Exploring the Fourier transform

Much of the processing you apply to images and videos in OpenCV involves the concept of the Fourier transform in some capacity. Joseph Fourier was an 18th-century French mathematician who discovered and popularized many mathematical concepts. He studied the physics of heat, and the mathematics of all things that can be represented by waveform functions. In particular, he observed that all waveforms are just the sum of simple sinusoids of different frequencies.

In other words, the waveforms you observe all around you are the sum of other waveforms. This concept is incredibly useful when manipulating images because it allows us to identify regions in images where a signal (such as the values of image pixels) changes a lot, and also regions where the change is less dramatic. We can then apply domain-specific logic to mark these regions as noise or regions of interests, background or foreground, and so on. These are the frequencies that make up the original...