PostDoc - Uncertainty-Aware Optimization in Inverse Problems for Next-Generation 3D Scanning

3Shape and DTU Compute (Department of Applied Mathematics and Computer Science at the Technical University of Denmark) invite applications for an Industrial Postdoctoral position partially funded by Innovation Fund Denmark. The position is a 2-year fixed-term appointment starting in January 2027 (small variations in the start date may be possible depending on the candidate’s preference).

The project addresses a fundamental challenge in computational imaging and large-scale optimization: how can uncertainty in measurements be quantified, propagated, and ultimately leveraged to improve the reliability of reconstructed 3d models?

Modern 3D scanning systems rely on advanced optimization algorithms to reconstruct geometry and color from large volumes of sensor data. While these algorithms produce highly accurate results, they typically provide limited information about the confidence and uncertainty associated with the reconstructed output. Developing methods that can efficiently estimate and propagate uncertainty in the input data through large-scale iterative optimization algorithms has the potential to improve reconstruction quality, enable more informed algorithmic decisions, and support the next generation of intelligent scanning systems.

The successful candidate will conduct research at the intersection of numerical linear algebra, optimization, uncertainty quantification, and computational imaging. The project will investigate: (i) how to characterize measurement uncertainty, (ii) how uncertainty propagates through iterative solvers, (iii) how to develop new mathematical frameworks for uncertainty-aware optimization, and (iv) how to validate the proposed methods through simulations and deployment in medical 3D reconstruction algorithms developed at 3Shape.

The position offers a unique opportunity to combine fundamental research with industrial impact. Working closely with leading researchers at DTU and engineers at 3Shape, the candidate will contribute to scientific publications, software prototype development, and innovation activities aimed at strengthening the theoretical foundations and practical performance of future 3D scanning technologies.

About us

At 3Shape we aim to advance dental treatment and diagnostics with advanced software and 3D scanners designed for dental professionals across the globe. Our purpose is to advance innovation in dentistry, continuously enhancing patient care and outcomes.

This role places you at the heart of our technological advancements within Product Creation, namely TRIOS & SCANNER SW, offering the chance to shape the trajectory of our innovative products and software applications.

About the project

The project is a 2-year project between 3Shape and the Technical University of Denmark, partly funded by Innovation Fund Denmark. The academic co-supervisor will be Professor Per Christian Hansen at DTU Compute (Department of Applied Mathematics and Computer Science).

The research focuses on uncertainty-aware methods for large-scale linear least squares problems, which form the mathematical backbone of many inverse problems and optimization tasks in 3D reconstruction. The objective is to develop new theoretical and computational tools for quantifying and propagating uncertainty through iterative solution methods, and to translate these developments into practical algorithms for medical 3D reconstruction systems.

What You’ll Do

In this role, you will contribute both to the theoretical foundation and the practical implementation of next-generation uncertainty-aware reconstruction algorithms. The work spans mathematical modelling, algorithm design, and software development in a medical imaging 3D reconstruction.

You will:

• Develop methods for characterizing measurement uncertainty in medical 3D scanning data, including data-driven approaches and machine learning methods where appropriate, to obtain realistic and application-relevant uncertainty models.

• Work hands-on with numerical algorithms, including iterative methods such as Krylov subspace methods and related solvers.

• Develop and analyse new methods for uncertainty-aware linear least squares optimization, with a focus on large-scale iterative solvers.

• Design mathematical frameworks for quantifying how uncertainty evolves through optimization algorithms used in 3D reconstruction.

• Contribute to the architectural design of uncertainty-aware components within existing reconstruction pipelines.

• Translate theoretical models into efficient, scalable implementations suitable for industrial use.

• Design and run simulation studies to validate theoretical developments under realistic conditions.

• Collaborate with researchers and engineers to integrate new methods into production-oriented 3D scanning systems.

• Contribute to scientific publications, conference presentations, technical reports, and potential patentable innovations.

What We’re Looking For

• A PhD in Mathematics, Statistics, or a related discipline. The PhD must have been awarded after March 2021 (or will be obtained within November 2026).

• Strong expertise in numerical linear algebra, optimization, and/or inverse problems.

• Solid understanding of linear least squares methods and iterative solvers, ideally methods based on Krylov subspace methods.

• Experience with or strong interest in uncertainty quantification, statistical modelling, or probabilistic methods.

• Strong programming skills in at least one programming language (ideally two), such as C#, C++, or Python.

• Familiarity with machine learning methods is an advantage, particularly for data-driven modelling of complex systems.

• Ability to work independently and take ownership of research problems while also contributing to a collaborative industrial-academic environment.

• Strong communication skills and the ability to present complex mathematical ideas clearly in both academic and applied settings.

What 3Shape offers

• A vibrant and international environment with social, diverse, and highly skilled and collaborative colleagues - we are more than 50 nationalities in our DK based office

• Breakfast every day, and delicious and healthy lunch cooked by our private chefs.

• We provide a great social work environment with many optional activities and social clubs, ranging from wine & beer, board games, running to bicycle clubs.

• Good work/life balance.

• Attractive offices and R&D lab spaces in downtown Copenhagen close to Kgs. Nytorv, Nyhavn, and the Copenhagen Canals.

• Purpose: Endeavor to improve dental patients on a global scale.

Staying true to our values and D&I efforts, we encourage all relevant applicants to apply, and we ask you NOT to add any photos or sensitive information (age, marital status, nationality) during the application process.

We encourage all relevant applicants to apply. We are committed to celebrating human diversity, and we trust that the best way to reach outstanding business results, is by welcoming diverse people into our community.

About us

3Shape started with a simple idea - to make 3D scanning better. First, we applied it to the hearing industry, then we succeeded in dentistry. Twenty years later, 3Shape has 2,000+ employees globally. With the help of dental professionals and amazing colleagues we’re creating award-winning scanning and CAD/CAM solutions to change dentistry together! Together, we contribute to a better world. Experience the everyday #lifeat3Shape across the globe on LinkedIn.