Gray-World assumption on perceptual color spaces. Universidad de Guanajuato División de Ingenierías Campus Irapuato-Salamanca

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1 Gray-World assumption on perceptual color spaces Jonathan Cepeda-Negrete Raul E. Sanchez-Yanez Universidad de Guanajuato División de Ingenierías Campus Irapuato-Salamanca

2 Outline 1. Introduction Color constancy Related work Our proposal 2. Methodology Gray-World assumption Our approaches 3. Experimental Results Benchmark used Metric for the evaluation Results 4. Conclusions 2

3 Section INTRODUCTION

4 Introduction Color Constancy The ability of a system to recognize the correct colors, independently of the color source present in a scene is known as Color Constancy [1]. Figure 1. Result of a color constancy algorithm upon an image. 4 [1] S. Zeki, A vision of the brain, J. Wiley and sons, Eds. Wiley-Blackwell, January 15, (1993).

5 Introduction Related Work Most color constancy algorithms have been proposed and implemented in the RGB color space, and, in spite of the existence of a considerable number of methods, there is not a general solution for the color constancy problem. Gray-World assumption. White-Patch Shades of Gray Gray-Edges...etc. Among the few research works addressing on the estimation of the illuminant on perceptual color spaces we can mention the study by Kloss [2], where the illuminant was estimated using WP and GW algorithms on CIELAB. 5 [2] Kloss GK. Colour Constancy using von Kries Transformations Colour Constancy goes to the Lab. Res Lett Inf Math Sci.; 13: pp (2009).

6 Introduction Our Proposal In this study, we propose the estimation of the illuminant directly on a perceptual color space. Thus, we focus on solving the color constancy problem. The GW assumption is analyzed in two perceptual color spaces. Specifically, the well-known CIE 1976 L a b (CIELAB) and the CIE 1976 L u v (CIELUV) in order to provide a simple and fast transformation. The standard GW approach on the RGB color space, and the GE algorithm [3] are included for reference purposes. 6 [3] van de Weijer J, Gevers T, Gijsenij A. Edge-Based Color Constancy. IEEE Trans Image Process; 16(9): pp (2007).

7 Section METHODOLOGY

8 Methodology Methodology The outcomes of GW approach in two perceptual color spaces are compared with those obtained using the standard GW, as depicted in the figure. Gray-World algorithm RGB CIELab Figure 2. Methodology for the experimental tests. 8 CIELuv

9 Methodology Image Transformation The algorithm considered throughout this work assumes that the illumination is uniform across the scene. Equation (1) gives the relationship for the color intensity, f ( x, y) = G( x, y) R ( x, y) I i i i (1) The outcome image is given by o i (x, y) = f i(x, y) I i = G(x, y)r i (x, y) (2) 9

10 Methodology Gray-World Algorithm The Gray World assumption (GW) is the most popular algorithm for color constancy. Proposed by Buchsbaum [4], it is used as reference for other algorithms. The GW is based on the assumption that, on average, the real world tends to gray, and estimates the illuminant using the average color of all pixels. a i = 1 MN M 1 N 1 x=0 y=0 f i (x, y) (3) o ( x, y) = i fi ( x, y) 2a i (4) 10 [4] G. Buchsbaum. A spatial processor model for object colour perception. Journal of The Franklin Institute-engineering and Applied Mathematics, 310:1 26, 1980.

11 Methodology Gray-World Assumption on Perceptual Color Spaces We propose to apply this assumption on two perceptual color spaces, and perform a comparison. Perceptual color spaces are conformed by two chromatic components, additionally to lightness. These two chromatic components are used in the estimation of the illuminant. CIELAB I a * = 1 MN M 1 N 1 x=0 y=0 a * (x, y) I b * = 1 MN M 1 N 1 x=0 y=0 b * (x, y) (5,6) I L * = max{ L * (x, y) } (7) 11

12 Section EXPERIMENTAL RESULTS

13 Experimental Results SFU Gray Ball F. Ciurea and B. Funt [5] 11,346 images 13 Bianco et al.[6] 1,135 images [5] F. Ciurea and B. Funt, A large image database for color constancy research, in Proceedings of the Imaging Science and Technology Eleventh Color Imaging Conference, Scottsdale, pp , Nov. (2003). [6] S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, Improving color constancy using indoor-outdoor image classification, IEEE Trans. Image Process., vol. 17, no. 12, pp , (2008).

14 Experimental Results Angular Error Metric Hordley and Finlayson [7] proposed a metric well suited for the evaluation of the color constancy, the angular error. # e ang = cos 1 % $ I r I e I r I e & ( ' (8) 14 [7] S. D. Hordley and G. D. Finlayson. Re-evaluating colour constancy algorithms. In Proceedings of the Pattern Recognition, 17th International Conference on (ICPR 04), pages 76 79, (2004).

15 Experimental Results Results 10 9 RGB CIELab CIELuv 8 Angular error Image Index 15 Figure 3. Curve fitting for each approach showing the trend of the angular errors given by the outcomes. The lower the angular error is, the better the estimation is.

16 Experimental Results Results Original Ideal 0.0º 0.0º 0.0º 16 RGB CIELab CIELuv 8.0º 11.2º 3.5º 3.9º 4.2º 4.7º a) b) c) 12.4º 7.6º 3.3º Figure 4. Three examples out of the 1135 images where the angular error is shown in the gray ball. The ideal image is included. a) ApacheTrial frame no , b) CIC2002 frame no , c) DeerLake frame no

17 Experimental Results Results (II) According to the results, the application of GW on any perceptual color space is significantly better than RGB. However, the GW algorithm applied on CIELUV is marginally better than the algorithm on CIELAB. The Gray-Edge (GE) algorithm is included in the experiments for comparison purposes. The difference in performance between GW using a perceptual space and GE is very small. However, the main difference is that the GW algorithm in any color space does not require any tuning process. TABLE I: Statistical angular errors (degrades) for the different approaches. 17 Algorithm Median Mean Max Gray-World (RGB) Gray-World (CIELAB) Gray-World (CIELUV) nd order Gray-Edge st order Gray-Edge

18 Experimental Results Results (II) According to the results, the application of GW on any perceptual color space is significantly better than RGB. However, the GW algorithm applied on CIELUV is marginally better than the algorithm on CIELAB. The Gray-Edge (GE) algorithm is included in the experiments for comparison purposes. The difference in performance between GW using a perceptual space and GE is very small. However, the main difference is that the GW algorithm in any color space does not require any tuning process. TABLE I: Statistical angular errors (degrades) for the different approaches. 18 Algorithm Median Mean Max Gray-World (RGB) Gray-World (CIELAB) Gray-World (CIELUV) nd order Gray-Edge st order Gray-Edge

19 Experimental Results Results (III) The processing time was measured for each algorithm and compared. We can appreciate that, the difference between GE and GW approaches is significant. The GW assumption, applied in any color space, takes a considerable smaller amount of time than the GE approach. TABLE II: Computing time for each approach. Algorithm Time (ms) Gray-World (RGB) 0.57 Gray-World (CIELUV) Gray-World (CIELAB) st order Gray-Edge nd order Gray-Edge

20 Section CONCLUSIONS

21 Conclusions Conclusions and Remarks A variation of the method using the GW assumption for color constancy has been analyzed in the CIELAB and CIELUV color spaces. According to the results, we conclude that outcomes from our approaches, a GW assumption in a perceptual color space, are better than those obtained using the standard procedure in RGB. Despite that the outcomes using the GE algorithm are slightly better than those using our approach, for practical applications we can choose the latter, because it is significantly faster and does not require a tuning process. 21 Also, we can appreciate that GW on CIELUV is marginally better than on CIELAB according to the accuracy of the estimated illuminant. Moreover, the processing time is considerably faster on CIELUV.

22 Gray-World assumption on perceptual color spaces Jonathan Cepeda-Negrete Raul E. Sanchez-Yanez Thanks for your attention!