The Complex Data School is intended for master's and PhD students. The programme will consist of two online modules, in addition to in-person lectures and exercise sessions at SNU, where participants will test and practice the methods learned.
The content and materials for the Shape Analysis module are provided below and will be updated further in the coming weeks. Information about the second module, which focuses on Nonlinear Statistics, will be published at a later date.
The complex data school will take place in room 210 in building 25 at the SNU campus. Please take a look to Directions on campus for further details.
The programme for the Complex Data School is available under Timetable and is also visible below.
For the in-person sessions with Prof. Ian Dryden and Dr. Mohsen Taheri Shalmani, please bring your laptop, as R and other software will be used during the lectures. Please make sure that you have installed:
- R: https://cran.r-project.org/
- RStudio: https://posit.co/download/rstudio-desktop
- R-package: ETRep, rgl, shapes, Rvcg, plotly, and ggplot2
- SlicerSALT: https://salt.slicer.org/
- Meshmixer: https://meshmixer.org/
Materials that will be used in the Complex Data School sessions by Prof. Ian Dryden can be found here: https://github.com/iandryden/shape-course
Materials that will be used in the sessions by Dr. Mohsen Taheri Shalmani can be found here: https://github.com/scoda-project/Shape-Analysis-via-Skeletal-Models
Wednesday, June 24, 2026
| 10:00 | 10:30 | Registration |
| 10:30 | 12:00 | Special Topic on Shapes by Prof. Ian Dryden |
| 12:00 | 13:30 | Lunch |
| 13:30 | 15:00 | Special Topic on Shapes by Prof. Ian Dryden |
| 15:00 | 15:30 | Break |
| 15:30 | 17:00 |
From Skeletal Model Generation to Analysis by Mohsen Taheri Shalmani & Jörn Schulz |
Thursday, June 25, 2026
| 9:30 | 11:00 | From Skeletal Model Generation to Analysis by Mohsen Taheri Shalmani & Jörn Schulz |
| 11:30 | Start of Workshop |
Online Module 1 - Shape Analysis
Lecture 1 - Introduction
- Content: In the first lecture, we introduce the field of shape analysis and present a range of shape representations, including surfaces, point distribution models, skeletal representations, deformation-based methods, elastic shape analysis, and topological shape analysis. We further discuss the concepts of shape and shape spaces, and motivate the need for non-Euclidean statistical methods for analyzing shape data.
- Lecture notes: lecture1.pdf
- Videos: Lect01-Part1, Lect01-Part2
Lecture 2 - Differential Geometry of Curves
- Content: In this lecture, we will look into the geometry of planar and space curves, how we can describe a curve including the arc-length parametrization, how we can define a tangent, normal, curvature and moving frames along the curve including the Frenet frame and material frames. Further, we will discuss the fundamental theorem, and give an introduction into discrete differential curve geometry.
- Lecture notes: lecture2.pdf
- Videos: Lect02-Part1, Lect02-Part2, Lect02-Part3, Lect02-Part4
Lecture 3 - Differential Geometry of Surfaces
- Content: In this lecture, we extend the differential geometry of curves to surfaces. We introduce surface parametrizations, tangent planes and normal vectors, and discuss curvature concepts including principal, Gaussian, and mean curvature. Furthermore, we define geodesics as locally shortest paths on a surface and use them to induce distances on surfaces. Finally, we briefly discuss discrete differential geometry of surfaces and its approximation on triangulated meshes.
- Lecture notes: lecture3.pdf
- Videos: Lect03-Part1, Lect03-Part2, Lect03-Part3, Lect03-Part4
Lecture 4 - Fréchet means, tangent-space statistics, PGA and PNS
- Content: As preparation for Lecture 5, we introduce basic concepts and notation from non-Euclidean statistics, including Fréchet means and variances, as well as their characterization via exponential and logarithm maps. We further discuss dimension reduction methods for manifold-valued data, including Principal Geodesic Analysis (PGA) and Principal Nested Spheres (PNS). Finally, we address geometric constraints in shape analysis and their implications for stratified shape spaces.
- Lecture notes: lecture4.pdf
- Videos: Lect04-Part1, Lect04-Part2
Lecture 5 - Landmark Models and Point Distribution Models
- Content: In this lecture, we discuss landmark-based shape representations and point distribution models (PDMs). We study the removal of translation, rotation, and scale, leading to the construction of shape spaces for landmark models. Furthermore, we discuss the issue of correspondence and its implications for statistical shape analysis using PDMs.
- Lecture notes: lecture5.pdf
- Videos: Lect05-Part1, Lect05-Part2, Lect05-Part3
Lecture 6 - Medial and skeletal representations
- Content: In this lecture, we introduce the classical medial and skeletal viewpoint for shape representation. We discuss branching issues in medial skeletons and present locally parameterized skeletal models. In particular, we study Local Parameterized Discrete Skeletal Representations (LPDSReps), Local Parameterized Discrete Swept Skeletal Representations (LPDSSReps), and Elliptical Tube Representations (ETReps). Finally, we discuss questions related to shape spaces and distances for skeletal representations.
- Lecture notes: lecture6.pdf
- Videos: Lect06-Part1, Lect06-Part2, Lect06-Part3, Lect06-Part4
Lecture 7 - Statistical Inference on Shapes
- Content: In the final lecture, we discuss advanced topics in statistical shape analysis, including inference on shape spaces, comparison of shape populations, and hypothesis testing for shape data.
- Lecture notes: To be uploaded later (August/September).
- Videos: To be uploaded later (August/September).