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Part II: Early Vision: Just One Image

7. Linear Filters

   • Linear filters and convolution
   • Shift invariant linear systems, including discrete and continuous convolution and edge effects in convolution
   • Spatial frequency and Fourier transforms
   • Sampling and aliasing, including smoothing and resampling
   • Filters as templates, including convolution as a dot product and filtering as a change of basis
   • Technique: normalized correlation and finding patterns
   • Technique: scale and image pyramids, including applications of scaled representations

   Slides

8. Edge Detection

   • Noise, including additive stationary gaussian noise, and why finite differences respond to noise
   • Estimating derivatives, including derivative of gaussian filters, why smoothing helps and choosing a smoothing filter
   • Detecting edges, including using the Laplacian to detect edges, gradient based edge detectors, and orientation representations near corners

   Slides

9. Texture

   • Representing texture, including extracting structure with filter banks and representing texture with statistics of filter outputs
   • Analysis and synthesis using oriented pyramids, including the Laplacian pyramid and oriented pyramids
   • Application: synthesizing textures for rendering, including homogeneity and synthesis by sampling local models
   • Shape from texture, including shape from texture for planes

   Slides

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