This time I’m going to write about image processing and computer graphics. Many of you may have seen procedurally generated textures – bitmaps that look like something from the real world such as rusted steel, marble or stone, but are not photos, being completely computer generated. It may initially seem strange that it’s possible to produce patterns with such natural-looking randomness with a mathematical algorithm. The trick is to use random noise (similar to static on an old television screen) and apply cleverly chosen filters on that.
Let me show how to produce an image with random black spots/stripes on a white background, similar to the pattern of a zebra or some breeds of dog. First, we need a free image processing program called ImageJ, downloadable for Windows or Linux from this address.
First, we will choose New > Image from the File menu, and set the resolution of a new blank image to 1000 x 1000 pixels.
The result is an all-black bitmap as you see below.
Next, we will add gray random noise with a specified standard deviation of pixel brightness. Choose Noise > Add Specified Noise from the Process menu, and set the standard deviation to value 3.00.
The resulting image looks like that below, where you see the familiar “TV static” appearance.
Next we will do a so-called bandpass filtering on the image. The idea here is that the program first converts the image to a Fourier transform, which is a function that tells how much of different “wavelengths” are present in the image. An image that consists of large features (with a characteristic diameter of a large number of pixels) has a high amount of large-wavelength Fourier components, while an image that contains small features has a high amount of short-wavelength components. After converting the image to the Fourier transform the bandpass filtering algorithm removes all components with wavelengths that don’t lie on a desired interval and then does an inverse Fourier transform to produce a filtered image.
Choose FFT > Bandpass Filter from the Process menu and set the lower limit to 30 pixels and the upper limit to 100 pixels. This will remove all features with characteristic lengths that are not in that interval. The result looks like this:
This resulting image is pretty much the same as Perlin’s fractal noise, which is very important in computer generated graphics.
Next, we have to do a “color quantization” that converts the image to a maximum contrast one, having only all-black or all-white pixels. To do this, choose Adjust > Brightness/Contrast from the Image menu.
Dragging the Contrast bar to maximum value, we obtain a two-color image that has random spots/stripes as wanted. If the contrast adjustment doesn’t seem to work, try changing the image type to “RGB Color” from the Image menu first.
Spots of different sizes can be created by changing the upper and lower limits in the bandpass filtering stage. If an image with a larger resolution is desired, the image can be converted to a vector image with a program such as Inkscape, and printed back into a .PNG bitmap file of a higher resolution. This will produce a larger image without blurring or pixelization.
More complicated filtering and coloring procedures can be done to produce images like this one here, but I will write more about it later.