2018/09/03 by Denis K. Samuylov, Gábor Székely, Grégory Paul · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Advanced Fluorescence Microscopy Techniques #Algorithm #Artificial intelligence #Bayesian probability #Cell Image Analysis Techniques #Computer science #Computer vision #Image (mathematics) #Image formation #Inverse problem #Iterative reconstruction #Mathematics #Maximum a posteriori estimation #Parametric statistics #Pattern recognition (psychology) #Single-cell and spatial transcriptomics #cs.CV #eess.IV
paper · pdf · doi:10.1109/tip.2018.2867946
published in IEEE Transactions on Image Processing 28(1), 410-425 (Institute of Electrical and Electronics Engineers) · This paper has been accepted in the IEEE Transactions on Image Processing
openalex publication_date 2018/09/03 · arxiv created 2018/09/05 · arxiv updated 2018/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Kymographs are widely used to represent and analyse spatio-temporal dynamics of fluorescence markers along curvilinear biological compartments. These objects have a singular geometry, thus kymograph reconstruction is inherently an analog image processing task. However, the existing approaches are essentially digital: the kymograph photometry is sampled directly from the time-lapse images. As a result, such kymographs rely on raw image data that suffer from the degradations entailed by the image formation process and the spatio-temporal resolution of the imaging setup. In this work, we address these limitations and introduce a well-grounded Bayesian framework for the analog reconstruction of kymographs. To handle the movement of the object, we introduce an intrinsic description of kymographs using differential geometry: a kymograph is a photometry defined on a parameter space that is embedded in physical space by a time-varying map that follows the object geometry. We model the kymograph photometry as a Lévy innovation process, a flexible class of non-parametric signal priors. We account for the image formation process using the virtual microscope framework. We formulate a computationally tractable representation of the associated maximum a posteriori problem and solve it using a class of efficient and modular algorithms based on the alternating split Bregman. We assess the performance of our Bayesian framework on synthetic data and apply it to reconstruct the fluorescence dynamics along microtubules in vivo in the budding yeast S. cerevisiae. We demonstrate that our framework allows revealing patterns from single time-lapse data that are invisible on standard digital kymographs.