Minkowski norm Triangular inequality: Equation (8) in this aer Monotonically increasing sequence X 1/ X q 1 q, ii q Infinity norm X = max 0 i X i 11/19

12 Proosed method Exression of Max-RGB & Gray-world with Minkowski norm Max-RGB R e G e B e = μ R μ G μ B Gray-World R e G e B e = μ 1 R μ 1 G μ 1 B 12/19

13 Order relationshi between Max-RGB and Gray-World Max-RGB μ 1 R μ 2 R μ R Gray-World μ 1 G μ 2 G μ G μ 1 B μ 2 B μ B Proosed method: (Shade of grey algorithm) Assuming that the average of ixels raised to the ower of is gray R,i = E λ S i λ R λ dλ = E λ S i λ R λ dλ (15) = E λ σ i λ R λ dλ = R i 13/19

14 Extension of this formula to R,G,B R,i = G,i = B,i = E λ S i λ R λ dλ E λ S i λ G λ dλ E λ S i λ B λ dλ = E λ σ i λ R λ dλ = E λ σ i λ G λ dλ = E λ σ i λ B λ dλ = R i = G i = B i (16) I:image Shade of grey algorithm Assumtion S i λ μ S λ = S i λ 1/ = k 14/19

15 μ R = E λ S i λ μ G = E λ S i λ μ B = E λ S i λ R λ dλ G λ dλ B λ dλ 1/ 1/ 1/ = k R e = k G e = k B e where R = R 1, R 2,, R T, G = G 1, G 2,, G T, B = B 1, B 2,, B T 15/19

16 Exerimental evaluation Evaluation by using angular error Using two databases Data set suggested Barnard et al. One consisting of 321 images of a variety of 32 scenes Another of 220 images of a variety of 22 scenes Both grous taken under 11 coloured illuminant\ Comarison measure Angular error: Equation (18) in this aer Distance error in the chromaticity sace: Equation (19) in this aer 16/19

17 L 6 norm: Working best overall Fig. 2. The figure shows the angular error of the grou A images for 30 values of Fig. 3. The figure shows the angular error of the grou B images for 30 values of 17/19

18 Table 1. Results for the shade of grey algorithm on two databases considered: the firsts two columns are the mean of angular errors and the lasts two reort the distance error in the chromaticities sace. 18/19

19 Shade of grey algorithm Performance Conclusion L 6 norm: Working best overall Comarable to many advanced colour constancy algorithm for the norm 6 algorithm But, significant comutational cost 19/19

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