Convolutional neural networks applied to modification of images

TL;DR

The chapter addresses how digital image modification relies on mathematical modeling and neural networks, bridging classical image processing with modern CNNs and diffusion-based generation. It presents representations such as $f(x,y)$ for images, transforms $T(u,v)$ via kernels $r(x,y,u,v)$, and convolution $(w*f)(x,y)$ that underpin filtering. Key contributions include explanations of histograms, images as matrices, filters, CNN architectures, and practical applications from classification to style transfer and text-to-image diffusion. The discussion also covers societal implications of AI-generated imagery and the need for responsible deployment.

Abstract

The reader will learn how digital images are edited using linear algebra and calculus. Starting from the concept of filter towards machine learning techniques such as convolutional neural networks.

Figures (14)

• Figure 1: Original figure and its histogram
• Figure 2: Modified image and its corresponding histogram
• Figure 3: Images and its histograms. a) original image, b) histogram of original image, c) modified image, d) histogram of modified image.
• Figure 4: Operations
• Figure 5: Fast Fourier Trasform FFT