XIV

In this activity, the use of Normalized Chromaticity Coordinates (NCC) gives us an advantage since it can separate brightness and chromaticity. 

 (1)

Eq. 1 shows the normalization where I is the sum of all channels. We can now write b=1-r-g, and thus the mapping is reduced to 2 dimensions.

Figure 2. NCC space, x is r and y is g

Fig. 2 shows the reduced space. Notice that the blue is when r and g is zero.

Figure 3. Top: Reference image. Bottom:  Region of Interest (ROI)

Fig. 3 shows the images that will be used in the next activities. 

Parametric Probability Distribution Estimation

This method uses the NCC of the image's ROI and then fits it in a Gaussian distribution to determine the probability that a pixel is indeed a part of the ROI.

 (2)

The actual probability used is of course dependent for the 2 channels. This is called the joint probability, p(r)*p(g). Knowing this, we search for the pixels in the whole image (not the ROI only) that is within the joint probability for the ROI.

Figure 3. Resulting image of the Parametric method

Non-Parametric Probability Distribution Estimation

This method involves backprojecting the known histogram of the ROI to the new estimated image. The algorithm is partly similar to the Parametric method but instead of using the joint probability, the method is reversed to associate pixels to a blank matrix from the known 2D histogram of the ROI.

Figure 4. Resulting image of the Non-Parametric method

From the Figs. 3 and 4, we notice that the Parametric method produced a more even and connected image since it has a Gaussian distribution for the PDF while the Non-Parametric method used only direct histogram to image (ROI to whole) backprojection to estimate the association of a certain pixel.

Self-Assessment: 9/10