‎"Behind every stack of books there is a flood of knowledge."

Geometrical image analysis


Lecture notes

HZ – Hartley, Zisserman, Multiple View Geometry in computer vision.


  • Math
  • Graphics
  • Factorization, camera matrices.
    • rq.m The RQ factorization.
    • cholesky.m Cholesky decomposition.
    • rotmat3d.m Generate rotation matrix from 3 Euler angles.
    • derotmat3d.m Unpack a rotation matrix into Euler angles.
    • melencomp.m Construct a camera matrix according to the paper by Melen.
    • melendecomp.m Unpack a camera matrix according to the paper by Melen.
  • Förstner-related code
    • corners.m Code that filters an image according to the Harris and Förstner papers.
    • localmax.m Local non-maxima suppression.
    • islocalmax.m Filter kernel to localmax.
    • seldomness.m Calculate the seldomness coefficient.
    • crosscorr.m Calculate normalized cross-correlation between two image.
    • foerstnerpttest.m Test code to illustra the refined, subwindow Förstner operator.
  • Optimization.
    • gaussn.m The Gauss-Newton method for solving weighted non-linear least squares problems.
    • sqpw.m The Gauss-Newton method for solving non-linear least squares problem with non-linear equality constraints (SQP=Sequential quadratic programming).
    • jacapprox.m Numerical approximation of jacobian.
  • The fundamental matrix
    • fmat7solve.m The 7-point algorithm for the fundamental matrix.
    • dist2lines.m Closest distance between points and lines.
    • calcfundgeom.m Find optimal fundamental matrix by minimizing the reprojection error. Uses sqpw.m and support functions
    • matchedpt.m Correctly matched points.


Course textbook

Richard Hartley and Andrew Zisserman Multiple View Geometry in computer vision, 2nd ed., Cambridge Press, 2004, ISBN-0-521-54051-8. Link to textbook homepage.Course textbook

Reference literature

  • Photogrammetry
    • Chris McGlone, ed., Manual of Photogrammetry, 5th ed., ASPRS 2004, ISBN 1-57083-071-1.
    • Edward M. Mikhail, James S. Bethel, J. Chris McGlone, Introduction to Modern Photogrammetry, Wiley 2001, ISBN 0-471-30924-9.
    • K. B. Atkinson, ed., Close Range Photogrammetry and Machine Vision, Whittles 2001, ISBN 1-870325-73-7.
    • H. M. Karara, ed. Non-Topographic Photogrammetry, 2nd ed., American Society for Photogrammetry and Remote Sensing 1989, ISBN 0-944426-10-7.
  • Computer vision
    • Emanuele Trucco, Alessandro Verri, Introductory Techniques for 3-D Computer Vision, Prentice-Hall 1998, ISBN 0-13-261108-2.
    • Olivier Faugeras, Three-dimensional Computer Vision – A Geometric Viewpoint, MIT Press 1996, ISBN 0-262-06158-9.
  • Image processing
    • Rafael C. Gonzalez, Richard E. Woods, Digital Image Processing, 2nd ed., Prentice-Hall 2002, ISBN 0-13-094650-8.
    • Kenneth R. Castleman, Digital Image Processing, Prentice-Hall 1996, ISBN-0-13-211467-4.
    • Gösta H. Granlund, Hans Knutsson, Signal Processing for Computer Vision, Kluwer 1995, ISBN 0-7923-9530-1.
  • Non-linear optimization
    • Stephen G. Nash, Ariela Sofer, Linear and Nonlinear Programming, McGraw-Hill 1996, ISBN 0-07-114537-0.

Sample chapters

  • Contents  pdf
  • Introduction  pdf
  • Epipolar Geometry and the Fundamental Matrix  pdf
  • The Trifocal Tensor  pdf
  • Bibliography  pdf


Matlab code

Corrections and Errata (pdf)



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