Final Review Course web page: vision.cis.udel.edu/~cv May 21, 2003 Lecture 37.

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