MATH6212 - Topics in Applied Mathematics II - 2022/23

Announcement

• Suggested reading for presentation:

  1. Discrete Surface Ricci Flow - Computation of surface conformal map using Ricci flow idea 

  2. Folding-Free Global Conformal Mapping for Genus-0 Surfaces by Harmonic Energy Minimization 

  3. Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory

  4. Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing

  5. Shape analysis via inconsistent surface registration

  6. Parallelizable Global Conformal Parameterization of Simply-Connected Surfaces via Partial Welding 

  7. A unifying framework for $n$-dimensional quasi-conformal mappings,

  8. Topology- and Convexity-Preserving Image Segmentation Based On Image Registration

General Information

Lecturer

• Ronald Lok Ming Lui
  • Office: LSB 207
  • Tel: 39437975
  • Email:

Course Description

Computational Quasiconformal Geometry (CQC) studies the deformation pattern between shapes. It has been widely used in applied mathematics and applied in various applications, such as image processing, medical image analysis, computer graphics, computer vision and so on. This course gives an overview of CQC from fundamental concepts, theoretical aspects, computational aspects as well as real-world applications. It is expected that students will get a better idea of this fascinating topic after taking the course.

Class Notes

• Lecture 1: Introduction (Powerpoint)

• Lecture 2: Basic mathematical concepts in topological surfaces and smooth manifolds
• Lecture 3: Smooth manifold and Riemann surface
• Lecture 4: Computation of harmonic mapping
• Lecture 5: More about harmonic parameterization and computational spherical conformal mappings
• Lecture 6: Fast conformal parameterization and quasiconformal mappings
• Lecture 7: Computational Quasiconformal Mappings algorithms
• Lecture 8: More about Linear Beltrami Solver and Beltrami Holomorphic Flow
• Lecture 9: Diffeomorphic Optimization Problem
• Lecture 10 (part A): QC Mapping Numerical Results
• Lecture 10 (part B): Computational Quasiconformality on General Riemann surfaces
• Lecture 11: Computation of Quasconformal Map using auxiliary metric technique

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