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Introduction

General Info. Lecture/Time/Session:L01, TR 15:30-16:45, Winter 2012Room: MS 623Office Hours: TR 14:00-15:00E-mail: samavati@cpsc.ucalgary.caWebsite: www.cpsc.ucalgary.ca/~samavati/Course: www.cpsc.ucalgary.ca/~samavati/cpsc601.13. Course Info. Prerequisites: CPSC 453 is recommendedGradin

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Introduction

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    1. Introduction Faramarz Samavati

    2. General Info Lecture/Time/Session: L01, TR 15:30-16:45, Winter 2012 Room: MS 623 Office Hours: TR 14:00-15:00 E-mail: samavati@cpsc.ucalgary.ca Website: www.cpsc.ucalgary.ca/~samavati/ Course: www.cpsc.ucalgary.ca/~samavati/cpsc601.13 There are many tools and methods that can provide 3D meshes. Also many databases.There are many tools and methods that can provide 3D meshes. Also many databases.

    3. Course Info Prerequisites: CPSC 453 is recommended Grading: Assignment 40%(homework, case studies and presentations) In-Class Exam 20% Project 40% Proposal Paper reading (10 minutes presentation of related works) Final Presentation Final report Program (if any)

    4. What is the main goal of the course? Mathematical modeling is the hurt of computer graphics and also visualization. we need computational techniques too Solve these models. A wide variety of models) techniques are used in the current graphics (see the recent siggraph papers), however many of these models/ techniques belong to 1- Numerical Linear Algebra/ matrix computations 2- mathematical optimization (Numerical ) 3 -Differential Equations (Numerical) 4-Differential Geometry ( Discrete)

    5. Criteria Exclude current knowledge of Computer science curriculum: Calculus/Advanced Calculus Probability and statistic Introductory Computational techniques(cpsc493) Graph based techniques(cpsc331, cpsc413) Computational geometry

    6. The course outline Introduction Vector and Matrix Norm, Null and range spaces Algorithmic methods for, SVD, LU and QR decompositions Least squares Eigen values/vectors Iterative methods for solving system of equations Minimization and optimization Case studies in Graphics and Visualization Selective topics (based on the case studies)

    7. Recommended references Mathematical Optimization in Computer graphics and Vision, Luiz Velho et. al. Morgan Kaufmann Publishers, 2008. Also siggraph course notes 2004. Numerical Mathematics and Computing, 5thEdition, Ward Cheney and David Kincaid, 2004. G.H. Golub and C.F. Van Loan, Matrix Computations, Third Edition. The Johns Hopkins University Press, 1996. P.E.Gill, W. Murray and M.H. Wright, Numerical Linear Algebra and Optimization, Addison Wesley Publishing Company, 1990. Many online papers/course-notes that will be provided during the semester Online course material (need to be updated)

    8. What are these methods? It is hard to answer. I randomly picked several recent SIGGRAPH proceedings. Focus on SIGGRAPH 2004 First fact: almost all (86 from 90) use a kind of general computational techniques!

    9. What remains? Numerical Linear algebra (Matrix Computation) Optimization (mostly linear and least squares) Differential Geometry( Discrete) Differential Equation Appear in more than 50% of the papers directly/indirectly

    10. Is it possible to cover all of these methods in just one course? No. There is wide variety of methods For example, several courses can be assigned just to Numerical Optimization Breath versus Depth in the course! Strategy: Cover basic concepts and methods in all topics More emphasize on Least squares, optimization Matrix Computations Cover as much as possible while you have a good depth.Cover as much as possible while you have a good depth.

    11. A case study Again from SIGGRAPH 2004 I tried to pick a random work that I have not read before and it does not directly relates to my current research

    12. Deformation Transfer To Triangles Meshes

    13. Abstract Methodology: Optimization Necessary tool: Matrix Computations

    14. Deformation Transfer Change in the source Change in the Target

    15. What is deformation? A collection of affine transformation One transformation per face (Q):

    16. Correspondence Correspondence is provided by user Arbitrary mapping from source triangles to target triangles

    17. Can we transfer the affine transformation? Use the same affine transformation for target Inconsistency of the faces

    18. How can we fix it? Maintain consistency by changing transformations using extra constraint Many solutions!!!

    19. Which solution is better? Smaller changes is better Minimization model: The The

    20. The problem What is this problem? What is ? How can we solve it? A constraint optimization Matrix norm (Frobenius) See the next page!!

    21. Proposed Solution Least squares problem Normal equation LU factorization

    22. Other parts Correspondence Energy Minimization Deformation smoothness Again models to minimization

    23. All necessary background will provide in this course! Course Outline 1-Introduction 2-Vector and Matrix Norm, Null and range Methods for 3-SVD decomposition 4-LU and QR decomposition 5-Least squares 6-Eigen values/vectors 7-iterative methods for solving system of equations 8-Conjugate gradient methods 9-minimization and optimization 10-Discrete Differential Geometry 11-Differential equations 12-Case studies in Graphics and Visualization Papers method Matrix Norm Minimization and Optimization Least Squares LU factorization

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