Assignment 1: Think About Waves. Due February 20

Overview

One of the first major topics covered in this course is the use of the Fourier transform to express the information present in an image in a fashion quite different from that most of us recognize. To say this in a more technical fashion, application of the Fourier transform to an image tells us how much energy is present at a number of different frequencies. Or, showing that there are many ways to say more or less the same thing, it decomposes an image into a series of waves and then expresses how much of each wave is required to construct the original image.

Any way you describe it, the Fourier transform represents a classic example of a broad range of image processing techniques that really express images in different ways. It is something that any student of computer vision should understand and know how to interpret. Therefore, this first assignment is designed to permit each of you to explore the "spectral decomposition" of three different image classes of your own choosing. There will be in this assignment great deal of latitude in the particulars of this assignment that will call upon you to provide the structure.

Specifics

Starting with the endpoint, each of you will submit a 2 to 5 page report presenting what you have learned and discovered in this assignment. The most preferable form in which to present your report will be a web page available to the instructor. A secondary format will be as a PDF document. A well put together PDF document will be worth of credit, but the webpage option is highlighted to get all of you thinking about more modern ways to express yourselves when it comes to technical work.

What you will describe in your report is an experiment in which you present the Fourier transforms of at least nine different images that you select from the web. Further, these images must be grouped into three categories of your own choosing. Clearly, there's a presumption that you will come up with three categories that exhibit some differences that are worthy of discussion when analyzed using the Fourier transform. By the nature of what you're being asked to do, your report is going to have to blend English prose with illustrative graphics. It is difficult to imagine a well constructed report that will not show visually the output of the Fourier transform for different object/image categories.

In this assignment, several common requirements of reports are being waived. You may have a bibliography if you wish, but you're not being asked to describe other people's work here and you may assume that the only requirement when describing the results of the Fourier transform is that your descriptions rewritten in a way they could be understood by a talented high school student. Particular attention to that last constraint, this is not an exercise in showing your mathematical sophistication, there will be other chances to do that. This is an exercise aimed at forcing you to think about simple straightforward English explanations. Do these certain that every sentence is your own, since basic rules of intellectual integrity and academic integrity will certainly be enforced.

How to Submit

You will submit your assignment to the instructor through email. That email will either include a PDF of your report as an attachment or it will include a link to a website where you are displaying your report.