Multiple View Geometry in Computer Vision
Richard Hartley and Andrew Zisserman
Cambridge University Press
Reference Texts
Computer Vision : A Modern Approach
David Forsyth and Jean Ponce
Prentice Hall, 2002
Three-Dimensional Computer Vision: A Geometric Approach
Oliver Faugeras
The MIT Press
The Geometry of Multiple Images
Oliver Faugeras and Quang-Tuan Luong
The MIT Press
Introductory Techniques for 3D Computer Vision
Trucco and Verri
Prentice Hall, 1998
Course Syllabus:
Projective Geometry and Transformations (Chapters 1-4)
Camera Geometry and Single View Geometry (Chapters 5-7)
Two-View Geometry, Epipolar Geometry, Fundamental Matrix and 3D
Reconstruction (Chapters 8-13).
If time permits, some discussion
of Three View Geometry and Trifocal Tensor.
Interesting Topics organized by Applications/Projects:
Image (affine, metric, perspective) Rectification
Automatic Computation of Homography using RANSAC
Camera Calibration and Radial Distortion
Camera Rotation and
Video Mosaicing
Camera Translation and Stratified 3D Reconstruction
Topics and Schedule:
Lecture 1: Overview, Expectations and Projects
Projective Geometry: Points, Lines, Duality
Line at Infinity, Conics, Topology
April 4
Chapter 1, Sections 1.1, 1.2, 1.6 of TextBook
Lecture 2: Projective Transformations
Euclidean, Similarity, Affine Transformations, Cross-Ratio
April 6
Chapter 1, Sections 1.3, 1.4 and 1.5 of TextBook
Lecture 3: Linear Alegbra
Eigenvalue Decomposition, Singular value Decomposition
RQ Decomposition, Cholesky Factorization
April 11
Part of Appendix 3 of TextBook and supplemented by classnotes
Lecture 4: Image Rectification
Affine Rectification, Metric Rectification
Circular Points, Angles on Projective Planes
April 13
Sections 1.7 of TextBook
Lecture 5: Conics, Fixed Points, Lines
April 18
Sections 1.8 and 1.9 of TextBook
Lecture 6: 3D Projective Geometry and Transformations
Points, Lines, Planes, Quadrics, Plucker Coordinates
Euclidean, Similarity, Affine Transformations
April 20
Sections 2.1, 2.2, 2.3, 2.4 of TextBook
Lecture 7: 3D Projective Geometry Concluded
Computation of 2D Projective Tranformations
Plane at Infinity, Absolute Conic, Absolute Dual Quadric
April 25
Section 2.5, 2.6, and 2.7 of TextBook
Section 3.1 of Textbook
Lecture 8: Computation of 2D Projective Transformations; RANSAC
April 27
Section 3.1, 3.2, 3.4.4, 3.7, 3.8 of TextBook
Lecture 9: Corner Detection, Point Correspondences,
Camera Matrix, Computation of Camera Matrix
May 2
Section 5.1, 6.1
Lecture 10: Camera Matrix Computation, Camera Calibration
Radial Distortion
Action of Projective Planes
Video Mosaicing
May 4
Section 6.1, 6.4, 7.1, 7.2, 7.3, 7.4
Class 11: No Class on May 9
There will be additional meeting time to make up.
Lecture 12: Deeper Understanding of Camera Internal Matrix
May 11
Sections 7.5, 7.6, 7.7
Lectures 13 and 14: Epipolar Geometry, Fundamental Matrix, Essential
Matrix
May 16 and 18
Chapter 8: 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 9, 10, 11
Lecture 15: 3D Reconstruction (Structure Computation), Image
Rectification
May 23
Chapter 9, 10, 11
Class 16: No Class on May 25
There will be additional meeting time to make up.
Lectures 17: Discussion of Presentation Topics/Final
Project/Exam
May 30
Lectures 19 and 20: Student Presentations/ Additional Topics
June 6 and June 8
Final Demonstration and Final Project Report
June 14, Wednesday, 12-3 (during exam Time)
Expectations and Evaluation:
Five Bi-Weekly Homeworks (40%)
Examination 1 (15%)
Class Presence and Participation (10%)
Class Presentation (15%)
Final Project Demo and Software and Report (20%)
Prerequisites:
Working knowledge of Matlab and/or OpenGL/FLTK(or XFORMS/GLUT) and
C (or C++) is required.
Maturity to read technical papers in the area
of vision/graphics is expected.
Ability to choose a project (with
assistance/guidance if necessary) and determination to follow through
with dedicated work is also expected.
Prior exposure to CMPS160/CMPS161/CMPS 262/CMPS290B/CE264/EE264
is a plus but not required.
Assignments:
Assignment 1: Linear Algebra and Projective Geometry
Target Due Date: April 25, Tuesday, 10:00am
Assignment 1
Assignment 2: Image Rectification
Target Due Date: May 4, Thursday, 10:00am
Assignment 2
Assignment 3: Homography Computation
Target Due Date: May 11, Thursday, 10:00am
Assignment 3
Assignment 4: Computation of Camera Matrix/Camera Calibration
Target Due Date: May 18, Thursday, 10:00am
Assignment 4
Assignment 5: Video Mosaicing
Target Due Date: May 30, Tuesday, 10:00am
Assignment 5