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Final Review
Course web page:vision.cis.udel.edu/~cv
May 21, 2003 Lecture 37
Announcements
• HW 6 due tonight by midnight• Final: Thursday, May 29, 1-3 pm in
this room
Outline
• Review of course since midterm• Course evaluations (including TA)
Lecture Topics
• Probability• Cameras• Camera
calibration• Single view
geometry• Stereo• Tracking
• Robust estimation• Structure from
motion• Optical flow• Segmentation• Classification
Probability
• Random variables– Discrete– Continuous (probability density
functions)
• Histograms as PDF representations• Joint, conditional probability• Probabilistic inference: Bayes’ rule
– MAP, ML inference
Cameras
• Lenses– Advantages (vs. pinhole camera),
disadvantages
• Discretization effects of image capture
Camera Calibration
• Estimating the camera matrix– Least-squares via Direct Linear Transform (DLT)
• Extracting the calibration matrix
– Nonlinear least-squares• Estimating radial distortion
• I won’t ask about steps of DLT in detail (for this and other estimation problems), but you should know:– (1) When a DLT-like method is applicable– (2) The basic approach (stacking equations given by
constraints on points)– (3) Number of points required– (4) Degenerate configurations
Single View Metrology
• Homogeneous representation of 2-D lines, 3-D planes
• Vanishing points and lines• Single view metrology
– Cross ratio• Distances between planes
– Homology (homography)• Lengths & areas on planes
• Rectification– Affine vs. using homography
Stereo
• Epipolar geometry– Baseline, epipolar lines, epipoles, epipolar pencil
• Point-to-line mapping: Fundamental matrix F– Estimating F
• DLT with manually chosen correspondences• Nonlinear minimization
– Essential matrix
• Texture mapping– Bilinear interpolation
Tracking
• Tracking as probabilistic inference– Measurement likelihood, prior probability
• Examples– Feature tracking– Snakes
• Filtering methods– Kalman filter – Particle filters
• Steps– Sampling– Predicting– Measuring
• Estimating state from particle set
Robust Estimation
• RANSAC– Purpose– Methods– Application to automatic fundamental
matrix estimation
Structure from Motion
• Triangulation– Covariance of structure estimates
based on camera motion
• Stratified reconstruction– Necessary information for “upgrades”
• Affine factorization
Optical Flow
• Motion field vs. optical flow• Brightness constancy constraint
– Aperture problem• Computing optical flow
– Smoothness constraint– Least-squares solution for small set of
motion parameters• Time to collision
Segmentation
• Definition of segmentation• Gestalt grouping strategies
– Bottom-up, top-down
• Segmentation applications– Detecting shot boundaries– Background subtraction
• Pixel covariance & Mahalanobis distance
• Clustering – k-means clustering– Graph-theoretic clustering
• Eigenvector methods for segmentation– Normalized cut
• Hough transform
Classification• Classification terminology• Methods for classifier construction
– Known probability densities• Decision boundaries for normal distributions
– Unknown densities• Nonparametric approximation: Kernel methods, k-nearest neighbors
• Performance measurement– Cross-validation
• Dimensionality reduction with PCA• Face recognition
– Nearest neighbor– Eigenfaces
Classification
• Linear discriminants– Two-class– Multicategory
• Criterion functions J for computing discriminants
– Learning as minimization of J• Generalized linear discriminants• Neural networks
– Application: Face finding