Abstract : The minisymposium is devoted to a wide range of novel mathematical models and methods for image reconstruction, segmentation and PDEs based deep-learning classification, applied to time-lapse laser scanning microscopy, medical imagery, airborne and satellite optical and SAR data, arising in various fields of application like developmental and cell biology, medicine, nature protection and Earth biodiversity modelling and monitoring.
[03551] Mathematical models and computational algorithms for 3D and 4D image processing in developmental biology and medicine
Format : Talk at Waseda University
Author(s) :
Karol Mikula (Slovak University of Technology in Bratislava)
Abstract : We present mathematical models and numerical algorithms based on nonlinear advection-diffusion equations used for image filtering, segmentation and tracking in 3D+time microscopy images leading to automated reconstruction of the cell lineage tree during the first hours of embryogenesis. To achieve that goal, we discretize the nonlinear partial differential equations by the finite volume method, natural to image processing applications, and develop efficient and stable numerical schemes suitable for massively parallel computer architecture.
[04223] Fractional graph Laplacian for image reconstruction
Format : Talk at Waseda University
Author(s) :
Marco Donatelli (University of Insubria)
Alessandro Buccini (University of Cagliari)
Abstract : We consider $\ell^2-\ell^q$ regularization with $0
[03561] Mathematical models for segmentation of Natura 2000 habitats in NaturaSat software
Format : Talk at Waseda University
Author(s) :
Michal Kollár (Algoritmy:SK s.r.o. and Slovak University of Technology in Bratislava)
Martin Ambroz (Slovak University of Technology in Bratislava)
Aneta Alexandra Ozvat (Slovak University of Technology)
Karol Mikula (Slovak University of Technology in Bratislava)
Lucia Čahojová (Slovak Academy of Sciences)
Mária Šibíková (Slovak Academy of Sciences)
Abstract : The contribution presents an overview of numerical methods and mathematical models designed for the NaturaSat software. The application allows botanists, environmentalists and nature conservationists across Europe to explore protected areas of Natura 2000 habitats using the Sentinel-2 optical data. The presented methods are designed for accurate area identification - semi-automatic and automatic segmentation of European protected habitats and monitoring of their spatio-temporal distribution and quality.
Aneta Alexandra Ozvat (Slovak University of Technology)
Karol Mikula (Slovak University of Technology in Bratislava)
Michal Kollar (Slovak University of Technology)
Martin Ambroz (Slovak University of Technology)
Maria Sibikova (Slovak Academy of Sciences)
Jozef Sibik (Slovak Academy of Sciences)
Abstract : The presentation introduces a novel method for PDE-based data classification using satellite optical data. The Natural Numerical Network (NatNet) is based on the numerical solution of the nonlinear forward-backward diffusion equation on a semi-complete directed graph. Partial differential equations on the directed graph are solved by a finite volume approach considering the balance of diffusion fluxes in the vertices of the graph. The presented natural numerical network is applied to Earth biodiversity modelling.
[02834] Segmentation-based tracking of macrophages in microscopy videos
Format : Talk at Waseda University
Author(s) :
Seol Ah Park (Slovak University of Technology in Bratislava)
Tamara Sipka (University of Montpellier)
Zuzana Kriva (Slovak University of Technology in Bratislava)
Georges Lutfalla (University of Montpellier)
Mai Nguyen-Chi (University of Montpellier)
Karol Mikula (Slovak University of Technology in Bratislava)
Abstract : We propose an algorithm to achieve automatic cell tracking in macrophage videos.
First, we design a segmentation method employing space-time filtering, local Otsu's threshold, and the SUBSURF method.
Then, the partial trajectories are extracted when segmented cells overlap in time. Finally, the extracted trajectories are linked by considering their direction of movement. The automatic tracking achieved 97.4% of accuracy for macrophage data under challenging situations, feeble fluorescent intensity, irregular shapes, and motion of macrophages.
[02927] Model-aware learning for super-resolution in fluorescence microscopy
Format : Talk at Waseda University
Author(s) :
Luca Calatroni (CNRS)
Abstract : In this talk, I will present image super-resolution approaches for fluorescence microscopy applications based on the use of combined model-based and data-driven learning methods. Namely, I will show how generative adversarial training and plug-and-play learning methods can be effectively used as new paradigms for obtaining precise reconstructions with guarantees beyond the use of purely model-based approaches. Numerical results on both simulated and challenging real-world data will be presented.
[02833] Macrophages trajectories smoothing by evolving curves
Format : Talk at Waseda University
Author(s) :
Giulia Lupi (Slovak University of Technology in Bratislava)
Karol Mikula (Slovak University of Technology in Bratislava)
Seol Ah Park (Slovak University of Technology in Bratislava)
Abstract : We present a mathematical model and numerical method based on evolving open-plane and 3D curve approach in the Lagrangian formulation. The model contains three terms: the curvature term, the attracting term, and the tangential redistribution. We use the flowing finite volume method to discretize the advection-diffusion partial differential equation. We present results for macrophage trajectory smoothing and define a method to compute the cell velocity for the discrete points on the smoothed curve.
Abstract : Regularization of certain linear discrete ill-posed problems, as well as of certain regression problems, can be formulated as large-scale, possibly nonconvex, minimization problems, whose objective function is the sum of the p-th power of the lp-norm of a fidelity term and the q-th power of the lq-norm of a regularization term, with 0 < p, q ≤ 2. We describe new restarted iterative solution methods that require less computer storage and execution time than the methods described by [Huang et al.,Majorization-minimization generalized Krylov subspace methods for lp-lq optimization applied to image restoration. BIT (2017)]. The reduction in computer storage and execution time is achieved by periodic restarts of the method. Computed examples illustrate that restarting does not reduce the quality of the computed solutions.
