Tuesday, July 29, 2008

Images As Signals

I want to explore this idea of signals and signal processing in relation to art. Wikipedia offers this definition of signal in the context of electrical engineering:

In the physical world, any quantity measurable through time or over space can be taken as a signal.

Photoshop, for example, is filled with code that uses signal processing techniques to process images. Filters, blur, sharpening, edge enhancement, etc. all come from signal processing.

To understand this a little better, remember that a digital image is basically a grid of picture elements, or pixels, arranged in rows and columns. For example, consider this image:


If we zoom in on Cindy's (the gray cat's) right eye, it looks like this:

Each of those colored squares is one pixel. If we consider each pixel, one row at a time, starting from the upper left corner, we get a sequence of values. There's the upper left pixel, then the one to the right of that, then the one to the right of that one, etc. until we get to the upper right pixel. Then we move down one row and consider the one just under the upper left, then right, etc.

If the image were 10 pixels wide, the order in which we'd consider the pixels is given by these numbers:


In this way, the whole image can be thought of as a sequence of numbers, each representing a pixel value. That's a signal.

Consider an image that has alternating black and white vertical stripes:

If we consider just one row of pixels in this image (indicated by the red box), we can think of the signal as a graph of how much light is given off by each pixel. So the graph of the signal for this row can be thought of as looking like this:

The graph is very low where the pixels are black, because almost no light is given off. It's very high for the white pixels, which are giving off the maximum level of light.

Let's consider another example:

Again, thinking of just the row highlighted in red, the graph of the signal for this looks like this:

The light value starts out very low, and gets gradually higher as we move toward the right edge of the image. But remember that when we get to the right end of the row, we move down a row and start again at the left, so the actual signal for this image looks more like this:

Of course, there are more than three rows. This pattern keeps repeating with one diagonal for each row of pixels.

Is this making sense so far? These are simple examples, but I think they illustrate how images can be thought of as signals (and, I suppose, how signals can be drawn as graphs, which are basically images.)

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