Learning and Optimisation for Visual Computing

University of Bonn

Below we summarise our high-level interests together with specific research directions.

Artificial Intelligence & Machine Learning
We are interested in the foundations of AI and ML, and in solving specific tasks by inferring general principles from data.

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For example, we develop methods for multi-model merging, LLM jailbreaking, certified training, or differentiable programming.

Computer Vision & Image Understanding
We are excited about leveraging fundamental principles (e.g. about 3D geometry or physics) to push the boundaries of image and video understanding.

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Examples include pixel-wise left-right image understanding, image-driven physically plausible 4D generation, unsupervised 3D structure inference in images, or physics inference from video.

Geometry & Shape Analysis
We develop methods to analyse and model geometric data, e.g. graphs, 3D shapes, 4D sequences, and high-dimensional manifolds.

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Examples include generative models based on hyper networks and diffusion, self-supervised symmetry understanding, self-supervised foundation model fine-tuning for partial 3D shapes, 3D shape matching benchmarks, globally optimal and geometrically consistent 3D shape matching, and statistical shape models.

Mathematical Modelling & Optimisation
We are excited about mathematical and algorithmic foundations, in many cases seeking for theoretical guarantees.

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Theoretical guarantees include global optimality, cycle consistency or neural network robustness.
For example, we develop globally optimal methods for 3D shape matching, 2D-3D matching, or sparse optimisation over the Stiefel manifold. We develop methods that achieve cycle consistency for multi-graph matching and multi-alignment, for example through higher-order projected power iterations, non-negative matrix factorisation, or convex relaxations. We also tackle certified neural network training.

Geometry Optimisation
We are interested in discovering novel geometries that have specific physical properties.

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For example, we are working on designing stellerator geometries for nuclear fusion based on physics simulation. Also, we are interested in designing mechanical meta-materials through geometry optimisation.

Physics-Grounded Visual Computing
We exploit physics as a prior to tackle diverse visual computing tasks. Also, we infer physics from visual data.

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Examples include
image-driven physically plausible 4D generation, or physics inference and physics-based video editing.

Correspondence Problems
We develop optimisation and machine learning approaches for identifying corresponding parts across objects.

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We work on image correspondences, graph matching, multi-graph matching, 3D shape matching, multi-shape matching, etc.

Graph-Based Modelling & Graph Algorithms
Many visual computing problems can be formalised as graph-theoretic problems, so that they can be solved using graph algorithms.

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For example, numerous variants of matching problems can be addressed by finding shortest paths in product graphs, e.g. 2D-to-3D shape matching, graph-to-image matching, or 3D shape matching.

Scalable Algorithms
We develop efficient algorithms that scale to very large data collections, which is often a prerequisite for training large-scale AI models.

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For example, we develop scalable algorithms for 3D shape matching, multi-graph matching, multi-shape matching, matrix synchronisation, or sub-label accurate energy minimisation.

Applications
Many problems that we study are driven by real-world applications.

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Examples of applications include medical shape models, bioimaging, 3D reconstruction and real-time tracking of interacting hands, morphable head models, and portrait image editing.

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We are hiring (PhD and Postdoc level)