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Before any network learns a filter, an image is a signal, and the classical tools of signal processing already explain much of what vision needs. This chapter starts with linear filtering: convolution, blurring, and derivatives, then extends them to time and to sampling. The image priors that follow describe what natural images have in common and turn that knowledge into denoising, texture synthesis, and inference with graphical models. Each section is written by a student of the course from a chapter of Foundations of Computer Vision by Torralba, Isola, and Freeman, with the book’s figures linked rather than reproduced.

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Filtering and sampling

Convolution and Linear Filters

Linear translation-invariant systems, convolution, boundary handling, and template matching.

Smoothing an Image with Blur Filters

Box, Gaussian, and binomial filters and their frequency responses.

Measuring Change with Image Derivatives

Discrete and Gaussian derivatives, the Laplacian, sharpening, and Retinex.

Filtering in Space and Time

A video as a space-time volume, velocity-tuned blur, and velocity-nulling filters.

Sampling an Image Without Aliasing

The sampling theorem, reconstruction, sampling lattices, and anti-aliasing.

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Image priors

What Natural Images Have in Common

The 1/f power law, heavy-tailed derivatives, and denoising with image priors.

Synthesizing Textures

Texture synthesis by histogram matching and by copying neighborhoods.

Markov Random Fields and Belief Propagation

Markov random fields and belief propagation for denoising, segmentation, and stereo.
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