Spatial Frequencies

Abstract

In this chapter we will take a look at the image itself, not at the objects that may be represented on it. We will look at the gray values as they are, and not try to segment the image into segments. We will look at how gray values change spatially, over short and long distances. Using the concept of spatial frequencies, we will interpret the image in terms of frequencies. Using the Fourier transform, more precisely, the Fast Fourier Transform (FFT), we will transform images from real space to the frequency domain where we can see dominant frequencies as dark spots, similar to optical diffraction patterns (for more detail on FFTs, consult a textbook such as Brigham, 1974). We will look at the frequency content of images, and see how we can recalculate the real image—again via FFT—from the frequency image, using either the whole frequency image or only parts of it. Applying filter masks, we can enhance and suppress selected frequencies. By the end of the chapter, we should be able to actually ‘see’ frequencies already in the real image, i.e., we should be able to judge the frequency content of an image and based on this and decide which—if any—frequency filtering is appropriate to enhance the image in the way that serves our needs.