Announcements

		Final is Thursday, March 20, 10:30-12:20pm
			EE 037
		Sample final out today

Filtering

		An image as a function
		Digital vs. continuous images
		Image transformation:  range vs. domain
		Types of noise
		Noise reduction by averaging multiple images
		Cross-correlation and convolution
			properties
			mean, Gaussian, bilinear filters
		Median filtering
		Image scaling
		Image resampling
		Aliasing
		Gaussian pyramids

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

Features

		What makes a good feature?
			Derivation in terms of shifting a window
		H matrix
			Definition
			Meaning of eigenvalues and eigenvectors
		Harris operator
			How to use it to detect features
		Feature descriptors
			MOPS (rotated square window)
			SIFT (high level idea)
		Invariance (how to achieve it)
			Rotation
			Scale
			Lighting
		Matching features
			Ratio test
			RANSAC

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
		Image reprojection
			homographies
			spherical projection
		Creating spherical panoramas
		Handling drift
		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
			computing height
		Cross ratio
		Camera calibration
			using vanishing points
			direct linear method

Stereo

		Epipolar lines
		Stereo image rectification (basic idea)
		Stereo matching
			window-based epipolar search
			effect of window size
			sources of error
			Energy-minimization (MRF) stereo (basic idea)
		Depth from disparity
		Active stereo (basic idea)
			structured light
			laser scanning

Structure from motion

		Correcting drift in mosaics through global optimization
		Least squares
		Structure from motion
			Solving for camera rotations, translations, and 3D points
			The objective function
			The pipeline (from Photo tourism slides:  detection, matching, iterative reconstruction…)
		Photo tourism

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)

Photometric stereo

		Shape from shading (equations)
		Diffuse photometric stereo
			derivation
			equations
			solving for albedo, normals
			depths from normals
			Handling shadows
		Computing light source directions from a shiny ball
		Limitations

Recognition

		Classifiers
		Probabilistic classification
			decision boundaries
			learning PDF’s from training images
			Bayes law
			Maximum likelihood
			MAP
		Principle component analysis
		Eigenfaces algorithm
			use for face recognition
			use for face detection

Segmentation

		Graph representation of an image
		Intelligent scissors method
		Image histogram
		K-means clustering
		Morphological operations
			dilation, erosion, closing, opening
		Normalized cuts method (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
		Lucas-Kanade equation
			Derivation
			Conditions for solvability
			Relation to Harris operator
		Iterative refinement
			Newton’s method
			Pyramid-based flow estimation

Texture

		Markov chains
		Text synthesis algorithm
		Markov random field (MRF)
		Efros and Leung’s texture synthesis algorithm
		Improvements
			Fill order
			Block-based
		Texture transfer (basic idea)

Guest Lectures

		Richard Ladner—Tactile graphics
		Jenny Yuen—cateract detection
		Jeff Bigham—object-based image retrieval
	(basic ideas)