2D Frequency Domain Filtering and the 2D DFT
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The 2D DFT:
o The Transforms
o Frequency Content Location
o Properties of 2D DFT
o Examples of Properties

Frequency Domain Image Filters:
o 2D Filtering Concepts
o Smoothing
o Edge Detection
o Sharpening
o Filter Design



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Exciting Real World Applications Power of Steam

One of the more exciting applications of image processing these days is the ability to bring out minute details in photos taken from very far away. With the hunt for Usama Bin Laden well underway, everyone loves looking at the spy photographs taken by either planes flying at astounding altitudes or even satelites. The practices which allow us to make out details in these photographs can be the same procedures used in bringing out detail in our car, particularly either sharpening or edge detection.

Given this aerial photo of Rice University, we could look at all kinds of things. For instance, where we interested in the layout of the campus and surrounding streets more than the actual look of the campus from above, knocking out the lower frequencies and normalizing the image would serve to bring out sharp contrast such as the edges of buildings and streets. Were we to add these edges to the origional image, we would have a sharper image of the campus. When this is done right the resulting image appears to have been taken that way in the first place, and you can't tell that someone has altered it.

Another real world application of working with images in the frequency domain is in compression. Put ridiculously simply, in lossy compression you throw away part of an image in order to make the file smaller. Commonly used lossy compression algorithms are jpeg, mpeg, and the currenly popular mp3 (mpeg layer 3). When you are "throwing away" part of any file in order to concerve space, it is important to know what you can throw away without noticbly effecting the quality of that file. In image compression, looking at the frequency domain characteristics of the image can be extremly useful. For instance, were we to take a look at the magnitude of the frequency content of this picture of Scott Baio, childhood idol/ star of the wildly succesful 80's sitcom Charles in Charge, we would likely see that the majority of the content is at a fairly low frequency, this is the case in most images, thus we are able to filter out the higher frequecys, often thought of as smoothing the image, decreasing the overall size of the file without greatly affecting the percieved image.