L19(Review)

L19(Review) - Final Review(Starts on Slide 17 CS/ECE 181b...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Final Review 6-6-06 (Starts on Slide 17) CS/ECE 181b Midterm Review May 11, 2006
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 • Image Formation • Projective Geometry • Camera Models •S te reo • Edge Detection Image Formation • Pinhole camera geometry – Perspective projection • Vanishing point – What is it? – How do you geometrically construct the vanishing point of a line in 3-D • Orthographic and Parallel Projections
Background image of page 2
3 2-D Projective Geometry • Homogeneous coordinates Points from lines and lines from points – Intersection of parallel lines – Line at infinity Duality principle • Conics and Conic Sections Five points define a conic – Tangent lines and dual conics Homography Projective Transformations – Isometries – Similarities – Affine Transformation – General projective transformation
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 Central Projection • Pinhole camera geometry revisited – Central projection Camera calibration matrix – Camera and World coordinate frames • Interior and Exterior Orientation Finite Projective camera Camera center Column points Principal plane Axis plane Principal point Principal ray Camera anatomy
Background image of page 4
5 [][ ] ± ± ± ± ² ³ ´ ´ ´ ´ µ = 0 0 1 0 p p p p p 4 3 2 1 2 Column Vectors : image of the world origin. The columns of the projective camera are 3-vectors that have a geometric meaning as particular image points. P1: vanishing point of the world coordinate x-axis P2: vanishing point of y-axis P3: vanishing point of z axis Principal Planes Row vectors of the camera projection matrix • Principal axis • Estimating the camera matrix P
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6 Topics • Image Formation • Projective Geometry • Camera Models Stereo • Edge Detection Stereo • Epipolar Geometry • Essential Matrix • Fundamental Matrix
Background image of page 6
7 Epipolar geometry Epipolar Plane Epipoles Epipolar Lines Baseline C 1 C 2 geometric derivation x H x' ± = x' e' l' ± = [] Fx x H e' ± = = ± mapping from 2-D to 1-D family (rank 2) Fundamental Matrix F
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
8 The eight-point algorithm 0 = ± p F p T Invert and solve for F The Correspondence Problem • Establishing correspondence between the two views • Disparity map and depth computations – Random dot stereograms
Background image of page 8
9 June 6, 2006 • Linear Filtering & Edge detection • Eigenfaces and face recognition • Motion and optic flow • Shape from shading Edge detectors • Gradient-based edge detectors – Approximate a spatial derivative – X and Y directions, or at various orientations – Fundamentally high-pass (accentuates noise) • Roberts, Sobel, Prewitt, Canny …. • Laplacian and other band-pass edge detectors
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
10 Digital Implementations • 1st order operator - 1x2 or 2x1 mask – simple – unbalanced (forward differencing) – sensitive to noise E ij , E + 1, ± E x EE i j ²³ + , E , E , + 1 E y + ,, 1 Another Implementation •1 st order operator - 2x2 mask – simple
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/29/2011 for the course ECE 181b taught by Professor Staff during the Fall '08 term at UCSB.

Page1 / 26

L19(Review) - Final Review(Starts on Slide 17 CS/ECE 181b...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online