Computer Vision

Image Processing

Signals, sampling, and the transforms that turn an image into a set of numbers a computer can compress, filter, and understand — built from EEL 5820 lecture notes.

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Unit 1 · Signals & Sampling

  1. 1 What Is a Signal? Continuous vs. discrete, analog vs. digital, and how an 8-bit image is really just a quantized 2-D signal.
  2. 2 The Impulse Function & Sampling The Dirac delta, its sifting property, and sampling as multiplying a signal by a train of impulses.
  3. 3 Nyquist, Aliasing & the Fourier Transform Why undersampling folds high frequencies back on themselves, and how the Fourier series becomes the Fourier transform.

Unit 2 · Image Transforms

  1. 1 Transform Theory & the 2-D DFT Orthogonal kernels, the general transform/inverse-transform pair, and the discrete Fourier transform of an image.
  2. 2 The Discrete Cosine Transform A real-valued cousin of the DFT, its basis images, and why it quietly powers JPEG compression.
  3. 3 The Walsh–Hadamard Transform Trading sinusoids for ±1 rectangular waveforms — sequency, and building the Hadamard matrix recursively.
  4. 4 The Haar Transform & Review The most localized of the four transforms, plus a side-by-side comparison to tie the unit together.