L19(Review)

L19(Review) - Final Review 6-6-06 (Starts on Slide 17)...

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1 Final Review 6-6-06 (Starts on Slide 17) CS/ECE 181b Midterm Review May 11, 2006
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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
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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
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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
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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
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6 Topics • Image Formation • Projective Geometry • Camera Models Stereo • Edge Detection Stereo • Epipolar Geometry • Essential Matrix • Fundamental Matrix
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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
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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
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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
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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
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L19(Review) - Final Review 6-6-06 (Starts on Slide 17)...

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