This is a sample from the Fall 1997 Math Clinic, which addressed the multi-image mosaic problem.

Large images can often be represented by taking multiple smaller images and piecing them together. The boundaries between the individual images are visible due to differences in the gray scale values of pixels representing the same location in different images. These differences arise from variations in illumination or exposure. We need to adjust the pixel values on the boundaries of the small images as well as in an appropriate neighborhood, so the gray scale differences between adjacent images are less distinct.

We will assume that the client will provide us with the following information:

1. Individual images in the form of a matrix of pixel gray scale values.
2. The exact position of the individual images relative to the entire mosaic. This information could be given by stating the location of the upper left pixel of each individual image in the large image.

Our solution to the problem will have the following characteristics:

1. Overlapping pixels between two adjacent images will have the same gray scale values in both images after the adjustments are made.
2. Adjustments to each small image will be as smooth as possible so as to minimize noticeable distortions to the image.
3. The final result will be in the form of a matrix of pixel gray scale values representing the entire mosaic.