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Below are a collection of links to computer vision related notes I've written  (as a mean of grasping certain topics) and collected during my tenure as a grad student.  Comments?  Suggestions?  Feel free to send me email at kosta at cs dot yorku dot ca

 


Table of contents:


 

Motion:

  • A review of the characterization and recovery of motion from image sequences by Konstantinos G. Derpanis (York University): link
  • The motion field and its affine approximation by Konstantinos G. Derpanis (York University): pdf
  • The kinematic parameterization of affine motion by Konstanitnos G. Derpanis (York University): pdf
  • A brief note on the computation of optical and affine flow by Konstantinos G. Derpanis (York University): pdf
  • Single 2D Orientation Estimation via the Structure Tensor by Konstantinos G. Derpanis (York University): pdf
  • A short review of Masahiko Shizawa and Kenji Mase's Superposition Principle for multiple motion analysis by Konstantinos G. Derpanis (York University): pdf
  • A short review of phase-based optical flow by Konstantinos G. Derpanis (York University): pdf
  • A summary of Bayesian motion estimation by Konstantinos G. Derpanis (York University): pdf
  • A summary of the derivation of the frequency space interpretation of a translating scene.  This forms the basis for several frequency domain motion estimation techniques by Konstantinos G. Derpanis (York University): pdf
  • Relationship between SSD and cross correlation template matching by Konstantinos G. Derpanis (York University): pdf

 

Frequency analysis:

  • A review of representing frequency content in complex notation by Konstantinos G. Derpanis (York University): pdf
  • Fourier transform definitions by Konstantinos G. Derpanis (York University): pdf
  • Review of Quadrature filters by Konstantinos G. Derpanis (York University): pdf
  • General proof of smoothness for Eero Simoncelli's Donut Operator by Konstantinos G. Derpanis (York University): pdf
  • Fast Gabor filtering by Konstantinos G. Derpanis (York University): pdf
  • Review of Fourier analysis and sampling by James W. MacLean (University of Toronto): pdf
  • A brief introduction to the Fourier transform by Hagit Shatkay (Queen's University): link
  • Proof of the Time-Frequency Uncertainty Principle by (Bob Williamson coauthor of the Fourier Song): link

 

Multiscale analysis:

  • Review of the Gaussian Pyramid by Konstantinos G. Derpanis (York University): pdf
  • A tutorial on scale-space theory by Tony Lindeberg (KTH NADA): link

           

(Left) original image, (Right) several slices from the linear scale-space representation.

 

  • A review of Gabor filters by Konstantinos G. Derpanis (York University): pdf
  • Outline of the relationship between the difference-of-Gaussian and Laplacian-of-Gaussian representations by Konstantinos G. Derpanis (York University): pdf
  • Review of scale-space relations of rescaled signals by Konstantinos G. Derpanis (York University): pdf
  • A review of integral image-based representations by Konstantinos G. Derpanis (York University): pdf

 

Steerable filters:

 

  
The three leftmost images represent the modulated G2 basis filters and the rightmost represents the resulting steered G2 filter. For an animation depicting the steering of the first to fourth derivative of the 2D Gaussian, see avi.

 

  • Notes on steerable filters by David J. Heeger (New York University): pdf
  • A summary of the steerability of one-dimensional nth-order derivatives by Konstantinos G. Derpanis (York University): pdf
  • A summary of Mats T. Andersson's adaptive (steerable) filters by Konstantinos G. Derpanis (York University): pdf

 

Expectation Maximization Algorithm (EM algorithm):

  • A summary of Jensen's Inequality by Konstantinos G. Derpanis (York University): pdf
  • A review of the Expectation Maximization (EM) Algorithm by Konstantinos G. Derpanis (York University): pdf
  • K-means clustering by Konstantinos G. Derpanis (York University): pdf
  • An introduction to mixture models and the EM algorithm by Justus H. Piater (Universite de Liege): pdf
  • A tutorial on the EM algorithm by Sean Borman (University of Notre Dame): pdf

 

Differential geometry:

  • A non-rigorous introduction to differential geometry by Bryan S. Morse (Brigham Young University): pdf
  • A summary of the Isophote Curvature in an Image by Konstantinos G. Derpanis (York University): pdf

 

Kalman filter:

  • R.E. Kalman's seminal paper on the Kalman filter: link
  • A Kalman filter introduction by Greg Welch and Gary Bishop (University of North Carolina at Chapel Hill): link
  • A historical view of Least Squares Estimation , beginning with Gauss' contributions up to Kalman's by H.W. Sorenson: pdf
  • Introduction to Linear Dynamical Systems by Konstantinos G. Derpanis (York University): pdf

 

Interest point operators:

  • A derivation of the Harris Corner Detector by Konstantinos G. Derpanis (York University): pdf, a copy of the original paper titled "A Combined Corner and Edge Detector" by  Chris Harris and Mike Stephens can be found here
  • A  draft survey (with slides) on local  invariant features by Tinne Tuytelaars (K.U.Leuven) and  Krystian Mikolajczyk (University of Surrey): link

 

Computer vision course notes:

  • Lecture notes covering introductory topics of computer vision by Richard Wildes (York University): link
  • Lecture notes covering mathematical methods for computer vision by George Bebis (University of Nevada): link
  • Video lecture on model-based vision (1987) by Joseph Mundy (Brown University): link

 

Mathematical methods:

  • Review of the calculus of variations by Konstantinos G. Derpanis (York University): pdf
  • Review of the Singular Value Decomposition by Konstantinos G. Derpanis (York University): pdf
  • Notes of standard material on mathematical methods for robotics and computer vision by Carlo Tomasi (Duke University): pdf
  • Notes on standard optimization methods in computer vision by Neil Thacker (University of Manchester) and Tim Cootes (University of Manchester): pdf

 

Statistics/probability notes:

  • Proof of the Cramer-Rao bound for a single parameter by Konstantinos G. Derpanis (York University): pdf
  • Summary of Mean Shift clustering by Konstantinos G. Derpanis (York University): pdf
  • Mean Shift derivation by Konstantinos G. Derpanis (York University): pdf

Mean shift path

 

 

  • A tutorial on the Mean Shift algorithm that covers both theory and applications by Yaron Ukrainitz and Bernard Sarel (Weizmann Institute of Science): ppt
  • An overview of RANdom SAmple Consensus (RANSAC) algorithm by Konstantinos G. Derpanis (York University): pdf
  • The integral of a Gaussian by Konstantinos G. Derpanis (York University): pdf

 

Linear algebra course notes:

  • Professor Gilbert Strang's Linear Algebra Class Lecture Videos: link
  • Reference material covering linear algebra and the properties of real and complex matrices: link

 

Machine learning:

  • Collection of machine learning related video lectures: link
  • Sam Roweis' (University of Toronto) collection of machine learning related tutorial notes: link
  • Max Welling's (University of California, Irvine) classnotes in machine learning: link

 

Technical writing:

  • "How to write a conference Paper", by William Freeman (MIT): ppt
  • "Notes on technical writing", by Don Knuth (Stanford): pdf
  • "What's wrong with these equations", by David Mermin, Physics Today, Oct., 1989: pdf

 

Miscellaneous:

  • A summary of the SVD approach for decomposing general 2D linear digital filters into the sum of separable filters by Konstantinos G. Derpanis (York University): pdf
  • The Bhattacharyya measure for measuring the dissimilarity between distributions by Konstantinos G. Derpanis (York University): pdf
  • Fourier transform of the Gaussian by Konstantinos G. Derpanis (York University): pdf
  • Implementing continuous convolutions by Konstantinos G. Derpanis (York University): pdf
  • Review of binomial filters by Konstantinos G. Derpanis (York University): pdf
  • Review of Lagrange multipliers by Konstantinos G. Derpanis (York University): pdf
  • A comparative study of the application of graph cut methods in vision, graphics and machine learning by Sudipta Sinha (University of North Carolina): pdf
  • Kermit Sigmon's Matlab Primer Third Edition: pdf
  • A quick introduction to OpenGL and GLUT by Bill Kapralos (York University): Part 1 (pdf) and Part 2 (pdf)
  • A review of linear least squares by David R. Martin (Boston College): pdf
  • A short introduction to rotations with quaternions by Peter Grogono (Concordia University): pdf
  • A list of titles of Jim Blinn's (Microsoft Research) column for the IEEE Computer Graphics and Applications journal.  The articles deal (at a fairly highly level) with topics in graphics and signal processing: link
  • Videos of ICCV 2003 podium presentations: link
  • Resources for students and scholars by Fredo Durand (MIT): link
  • Videos of talks on a wide range of topics in computer vision: link
  • "Paper Gestalt" (appearing in the Secret Proceedings of CVPR 2010) describes an automated system for deciding whether to accept/reject a conference paper using state-of-the-art computer vision methods by Carven von Bearensquash (University of Phoenix)

 

 

Last Updated: August 1, 2010.

 


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