Notion of scale in physics and mathematics
Physics of observation, apertures
Axiomatic derivation of filters
Differentiation, scale and regularization
History of scale-space theory
The human visual pathway, receptive field structure
Retinal distribution of receptive fields, feedback in the visual system
Information processing in the visual cortex
Multi-scale (Gaussian) derivatives, their properties and the diffusion equation
Some differential geometry on images in 2D, 3D, 2D-time for robust feature detection and shape analysis
Geometric invariants, landmarks
Derivation of formulas for isophote curvature in 2D and 3D, high order differential features (a.o. corners, T-junctions)
Applications in medical imaging: computer-aided detection (CAD)
Mathematical morphology, multi-scale erosion and dilation
Nonlinear, geometry-driven diffusion (evolution of images by partial differential equations), edge preserving smoothing
Deep structure of images, edge focusing, multi-scale watershed segmentation
Top-points, winding numbers and SIFT features, content based image retrieval
Multi-orientation analysis, enhancing lines (even when crossing)