Computer Vision in Frequency: the Fourier Transform and New Artificial Intelligence

This book bridges the foundational theory of Fourier analysis with cutting-edge applications in computer vision and artificial intelligence, focusing on frequency-domain methods to enhance and accelerate modern learning systems. In an era where convolutional neural networks (CNNs) dominate computer vision but face significant computational challenges—especially with large-scale image data—this work presents a timely and innovative alternative. By shifting computations to the Fourier domain, the authors address critical limitations in efficiency and scalability, offering readers a pathway to more intelligent, high-performance vision systems. Starting from harmonic waves and Fourier series, the book systematically progresses toward the Fourier transform, discrete transforms, and the Fast Fourier Transform (FFT). It further covers signal digitization, quantization, and fast convolution algorithms, culminating in the design of Fourier Convolutional Neural Networks (FCNNs). Key topics include spectral representations of images, frequency-based convolution, and practical FFT-based architectures that reduce computational load while preserving accuracy. Readers will gain both deep theoretical insight and practical methodology for implementing Fourier-based vision systems. The book is suited for graduate students, researchers, and engineers in signal processing, computer vision, and machine learning who seek to leverage frequency-domain techniques to build faster, more scalable AI models. A basic understanding of linear algebra, calculus, and signal processing is recommended.