13. Image Processing

What is a digital image? For a mathematical programmer, the answer is simple: it’s just a large array of numbers. A grayscale image is a 2D matrix where each element represents an intensity value, and a color image is a 3D array stacking the Red, Green, and Blue color channels. This “image-as-array” perspective is incredibly powerful. It means we can use our existing knowledge of array operations, linear algebra, and calculus to directly analyze and manipulate visual information. This chapter will focus on this “from first principles” approach, where we will write our own functions to understand the algorithms that power modern image processing.

We’ll begin with the fundamentals: loading image files into Julia arrays and visualizing their separate components. From there, we’ll explore common transformations by implementing the algorithms ourselves. We’ll see how operations like averaging and interpolation allow us to resize (scale) an image. We’ll then implement filters, which can be seen as small, sliding “kernels” to blur images, remove noise, and detect edges by approximating the image’s gradient. Finally, we’ll move from the spatial domain to the frequency domain using the Fourier Transform, a powerful technique for analyzing an image’s underlying patterns and performing sophisticated, targeted filtering.