From understanding how cell shape can be a biomarker in cancer diagnosis and prognosis to how change in cell shape dictates embryogenesis, morphology quantification is crucial in different areas of biology. Morphology-related measurements are extracted from segmented objects in bioimages, and their quality is therefore directly depend on the number of pixels composing each object. In contrast, geometrical models representing the contour of objects as continuous parametric curves are free from discretisation artefacts and are therefore excellent alternative candidates for morphometry. The extraction of this kind of contour representation from bioimages is however tedious and poorly scalable. In this thesis, we investigate how deep learning can be leveraged to infer geometrical models directly from bioimages.

We developed SplineDist, a supervised deep learning algorithm to extract geometrical models across a variety of imaging modalities. We show that it can be used as an alternative instance segmentation method with state-of-the-art results, and packaged it as a plugin for the popular microscopy image analysis platform napari to facilitate its use. We also explored the use of geometrical model parameters as direct measures of morphology, with applications to nuclear phenotyping. Finally, we developed a generative approach to sample geometrical model parameters from a known distribution and illustrate its use in the context of synthetic data generation.