Summer Semester 2026, TU München

Organisers: Dr. Thomas Dagès, Dr. Riccardo Marin

Contact : sma-ss26@vision.in.tum.de

• 05.02.2026 Preliminary meeting material: Recording (Passcode: YcB9v@#y) Slides
• 01.02.2026 Preliminary meeting at 10AM; Room: 02.09.023, Seminarraum (5609.02.023); Zoom Link: https://tum-conf.zoom-x.de/j/66205862148?pwd=DuqiHLp7sVeoecP1HPCFUE6b7U4Krw.1

Apply to the matching system, and send us an email, attaching your CV and transcripts (Bachelor+Master) and with the following structure:

In the body, please give at least the following details: Subject: Application [Your Matriculation Number]

Matriculation #:
Name:
Name of Degree:
Masters Semester #:
Average Grade:
○ Bachelor:
○ Master (For the previous semester, if available)
List of Relevant courses taken with grade

Share any additional documents, information (eg. link to git, past research projects) that could support your application.

The world we live in is fundamentally geometric. All around us, our 3D world is filled with fascinating geometry: objects are curved, they can be moved around, they can be bent, they can be stretched, they can be compared, they can be combined, they can be painted and repainted… While our human brain tends to have a great intuitive understanding of the 3D geometrical world, translating such insight to machines via algorithms for analysing and processing geometric data is a challenge. Even worse, our monkey brains struggle to understand the geometry of higher dimensional spaces such as data manifolds, which have become omnipresent in the current age of big data. By advancing numerical geometric tools and methods, we open the door to incredible advancements in many (if not most) application fields: computer graphics and animation, video games, robotics and motion planning, medical imaging, augmented reality, data visualisation, data generation, social networks… In this course, we will explore and apply the fundamentals of shape analysis, which revolves around how to encode a shape or manifold, compare two different ones, find correspondences between them, measure distances on curved spaces, and reveal the simple structure of complex shapes.

In this applied course, you will work on topics related to

• Shape analysis
• Shape matching
• Point-cloud registration
• Manifold analysis
• Manifold learning
• Geometric deep learning
• Metric geometry

Previous knowledge expected Students are expected to be highly proficient in scientific programming (e.g., Python), have a thorough understanding of algorithms and data structures, and possess a strong mathematical foundation, including solid knowledge of linear algebra and calculus. Prior knowledge or experience in the following fields is beneficial: 3D and high-dimensional geometry, geometric computer vision, computer graphics, deep learning, and differential geometry.

Expected results of study By the end of the course, students will acquire a deep theoretical understanding and practical expertise in how to encode and process shapes or high-dimensional manifolds to address practical problems such as shape correspondence. They will be familiar with recent trends in the field and gain first-hand experience in solving challenging problems. They will also learn to work in small groups and present their findings.

Teaching and learning method This practical course is primarily project-based and includes only a small number of introductory sessions. First, we will cover the basics of shape and manifold analysis, shape matching, and manifold learning. Students will then work in small groups (typically of two to three) on a practical problem. Throughout the semester, projects will progress with regular communication with the tutors and mid-term presentations.

Recommended reading:

• Bronstein et al. Numerical Geometry of Non-Rigid Shapes, 2009
• Numerical Optimization, 2006 - Solomon.
• Further relevant references will be provided during the course.