Stefan Sommer
Professor at Department of Computer Science, University of Copenhagen
DIGIFABA Kick-off
Stefan Sommer, University of Copenhagen
Faculty of Science, University of Copenhagen
Ringe, January, 2026
Mathematical models of shapes
Shape models should
- apply to landmarks, curves, surfaces and images
- be independent of discretization
- preserve shape structure
- equivariant to acting groups
- be recovered from discretizations
\(\Large\Rightarrow\) - model correlations between points
- nonlinear
Shapes, deformations and nonlinearity
E_{s_0,s_1}(\phi)=R(\phi)+\frac1\lambda S(\phi.s_0,s_1)
action: \(\phi.s=\phi\circ s\) (shapes)
\(\phi.s=s\circ\phi^{-1}\) (images)
\( \phi \)
\( \phi \) warp of domain \(\Omega\) (2D or 3D space)
landmarks: \(s=(x_1,\ldots,x_n)\)
curves: \(s: \mathbb S^1\to\mathbb R^2\)
surfaces: \(s: \mathbb S^2\to\mathbb R^3\)
s_0
s_1
Geometric + metric view
R(\phi_t)=\int_0^T\|\partial_t \phi_t\|_{\phi_t}^2dt
\( \phi_t:[0,T]\to\mathrm{Diff}(\Omega) \) path of diffeomorphisms (parameter t)
\mathrm{Diff}(\Omega)
\mathrm{Id}_{\mathrm{Diff}(\Omega)}
\phi_t
LDDMM: Grenander, Miller, Trouve, Younes, Christensen, Joshi, et al.
\partial_t \phi_t
\phi
Action on leafs
- define action on leaf shape and internal structure
- define fiber of internal structure change
- geometric and metric structure on fiber bundle
- statistics
People
- Thomas Besnier (postdoc from Jan 1 2026, 50%)
- Lili Bao (postdoc from Mar 1 2026, 50%)
- Gabriel D'hulst (PhD, from Jun 1 2026)
MSc students:
- spring 2026: Mark, Nynne
WP 2, 3
WP2 Computer vision for detection and segmentation
2.1) Identify relevant object detection and segmentation models. Set up computational pipelines for processing of the field images,
2.2) Develop a fine-tuning methodology to further optimise the base models,
2.3) Evaluate the results with a particular focus on the robustness of the models. For this, adequate fine-grained evaluation metrics need to be developed.
WP3 Shape analysis for plant morphology
3.1) Adapt infinite-dimensional shape models based on actions of diffeomorphisms to plant shape analysis, particularly defining appropriate actions for the overall shape and fine-grained internal structure,
3.2) Develop methodology for low-dimensional representation and visualisation of shape data using the diffeomorphic models,
3.3) Develop statistical methodology for regression analysis, hypothesis testing and analysis of time series of shape data.
DIGIFABA Kick-off
By Stefan Sommer
