White Patch Retinex

The white patch retinex algorithm is basically just a simplified version of the retinex algorithm (Cardei and Funt 1999 Funt et al. 1998, 1996 Land and McCann 1971), which is described in the next chapter. The retinex algorithm relies on having a bright patch somewhere in the image. The idea is that, if there is a white patch in the scene, then this patch reflects the maximum light possible for each band. This will be the color of the illuminant, i.e. if R,(x, v) = 1 for all i e r, g, b) and G(x, y) = 1, then 

If one assumes a linear relationship between the response of the sensor and pixel colors, i.e. Ci (x, y) = I, (x. y). and one also assumes that the sensor s response characteristic is similar to delta functions, then the light illuminating the scene simply scales the product of the geometry term G and the reflectance Rt of the object. 

Therefore, we can rescale all color bands once we have located such a bright patch. In practice, one does not look for a white patch but looks for the maximum intensity of each color channel. Let L, max be the maximum of each band over all pixels. 

This maximum is then used to scale each color band of the pixels back to the range [0, max] 

---

Figure 6.2 The white patch retinex algorithm is able to perform some color adjustments for the image shown in (a) but the image still looks very yellow. The white patch retinex algorithm does not work very well for the image shown in (b) because of the nonuniform illuminant.

Figure 6.3 Results for the white patch retinex algorithm where histograms were used to find a white patch. The histograms for all the three color bands of the input image are also shown. The cutoff value is marked with a vertical line. All the three cutoff values represent an estimate of the illuminant.

The gray world assumption as well as the white patch retinex algorithm are used frequently for automatic white balance. The popular draw utility written by Coffin (2004) scales each color channel using the average as an automatic white-balance option. After rescaling, the white point is set at the 99th percentile. In other words, all channels are scaled equally such that only the top 1% of all pixels are clipped. This assumes that there are only a few highlights. 

Combining White Patch Retinex and the Gray World Assumption... 

Random recognition rate Full range per band White patch retinex Gray world assumption Simplified hom Gamut constraint 3D Gamut constraint 2D Color cluster rotation Comprehensive normalization Risson (2003)... 

Again, the color of the output pixel is independent of the illuminant. Note that both the sample and the background are achromatic. Therefore, the sample will appear to be achromatic because all color channels will have the same value. Hence, the white patch retinex algorithm is not in agreement with the results obtained by Helson. 

If this map is applied to the color measured by the sensor in the center of the image, we obtain the same result as we obtained for the white patch retinex algorithm. The output color will be achromatic for all three cases. 

Combined White Patch Retinex and Local Space Average Color... 

White patch retinex algorithm, maximum value per channel. 

Local space average color, combined white patch retinex and gray world assumption, linear output. 

White patch retinex Described in Section 6.1. The white point is set at 4% per channel. A histogram quantization of 256 per channel is used. (pBlack=0, pWhite=0.04)... 

---