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) 7846463
 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
Useful Mathematics, Statistics, and Geometry resources
Course Description
Computer Vision is a broadbased 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 IIII, 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
Ghostview(software for viewing postscript files)
ResearchIndex (a scientific literature digital library  find papers easy !)
Syllabus
Course Project
Course Material
Linear Algebra Review
 Lecture Slides
 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, 1.31.4, 1.6, 3.13.4, 4.14.2, 5.35.6, 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(by Zehang Sun)
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. 3744  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, JohnWiley,
2nd edition, 2001 (Chapt 1, hard copy)
 C. Bishop Neural Networks for Pattern Recognition, Oxford, 1997 (pp. 117, 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. 417, 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. 168173 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. 1113).
 Case Studies
 M. Turk and A. Pentland, Eigenfaces for Recognition, Journal of Cognitive Neuroscience, vol. 3, no. 1, pp. 7186, 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. 524, 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. 173175 and Appendix C: Mathematical Details, hard copy)
 R. Duda, P. Hart, and D. Stork Pattern Classification, JohnWiley,
2nd edition, 2001 (pp. 117124, hard copy)
 A. Webb Statistical Pattern Recognition, Arnold, 1999 (pp. 112116,
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. 831836, 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. 711720, 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, AddisonWesley,
1992 (pp. 81100, hardcopy)
 Case Studies
 T. Wallace and P. Wintz, "An efficient threedimensional aircraft recognition algorithm using normalized fourier descriptors", Computer Graphics and Image
Processing, vol. 13, pp. 99126, 1980 (hardcopy).
 G.Voyatzis, N.Nikolaidis and I.Pitas, DIGITAL IMAGE WATERMARKING : AN OVERVIEW, ICMCS, Vol. 1, 1999.
 Ruanaidh, Joseph J.K.Ò.; Pun, Thierry Rotation, scale and translation invariant spread spectrum digital image watermarking , Signal Processing, vol. 66, no. 3, pp. 303317, 1998.
 V. Solachidis and I.Pitas, Circularly Symmetric Watermark Embedding In 2D DFT Domain, Proceedings of the IEEE Int. Conf. on Acoustics, Speech, and Signal
Processing , Vol. 6, pp. 34693472, 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. 7684, 1995.
 C. Burrus, R. Gopinath, and H. Guo, Introduction to Wavelets and Wavelet
Transforms: A Primer, Prentice Hall, 1998 (Chapters 13, hardcopy).
 S. Umbaugh, Computer Vision and Image Processing: A Practical Approach
Using CVIPtools, Prentice Hall, 1998 (pp. 125130, hardcopy).
 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. 277286, 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. 235245, 1995.
 Software
 Wavelab Wavelet Analysis Toolbox (Matlab software)
 Resources
Probability Review
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, JohnWiley,
2nd edition, 2001 (2.1, 2.42.6, 3.13.2 , hardcopy).
 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.
4551, 1998.
 K. Sung and T. Poggio, Examplebased learning for viewbased human face detection, IEEE Transaction on Pattern Analysis and Machine Intelligence,
vol. 20, no. 1, pp. 3951, 1998.
 A. Madabhushi and J. Aggarwal, A bayesian approach to human activity recognition, 2nd International Workshop on Visual Surveillance, pp. 2530, 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 Realtime Face Tracker, Proceedings of WACV'96, 1996.
 Resources
 Software
Mixtures and the ExpectationMaximization (EM) Algorithm
 Lecture Slides
 Case Studies Slides
 Reading Assignments
 T. Mitchell, "Machine Learning", McGrawHill, 1997 (section 6.12 hardcopy).
 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 ExpectationMaximization 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. 696710, 1997.
 S. McKenna, Y. Raja, and S. Gong, Tracking color objects using adaptive mixtur e models, Image and Vision Computing, vol. 17, pp. 225231, 1999.
 C. Stauffer and E. Grimson, Adaptive background mixture models for realtime tracking, IEEE Computer Vision and Pattern Recognition Conference, Vol. 2, pp. 246252, 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. 913, 2000.
 Resources
Neural Networks (NNs)
 Lecture Slides
 Case Studies Slides
 Reading Assignments
 Case Studies
 H. Rowley, S. Baluja, and T. Kanade Neural NetworkBased Face Detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 20, No. 1, January, 1998, pp. 2338.
 H. Rowley, S. Baluja, and T. Kanade Rotation Invariant Neural NetworkBased 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, JohnWiley,
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. 637646,
1998.
 A. Mojan, C. Papageorgiou and T. Poggio, Examplebased object detection in images by components, IEEE Transaction on Pattern Analysis and Machine Intelligence, vol. 23, no. 4, pp. 349361, 2001.
 B. Moghaddam and M. Yang, Gender Classification with SVM, IEEE Conference on Face and Gesture Recognition, pp. 306311, 2000.
 Resources
 Software
mySVM  an implementation of the Support Vector Machine.
Genetic Algorithms (GAs)
 Lecture Slides
 Reading Assignments
 GA Tutorial.
 M Srinivas and L. Patnaik, Genetic Algorithms: A Survey, IEEE Computer, pp. 1726, 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. 165170, 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. 132146, 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. 225246, 2000.
 Software
Hidden Markov Models (HMMs)
 Lecture Slides
 Reading Assignments
 R. Duda, P. Hart, and D. Stork Pattern Classification, JohnWiley,
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. 257286, 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
 Resources
 Software
Bayesian Networks
 Reading Assignments
 Case Studies
 Web Resources
 Software
Kalman filter
 Reading Assignments
 Case Studies
 Web Resources
 Software
Programming Assignments