Computer Science Department

CS4/791Y: Mathematical Methods for Computer Vision (Fall 2003)

Meets: TR: 2:30 - 3:45pm (MS 227)

Instructor: Dr. George Bebis

Email: bebis@cs.unr.edu
Phone: (775) 784-6463
Office: 235 SEM
Office Hours: TR noon - 1:00PM

Texts:

No text is required for this class. Reading assignments, based on notes and papers, will be posted on the web on a weekly basis.

Related UNR Courses

Computer Vision resources

Useful links to Neural Networks and Genetic Algorithms resources

Useful links to Pattern Recognition resources

Useful links on Algorithms resources

The Stony Brook Algorithm Repository

Useful Mathematics, Statistics, and Geometry resources

Course Description

Computer Vision is a broad-based field of computer science that requires students to understand and integrate knowledge from numerous disciplines such as Image Processing, Computer Graphics, Pattern Recognition, Machine Learning, Neural Networks, Genetic Algoritnms, Fuzzy Logic, and Artificial Intelligence. Students are expected to strong background in calculus, linear algebra, probabilities, statistics, geometry, and algorithms. Scientists engaged in this field inevitably have to learn many things about a discipline in which they did not receive formal training. Computer science and electrical engineering majors, however, do not necessarily have an interdisciplinary background. In an effort to makeup for students' weak background, many instructors either spend too much time on teaching background concepts or just skip the mathematical details and proceed immediately to demos and implementation. The purpose of this course is to help bridge the gap for more students to do research in computer vision by teaching them some of the most important and essential mathematical tools used in computer vision research. Our goal is to emphasize those mathematical techniques which have been extensively evaluated and demonstrated to be useful in practical applications. Our emphasis will be on the application aspect of these mathematical techniques in computer vision. We will try to cover at least one technique each week. Once we have discussed the necessary mathematical details, we will concentrate on discussing applications.

Course Policies

Exams/Quizzes: there will be no exams but there will be short quizzes every time we finish a topic.

Course Project: there will a course project which should be done on an individual basis. Specific project ideas will be discsused in class. You will be using C++ or Matlab. You will be required to turn in regular progress reports and a final report which should include a description of the problem, a description of your approach, and your evaluation of the results. You will be also required to do a presentation of your project work at the end of the semester.

Presentations: each student is required to present a few papers to the rest of the class. The presentations should be professional as if it was presented in a formal conference (i.e., slides/projector).

Course Prerequisites

Calculus I-III, Probabilities and Statistics, Data Structures and basic knowledge of image manipulation. Background on Linear Algebra will be very useful. Courses on image processing, computer vision, pattern recognition, machine learning, neural networks, artificial intelligence, and genetic algorithms are recommended, but not required. Good programming skills are essential.

Matlab Resources

Matlab
Matlab(1) is a numeric computation and visualization environment. The image processing and signal processing toolboxes are especially useful. See also: Matlab Tutorial (Univ Utah), Matlab Basics (RPI), Matlab Primer (200K postscript; 25 pages).
Matlab Tutorial - Rice University
Other Matlab Tutorials
Building GUIs with Matlab
Octave a public-domain matlab compatible language
PRTools a Matlab Toolbox for Pattern Recognition
DIPimageA Scientific Image Processing Toolbox for MATLAB
Genetic/Evolutionary Algorithms for MATLAB

Ghostview(software for viewing postscript files)

ResearchIndex (a scientific literature digital library - find papers easy !)

Syllabus

Syllabus (pdf)

Course Project

Guidelines(pdf)

Course Material

Linear Algebra Review

Lecture Slides
- Vectors(in pdf)
- Vector Spaces(in pdf)
- Matrices(in pdf)
- Eigenvalues and Eigenvectors(in pdf)
- Linear Systems of Equations(in pdf)
Reading Assignments
- A Brief Review of Linear Algebra
- Matrix Algebra Review
- H. Anton and C. Rorres Elementary Linear Algebra (Applications Version), 8th edition, John Wiley, 2000 (1.1, 1.3-1.4, 1.6, 3.1-3.4, 4.1-4.2, 5.3-5.6, 7, hard copy)
- J. Pricipe et al. Neural and Adaptive Systems: Fundamentals Through Simulations (Appendix A: Elements of Linear Algebra and Pattern Recognition, hard copy)
- K. Kastleman Digital Image Processing (Appendix 3: Mathematical Background, hard copy)
- F. Ham and I. Kostanic Principles of Neurocomputing for Science and Engineering, Prentice Hall, (Appendix A: Mathematical Foundation for Neurocomputing, hard copy)
- B. Kolman and D. Hill Introductory Linear Algebra with Applications, 2nd edition, Prentice Hall, 2001 (Chapter 12: Matlab for Linear Algebra, hard copy)
Other Good Linear Algebra Books
- B. Kolman and D. Hill Introductory Linear Algebra with Applications, 2nd edition, Prentice Hall, 2001
- L. Johnson, R. Riess, and J. Arnold Introduction to Linear Algebra, 4th edition, Addison Wesley, 1998

Matlab Tutorial Presentation

Singular Value Decomposition (SVD)

Lecture Slides(in pdf)
Reading Assignments
- Introduction to SVD
- E. Trucco and A. Verri Introductory Techniques for 3D Computer Vision (Appendix 6, hard copy)
- K. Kastleman Digital Image Processing (Appendix 3: Mathematical Background, hard copy)
- F. Ham and I. Kostanic Principles of Neurocomputing for Science and Engineering, Prentice Hall, (Appendix A: Mathematical Foundation for Neurocomputing, hard copy)
- M. Petrou and P. Bosdogianni Image Processing: The Fundamental John Wiley, 2000 (pp. 37-44 - examples of SVD, hard copy)
Case Studies
Software

Review on Pattern Recognition

Lecture Slides(sorry, no figures)
Reading Assignments
- R. Duda, P. Hart, and D. Stork Pattern Classification, John-Wiley, 2nd edition, 2001 (Chapt 1, hard copy)
- C. Bishop Neural Networks for Pattern Recognition, Oxford, 1997 (pp. 1-17, hard copy)
- Jain, A.K.; Duin, P.W.; Jianchang Mao, Statistical pattern recognition: a review, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 22 No 1 , Jan. 2000 (read pp. 4-17, skip what you do not understand)
Case Studies
Software
- PRTools a Matlab Toolbox for Pattern Recognition

Principal Components Analysis (PCA)

Lecture Slides(in pdf)
Case Study 1 Slides(in pdf)
Case Study 2 Slides(in pdf)
Reading Assignments
- S. Gong et al. Dynamic Vision: From Images to Face Recognition, Imperial College Pres, 2001 (pp. 168-173 and Appendix C: Mathematical Details, hard copy)
- K. Kastleman Digital Image Processing (Appendix 3: Mathematical Background, hard copy)
- F. Ham and I. Kostanic Principles of Neurocomputing for Science and Engineering, Prentice Hall, (Appendix A: Mathematical Foundation for Neurocomputing, hard copy)
- Jain, A.K.; Duin, P.W.; Jianchang Mao, Statistical pattern recognition: a review, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 22 No 1 , Jan. 2000 (read pp. 11-13).
Case Studies
- M. Turk and A. Pentland, Eigenfaces for Recognition, Journal of Cognitive Neuroscience, vol. 3, no. 1, pp. 71-86, 1991 (hard copy)
- H. Murase and S. Nayar, Visual Learning and Recognition of 3D Objects from Appearance, Interantional Journal of Computer Vision, vol 14, pp. 5-24, 1995 (hard copy)
- K. Ohba and K. Ikeuchi, Detectability, Uniqueness, and Reliability of Eigen Windows for Stable Verification of Partially Occluded Objects, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 19 No 9 , Sept. 1997
Software

Linear Discriminant Analysis (LDA)

Lecture Slides(in pdf)
Case Studies Slides(in pdf)
Reading Assignments
- S. Gong et al. Dynamic Vision: From Images to Face Recognition, Imperial College Pres, 2001 (pp. 173-175 and Appendix C: Mathematical Details, hard copy)
- R. Duda, P. Hart, and D. Stork Pattern Classification, John-Wiley, 2nd edition, 2001 (pp. 117-124, hard copy)
- A. Webb Statistical Pattern Recognition, Arnold, 1999 (pp. 112-116, hard copy).
Case Studies
- Daniel L. Swets, John (Juyang) Weng Using Discriminant Eigenfeatures for Image Retrieval , IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 18, No 8 , pp. 831-836, 1996.
- A. Martinez and A. Kak PCA versus LDA, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 23, No 2, pp. 228 -233, 2001.
- P. Belhumeur et al. Eigenfaces vs Fisherfaces: Recognition Using Class Specific Linear Projection, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 19, No 7 , pp. 711-720, 1997.
Resources
Software

Fourier Transform

Lecture Slides
Case Studies Slides (revised on 9/19/02)
Reading Assignments
- R. Gonzalez and R. Woods, Digital Image Processing, Addison-Wesley, 1992 (pp. 81-100, hard-copy)
Case Studies
- T. Wallace and P. Wintz, "An efficient three-dimensional aircraft recognition algorithm using normalized fourier descriptors", Computer Graphics and Image Processing, vol. 13, pp. 99-126, 1980 (hard-copy).
- G.Voyatzis, N.Nikolaidis and I.Pitas, DIGITAL IMAGE WATERMARKING : AN OVERVIEW, ICMCS, Vol. 1, 1999.
- Ruanaidh, Joseph J.K.�.; Pun, Thierry Rotation, scale and translation invariant spread spectrum digital image watermarking , Signal Processing, vol. 66, no. 3, pp. 303-317, 1998.
- V. Solachidis and I.Pitas, Circularly Symmetric Watermark Embedding In 2-D DFT Domain, Proceedings of the IEEE Int. Conf. on Acoustics, Speech, and Signal Processing , Vol. 6, pp. 3469-3472, 1999.
Software

Wavelets

Lecture Slides(revised on 9/24/02)
Case Studies Slides(revised on 9/24/02)
Fingerprint Compression Slides
Reading Assignments
- E. Stollnitz, T. DeRose, and D. Salesin, Wavelets for Computer Graphics: A Primer (part 1), IEEE Computer Graphics and Applications, vol. 15, no. 3, pp. 76-84, 1995.
- C. Burrus, R. Gopinath, and H. Guo, Introduction to Wavelets and Wavelet Transforms: A Primer, Prentice Hall, 1998 (Chapters 1-3, hard-copy).
- S. Umbaugh, Computer Vision and Image Processing: A Practical Approach Using CVIPtools, Prentice Hall, 1998 (pp. 125-130, hard-copy).
Case Studies
- Christopher M. Brislawn, The FBI Fingerprint Image Compression Standard
- C. Jacobs, A. Finkelstein, and D. Salesin, Fast multiresolution image quering, Proceedings of SIGGRAPH, pp. 277-286, 1995.
- H. Li, B. Manjunath, and S. Mitra, Multisensor Image Fusion Using the Wavelet Transform, Graphical Models and Image Processing, vol. 57, no. 3, pp. 235-245, 1995.
Software
- Wavelab Wavelet Analysis Toolbox (Matlab software)
Resources
- Surfing the Wavelets
- Wavelet Resources

Probability Review

Lecture Slides (in pdf)
Reading Assignments
- R. Duda, P. Hart, and D. Stork Pattern Classification, John-Wiley, 2nd edition, 2001 (appendix A.4, hard copy)
- Everything I need to know about Probability
Resources

Bayes rule, Maximum Likelihood, MAP

Lecture Slides (in pdf)
Case Studies Slides(in pdf)
Reading Assignments
- R. Duda, P. Hart, and D. Stork, Pattern Classification, John-Wiley, 2nd edition, 2001 (2.1, 2.4-2.6, 3.1-3.2 , hard-copy).
- Rusell and Norvig, Artificial Intelligence: A Modern Approach (Chapter 14, hard copy)
- S. Gong et al. Dynamic Vision: From Images to Face Recognition, Imperial College Pres, 2001 (Chapt. 3 hard copy)
Case Studies
- H. Schneiderman and T. Kanade, A Statistical Method for 3D Object Detection Applied to Faces and Cars, Computer Vision and Pattern Recognition Conference, pp. 45-51, 1998.
- K. Sung and T. Poggio, Example-based learning for view-based human face detection, IEEE Transaction on Pattern Analysis and Machine Intelligence, vol. 20, no. 1, pp. 39-51, 1998.
- A. Madabhushi and J. Aggarwal, A bayesian approach to human activity recognition, 2nd International Workshop on Visual Surveillance, pp. 25-30, June 1999 (postscript).
- M. Jones and J. Rehg, Statistical color models with application to skin detection, International Journal of Computer Vision Vol. 46, No. 1, 2002.
- J. Yang and A. Waibel, A Real-time Face Tracker, Proceedings of WACV'96, 1996.
Resources
Software

Mixtures and the Expectation-Maximization (EM) Algorithm

Lecture Slides
Case Studies Slides
Reading Assignments
- T. Mitchell, "Machine Learning", McGraw-Hill, 1997 (section 6.12 hard-copy).
- S. Gong et al. "Dynamic Vision: From Images to Face Recognition", Imperial College Pres, 2001 (Appendix C, hard copy)
- A. Webb, "Statistical Pattern Recognition", Arnold, 1999 (section 2.3, hard copy)
- Todd Moon The Expectation-Maximization Algorithm, IEEE Signal Processing Magazine, November 1996.
Case Studies
- B. Moghaddam and A. Pentland, Probabilistic visual learning for object representation, IEEE Transaction on Pattern Analysis and Machine Intelligence, vol. vol. 19, no. 7, pp. 696-710, 1997.
- S. McKenna, Y. Raja, and S. Gong, Tracking color objects using adaptive mixtur e models, Image and Vision Computing, vol. 17, pp. 225-231, 1999.
- C. Stauffer and E. Grimson, Adaptive background mixture models for real-time tracking, IEEE Computer Vision and Pattern Recognition Conference, Vol. 2, pp. 246-252, 1998.
Resources
Software

Statistical Learning

Lecture Slides
Reading Assignments
- S. Gong et al. Dynamic Vision: From Images to Face Recognition, Imperial College Press, 2001 (Chapt. 3, hard copy).
- T. Evgeniou, M. Pontil, and T. Poggio, Statistical Learning Theory: A Primer, International Journal of Computer Vision, vol. 38, no. 1, pp. 9-13, 2000.
Resources

Neural Networks (NNs)

Lecture Slides
Case Studies Slides
Reading Assignments
- BP Neural Network Tutorial.
- K. Mehrotra, C. Mohan, and S. Ranka, Elements of Artificial Neural Networks, MIT Press, 1997 (Chapter 1).
- G. Bebis and M. Georgiopoulos, " Feed-forward neural networks: why network size is so important" , IEEE Potentials, pp. 27-31, October/November 1994.
Case Studies
- H. Rowley, S. Baluja, and T. Kanade Neural Network-Based Face Detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 20, No. 1, January, 1998, pp. 23-38.
- H. Rowley, S. Baluja, and T. Kanade Rotation Invariant Neural Network-Based Face Detection ,IEEE Conference on Computer Vision and Pattern Recognition, June, 1998.
Resources
Software

Support Vector Machines (SVM)

Lecture Slides
Case Studies Slides
Reading Assignments
- C. Burges, A tutorial on support vector machines for pattern recognition, Data Mining and Knowledge Discovery, Kluwer Academic Publishers, 1998.
- R. Duda, P. Hart, and D. Stork Pattern Classification, John-Wiley, 2nd edition, 2001 (section 5.11, hard copy)
- S. Gong et al. Dynamic Vision: From Images to Face Recognition, Imperial College Press, 2001 (sections 3.6.2, 3.7.2, hard copy).
Case Studies
- M. Pontil and A. Verri, Support vector machines for 3D object recognition, IEEE Transaction on Pattern Analysis and Machine Intelligence, vol. 20, no. 6, pp. 637-646, 1998.
- A. Mojan, C. Papageorgiou and T. Poggio, Example-based object detection in images by components, IEEE Transaction on Pattern Analysis and Machine Intelligence, vol. 23, no. 4, pp. 349-361, 2001.
- B. Moghaddam and M. Yang, Gender Classification with SVM, IEEE Conference on Face and Gesture Recognition, pp. 306-311, 2000.
Resources
Software

Genetic Algorithms (GAs)

Lecture Slides
- Lecture Slides
- Case Studies Slides (set 1)(powerpoint)
- Case Studies Slides (set 2)
Reading Assignments
- GA Tutorial.
- M Srinivas and L. Patnaik, Genetic Algorithms: A Survey, IEEE Computer, pp. 17-26, June 1994.
Case Studies
- Z. Sun, G. Bebis, X. Yuan, and S. Louis, Genetic Feature Subset Selection for Gender Classification: A Comparison Study<, IEEE Workshop on Applications of Computer Vision, pp. 165-170, Orlando, 2002.
- G. Bebis. S. Louis, Y. Varol, and A. Yfantis, Genetic Object Recognition Using Combinations of Views, IEEE Transactions on Evolutionary Computation, vol 6, no. 2, pp. 132-146, April 2002.
- G. Bebis, S. Uthiram, and M. Georgiopoulos, Face Detection and Verification Using Genetic Search,International Journal on Artificial Intelligence Tools, vol 9, no 2, pp. 225-246, 2000.
Software

Hidden Markov Models (HMMs)

Lecture Slides
Reading Assignments
- R. Duda, P. Hart, and D. Stork Pattern Classification, John-Wiley, 2nd edition, 2001 (section 3.10, hard copy)
- L. Rabiner, "A tutorial on HMMs and selected applications in speech recognition", Proceedings of IEEE, vol. 77, pp. 257-286, 1989 (hard copy).
- R. Dugad and U. B. Desai, An Introduction on Hidden Markov Models .
- Ali Rahimi, An Erratum for: A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition
Case Studies
- F. Samaria, Face segmentation for identification using HMMs, British Machine Vision Conference, pp. 399-408, 1993.
- A. Nefian and M. Hayes III, Face Recognition Using An Embedded HMM, Intel, 1999.
Resources
Software
- Hidden Markov Model (HMM) Toolbox (Matlab software)

Bayesian Networks

Reading Assignments
- E. Charniak, 1991. Bayesian Networks without Tears, AI magazine, 1991.
Case Studies
Web Resources
- A Brief Introduction to Graphical Models and Bayesian Networks
- Bayesian Networks
Software

Kalman filter

Reading Assignments
- An Introduction to the Kalman Filter by Greg Welch and Gary Bishop, University of North Carolina at Chapel Hill, Department of Computer Science
- Chapter 1 of Peter Maybeck's Stochastic Models, Estimation, and Control, Volume 1, Academic Press, Inc.
Case Studies
Web Resources
- The Kalman Filter
Software
- Kalman filter toolbox (Matlab software)

Programming Assignments

Programming Assignment 1