Mathematical Models for Bioimage Analysis

Mathematical models for bioimage analysis

Our group develops tools that blend mathematical models and image processing (e.g., learning-based) algorithms to quantitatively characterize the content of bioimages.

Bioimages grant visual access to the biological world at an incredible wide range of scales. The reflection of nature they provide is however restricted by the way images are represented in a computer, as a digital array of pixels. The Uhlmann Group develops mathematical models that are able to capture image information complemented by prior knowledge from external sources. These tools allow representing image content in an abstract and formal manner, thereby creating a bridge between the digital world of images and the analog world of mathematics. In that way, biological objects can be precisely characterised in a quantitative manner from images, overcoming the pixellated nature of these media.

The work carried out in the Uhlmann Group aims at building tools at the interface of computer science and applied mathematics to capture the full richness of information contained in bioimages. It finds its foundations in differential geometry, approximation and information theory, and signal processing. Practically, this involves on one hand addressing the challenges related to the use of mathematical models in bioimage analysis, developing generic tools that can be readily used by life science researchers and tailored to specific problems. On the other hand, our work explores the potential of abstract representations to characterise, compare and explore phenotypical variations at the single-cell or single-individual level in experiments ranging from genome-wide knockout screens to population dynamics studies.

More generally, the group investigates the whole pipeline from the design of custom geometrical models to challenging implementations into practical image-based solutions for quantitative analysis.

We are recruiting postodoctoral researchers and research interns with a strong background in signal/image processing or computer vision, with interests in approximation theory and differential geometry.

Selected publications

Uhlmann V, Ramdya P, Delgado-Gonzalo R, Benton R, Unser M (2017) FlyLimbTracker: An active contour based approach for leg segment tracking in unmarked, freely behaving Drosophila. PLOS ONE 12:1-21.

Uhlmann V, Fageot J, Unser M (2016) Hermite snakes with control of tangents. IEEE Transactions on Image Processing 25:2803-2816.

Delgado-Gonzalo R, Uhlmann V, Schmitter D, Unser M (2015) Snakes on a plane: A perfect snap for bioimage analysis. IEEE Signal Processing Magazine 32:41-48.

Uhlmann V, Haubold C, Hamprecht FA, Unser M (2018) DiversePathsJ: Diverse shortest paths for bioimage analysis. Bioinformatics 34:538–540.