Learning the Math of Image Processing Summary

Monday - Friday, July 5 - 9, 2010

The members of our group attended the first half (6-7 lectures) of Luminita Vese's course, "An Introduction to Mathematical Image Processing." She provided an overview of where images come from and of the various levels of analysis and processing that can be done on them. She spoke briefly about histogram equalization, a technique for enhancing the contrast of images, before turning to the general topic of spatial filtering. That led naturally into a discussion of the Fourier transform and the frequency domain, where one analyzes an image not pixel by pixel, but by building it up out of sine waves of varying frequency. She then moved to the topic of image reconstruction, in which one tries to recover some unknown original image by analyzing a degraded (e.g. blurred and noisy) version of the image. Two themes that went through most lectures were the interplay between the spatial domain and the frequency domain, and the relationship between continuous functions and operators and their discrete analogues.

As a group, we found the exposure to the basic ideas of image processing enlightening, and we immediately started thinking about how to take the simplest methods of analysis (such as histograms) and processing (such as linear spatial filters) and implement them in a way that would be understandable to high school students and require no software that was unavailable to most teachers (such as Matlab).

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.