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. FoldingFree Global Conformal Mapping for Genus0 Surfaces by Harmonic Energy Minimization
3. Efficient conformal parameterization of multiplyconnected surfaces using quasiconformal theory
4. Spherical Conformal Parameterization of Genus0 Point Clouds for Meshing
5. Shape analysis via inconsistent surface registration
6. Parallelizable Global Conformal Parameterization of SimplyConnected Surfaces via Partial Welding
7. A unifying framework for $n$dimensional quasiconformal mappings,
8. Topology and ConvexityPreserving 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 realworld applications. It is expected that students will get a better idea of this fascinating topic after taking the course.
Class Notes
 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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Assessment Policy Last updated: March 24, 2023 21:27:02