Colour changes in a natural scene due to the interaction between the light and the atmosphere Raúl Luzón González Colour Imaging Laboratory Department of Optics, University of Granada

Members Javier Romero Professor Juan L. Nieves Associate Professor Javier Hernández-Andrés Associate Professor Eva M. Valero Associate Professor Clara Plata Post-graduate student Raúl Luzón Post-graduate student Juan Ojeda Post-graduate student

3 Contents Introduction Physical model Method Colour changes in the object with observation distance Conclusions and future work References

4 Contents Introduction Physical model Method Colour changes in the object with observation distance Conclusions and future work References

5 Introduction Light interaction with particles and molecules of different sizes present in the atmosphere leads to the following process: Absorption Emission Scattering

There are two fundamentals process associated with scattering: Introduction Scattering Attenuation: flux is removed from a light beam. Airlight: the atmosphere acts as a light source. 6

7 The mixing of attenuation and airlight produces loss in saturation and a possible hue change, depending on the atmospheric particles sizes. Introduction Scattering

8 There are several works in the field of atmospheric image restoration, some of them based on statistical information of the scene (Pitas and Kiniklis 1 ) and others on physical model (Tan and Oakley 2 ). Introduction Models

The physics based models usually need information about meteorological conditions (Yitzhaky et al. 3 ), distances from the objects (Narasimhan and Nayar 4 ) or some images taken under different weather conditions (Narasimhan and Nayar 6 ). The better physics based models are those constructed over the dichromatic model (Narasimhan and Nayar 7 ). Introduction Models 9

10 Contents Introduction Physical model Method Colour changes in the object with observation distance Conclusions and future work References

11 Physical Model We use the dichromatic model in with the radiance of the object at the observation plane has two terms: direct light coming from the object but attenuated by the atmosphere and airlight Where: L is the object radiance viewed from the observer plane L 0 is the object radiance β is the attenuation coefficient in the atmosphere L ∞ is the radiance of the horizon d is the distance between the object and the detector Direct lightAirlight (1)

12 If we suppose a lambertian object receiving an irradiance E d, for clear skies the irradiance on the detector is: Physical Model (2) Where: Ω is the solid angle subtended from the object into the detector E d is the irradiance over the object ρ is the spectral reflectance of the object β is the attenuation coefficient d is the distance between the object and the detector L ∞ is the horizon radiance

And if we suppose that the horizon radiance is the same at any point on the sky and the object is lambertian, for overcast skies we use the following expression: (3) Physical Model 13 Where: Ω is the solid angle subtended from the object into the detector ρ is the spectral reflectance of the object β is the attenuation coefficient d is the distance between the object and the detector L ∞ is the horizon radiance

14 Contents Introduction Physical model Method Colour changes in the object with observation distance Conclusions and future work References

15 Method At first, we have calculated the CIE 1931 (x,y,Y) and the CIELAB (L*,a*,b*) values corresponding to 23 objects of the Macbeth Color-Checker, whose spectral reflectances are known, for three clear days and for three overcast days.

The scattering and the absorption coefficients must be known in order to apply the last equations. We know the scattering coefficient at 450, 550 and 700 nm (thanks to ours partners from Centro Andaluz del MedioAmbiente) and we can extrapolate to the rest of visible spectrum assuming that: Method We suppose that the absorption coefficient keep constant in the visible range. (4) 16

Method In the following table we show the scattering coefficient at 550 nm, the absorption coefficient at 670 nm and the u value for several days. Dayβ sct (550 nm) Mm -1 β abs (670 nm) Mm -1 u 1 (clear) (overcast) (clear) (clear) (overcast) (overcast)

18 Contents Introduction Physical model Method Colour changes in the object with observation distance Conclusions and future work References

19 Colour changes in the object with observation distance

Direct light coming from the object decrease increasing distance between the object and the observer. For a specific distance, the airlight factor is more noticeable than the attenuation factor. 19 Colour changes in the object with observation distance

20 Colour changes in the object with observation distance

20 Colour changes in the object with observation distance

21 We included the chromaticity threshold discrimination circle for the horizon, considering 3 CIELAB units.. The visibility calculated with colorimetric criterion gives a lower value than one calculated with the classical form. Colour changes in the object with observation distance

22 Contents Introduction Physical model Method Colour changes in the object with observation distance Conclusions and future work References

In this work we pretend to study the influence of the atmosphere in the objects color with the distance. Making a computational work based on a physical model we see how the objects loose their chromaticity. For future work we pretend make more measures, including more meteorological conditions and improve the theoretical model. Conclusions and future work 23

24 Contents Introduction Physical model Method Colour changes in the object with observation distance Conclusions and future work References

25 References 1. I. Pitas and P. Kiniklis, “Multichannel Techniques in Color Image Enhancement and Modeling”, Image Processing, IEEE Transactions, Vol 5,No. 1, pp , K. Tan and J.P. Oakley, “Physics-Based Approach to Color Image Enhancement in Poor Visibility Conditions”, Journal of the Optical Society of America, Vol. 18, No. 10, pp , Y. Yitzhaky, I. Dror and N. S. Kopeika, “Restoration of atmospherically Blurred Images According to Weather-predicted Atmospheric Modulation Transfer Functions”, Optical Engineering, Vol 36, pp , S. G. Narasimhan and S. K. Nayar, “Chromatic Framework for Vision in Bad Weather”, Conference on Computer Vision and Pattern Recognition, IEEE Proceedings. Vol. 1, pp , S. G. Narasimhan and S. K. Nayar, “Contrast Restoration of Weather Degraded Images”, Pattern Analysis And Machine Intelligence, IEEE Transactions, Vol. 25, No. 6, pp , S. G. Narasimhan and S. K. Nayar, “Vision in Bad Weather”, Seventh IEEE International Conference in Computer Vision, IEEE Proceedings, Vol 1, pp , W. E. K. Middleton, “Vision through the atmosphere”, 2nd Edition, University of Toronto Press, 1952.

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