Filtering

		An image as a function
		Digital vs. continuous images
		Image transformation:  range vs. domain
		Types of noise
		LSI filters
			cross-correlation and convolution
			properties of LSI filters
			mean, Gaussian, bilinear filters
		Median filtering
		Image scaling
		Image resampling
		Aliasing
		Gaussian pyramids
		Bilinear Filters

Edge detection

		What is an edge and where does it come from
		Edge detection by differentiation
		Image gradients
			continuous and discrete
			filters (e.g., Sobel operator)
		Effects of noise on gradients
		Derivative theorem of convolution
		Derivative of Gaussian (DoG) operator
		Laplacian operator
			Laplacian of Gaussian (LoG)
		Canny edge detector (basic idea)
			Effects of varying sigma parameter
		Approximating an LoG by subtraction
		Hough Transform (lines, circles, “generalized” (from midterm))

Segmentation

		Graph representation of an image
		Intelligent scissors method
		Image histogram
		K-means clustering
		Morphological operations
			dilation, erosion, closing, opening
		Normalized cuts method
		Matting—separate foreground from background (basic idea)

Motion

		Optical flow problem definition
		Aperture problem and how it arises
		Assumptions
			Brightness constancy, small motion, smoothness
		Derivation of optical flow constraint equation
		Lukas-Kanade equation
			Derivation
			Conditions for solvability
			meanings of eigenvalues and eigenvectors
		Iterative refinement
			Newton’s method
			Coarse-to-fine flow estimation
		Feature tracking
			Harris feature detector
			L-K vs. discrete search method

Projection

		Properties of a pinhole camera
			effects of aperture size
		Properties of lens-based cameras
			focal point, optical center, aperture
			thin lens equation
			depth of field
			circle of confusion
		Modeling projection
			homogeneous coordinates
			projection matrix and its elements
			types of projections (orthographic, perspective)
		Camera parameters
			intrinsics, extrinsics
			types of distortion and how to model

Mosaics

		Image alignment (using Lucas-Kanade)
		Image reprojection
			homographies
			cylindrical projection
		Creating cylindrical panoramas
		Image blending
		Image warping
			forward warping
			inverse warping

Projective geometry

		Homogeneous coordinates and their geometric intuition
		Homographies
		Points and lines in projective space
			projective operations: line intersection, line containing two points
			ideal points and lines (at infinity)
		Vanishing points and lines and how to compute them
		Single view measurement
			within a reference plane
			height
		Cross ratio
		Camera calibration
			using vanishing points
			direct linear method

Stereo

	Things to take away from this lecture
		Cues for 3D inference, shape from X (basic idea)
		Epipolar geometry
		Stereo image rectification
		Stereo matching
			window-based epipolar search
			effect of window size
			sources of error
		Active stereo (basic idea)
			structured light
			laser scanning

Multiview stereo

		Baseline tradeoff
		Multibaseline stereo approach
		Voxel coloring problem
		Volume intersection algorithm
		Voxel coloring algorithm

Light, perception, and reflection

		Light field, plenoptic function
		Light as EMR spectrum
		Perception
			color constancy, color contrast
			adaptation
			the retina:  rods, cones (S, M, L), fovea
			what is color
				response function, filters the spectrum
				metamers
		Finding camera response function (basic idea, not details)
		Materials and reflection
			what happens when light hits a surface
			BRDF
			diffuse (Lambertian) reflection
			specular reflection
			Phong reflection model
			measuring the BRDF (basic idea)

Recognition

		Classifiers
		Probabilistic classification
			decision boundaries
			learning PDF’s from training images
			Bayesian estimation
		Principle component analysis
		Eigenfaces algorithm
			use for face recognition
			use for face detection

Texture  (not on exam!!)

		Markov chains
		Text synthesis algorithm
		Markov random field (MRF)
		Texture synthesis algorithm (basic idea)