Local space average color

Color Constancy M. Ebner 2007 John Wiley Sons, Ltd 

This constant k takes care of normalizing the result. For a large kernel that extends outside the image, this factor has to be computed for each pixel. A possible choice for a kernel is a Gaussian. 

Instead of using a Gaussian as a kernel we can also use an exponential kernel with 

---

Figure 6.28 Results of comprehensive color normalization using local space average color instead of global space average color. The intensities of the input image were used to rescale the output pixels.

Computing Local Space Average Color on a Grid of Processing Elements... 

We can view this as local space average color having a carrying capacity of 2000, where we have 1999 components of a- and one component of c,. ... 

Local space average color is then computed iteratively by averaging the data from all available neighboring elements. 

Figure 10.10 Snapshots of the computation of local space average color are shown after 1, 50, 200, 1000, 5000, and 20000 time steps.

Figure 10.18 A comparison between the computed and the actual illuminant along a horizontal line of the image (marked by a white line in Figure 10.17). Local space average color is computed using an exponential kernel, a Gaussian kernel, or a resistive grid.

Using Local Space Average Color for Color Constancy... 

Now that we have calculated local space average color as described in Chapter 10, we can use it to adjust the colors of the input image. We can distinguish between several different methods to calculate the colors of the output image. In each case we will use the assumption that, on average, the world is gray. 

USING LOCAL SPACE AVERAGE COLOR FOR COLOR CONSTANCY... 

Figure 11.1 Implementation of color constancy algorithm that uses local space average color to scale the input values. Data from surrounding pixels is iteratively averaged. Input values are divided by twice the local space average color.

Figure 11.2 Output images that were generated by dividing the input values by twice the local space average color.

The light illuminating the scene can be approximated by a constant factor times the local space average color. 

Let us now have a different look on the use of local space average color for color constancy using color shifts. Consider the standard RGB color space. A unit cube is spanned by the... 

Figure 11.4 The gray vector passes from [0, 0, 0] to [1,1, 1] directly through the middle of the color cube. If local space average color is located away from the gray vector, we can use a shift perpendicular to the gray vector to move the color back to the center.

If we subtract this vector from the current color, we move local space average color back to the gray vector. This is visualized in Figure 11.6. Let C = [cr, c . cb T be the color of the input pixel. Thus, output colors can be calculated by subtracting the component of local space average color, which is perpendicular to the gray vector. 

Figure 11.5 For these images, output pixels were calculated by subtracting the component of local space average color, which is perpendicular to the gray vector, from the current pixel color.

---