Matched filters can be multi-dimensional. In this exercise we look at two-dimensional images as both signals and matched filters. The filters can also be thought of as templates. The image is one of the photographs taken in Brussels, Belgium at the famous Solvay conference in 1927 where most of the world’s great physicists were present. The image is in color meaning that each pixel value is a triplet of numbers {r, g, b}. The actual computation will be performed on the basis of an intensity image derived from the color image. The intensity Y' is a linear combination of r, g, and b. (See the definition of Y' for an example of how this can be done.)

The Y' (grey level) image on top shows the effects of the additive, independent, Gaussian noise process. The aqua rectangle in the bottom color photograph shows the part of the picture that has produced the maximum cross-correlation between the template and the noisy image.

1. Starting from a SNR = 1000:1, choose one of the four physicist templates and see if the correct person is identified in the Solvay photograph.


2. How does this change if the SNR is decreased? In particular, at what SNR is it no longer possible to correctly identify the individual in the photograph?


3. As you choose other templates, that is other physicists, does the SNR—where correct identification is no longer possible—change? Can you explain this?


4. At what SNR are you no longer able to identify a face in the intensity (grey level) photograph?