@inproceedings{AmiranashviliLuedkeLietal.2022, author = {Amiranashvili, Tamaz and L{\"u}dke, David and Li, Hongwei and Menze, Bjoern and Zachow, Stefan}, title = {Learning Shape Reconstruction from Sparse Measurements with Neural Implicit Functions}, booktitle = {Medical Imaging with Deep Learning}, year = {2022}, abstract = {Reconstructing anatomical shapes from sparse or partial measurements relies on prior knowledge of shape variations that occur within a given population. Such shape priors are learned from example shapes, obtained by segmenting volumetric medical images. For existing models, the resolution of a learned shape prior is limited to the resolution of the training data. However, in clinical practice, volumetric images are often acquired with highly anisotropic voxel sizes, e.g. to reduce image acquisition time in MRI or radiation exposure in CT imaging. The missing shape information between the slices prohibits existing methods to learn a high-resolution shape prior. We introduce a method for high-resolution shape reconstruction from sparse measurements without relying on high-resolution ground truth for training. Our method is based on neural implicit shape representations and learns a continuous shape prior only from highly anisotropic segmentations. Furthermore, it is able to learn from shapes with a varying field of view and can reconstruct from various sparse input configurations. We demonstrate its effectiveness on two anatomical structures: vertebra and femur, and successfully reconstruct high-resolution shapes from sparse segmentations, using as few as three orthogonal slices.}, language = {en} } @inproceedings{PaskinDeanBaumetal.2022, author = {Paskin, Martha and Dean, Mason and Baum, Daniel and von Tycowicz, Christoph}, title = {A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks}, booktitle = {Computer Vision -- ECCV 2022}, publisher = {Springer Nature Switzerland}, arxiv = {http://arxiv.org/abs/2207.12687}, doi = {10.1007/978-3-031-20086-1_21}, pages = {363 -- 379}, year = {2022}, abstract = {3D shapes provide substantially more information than 2D images. However, the acquisition of 3D shapes is sometimes very difficult or even impossible in comparison with acquiring 2D images, making it necessary to derive the 3D shape from 2D images. Although this is, in general, a mathematically ill-posed problem, it might be solved by constraining the problem formulation using prior information. Here, we present a new approach based on Kendall's shape space to reconstruct 3D shapes from single monocular 2D images. The work is motivated by an application to study the feeding behavior of the basking shark, an endangered species whose massive size and mobility render 3D shape data nearly impossible to obtain, hampering understanding of their feeding behaviors and ecology. 2D images of these animals in feeding position, however, are readily available. We compare our approach with state-of-the-art shape-based approaches both on human stick models and on shark head skeletons. Using a small set of training shapes, we show that the Kendall shape space approach is substantially more robust than previous methods and always results in plausible shapes. This is essential for the motivating application in which specimens are rare and therefore only few training shapes are available.}, language = {en} } @misc{PaskinBaumDeanetal.2022, author = {Paskin, Martha and Baum, Daniel and Dean, Mason N. and von Tycowicz, Christoph}, title = {A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks -- Source Code and Data}, doi = {10.12752/8730}, year = {2022}, abstract = {Source code and novel dataset of basking shark head skeletons facilitating the reproduction of the results presented in 'A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks' - ECCV 2022.}, language = {en} } @inproceedings{HarthVohraUdvaryetal.2022, author = {Harth, Philipp and Vohra, Sumit and Udvary, Daniel and Oberlaender, Marcel and Hege, Hans-Christian and Baum, Daniel}, title = {A Stratification Matrix Viewer for Analysis of Neural Network Data}, booktitle = {Eurographics Workshop on Visual Computing for Biology and Medicine (VCBM)}, address = {Vienna, Austria}, doi = {10.2312/vcbm.20221194}, year = {2022}, abstract = {The analysis of brain networks is central to neurobiological research. In this context the following tasks often arise: (1) understand the cellular composition of a reconstructed neural tissue volume to determine the nodes of the brain network; (2) quantify connectivity features statistically; and (3) compare these to predictions of mathematical models. We present a framework for interactive, visually supported accomplishment of these tasks. Its central component, the stratification matrix viewer, allows users to visualize the distribution of cellular and/or connectional properties of neurons at different levels of aggregation. We demonstrate its use in four case studies analyzing neural network data from the rat barrel cortex and human temporal cortex.}, language = {en} } @article{UdvaryHarthMackeetal.2022, author = {Udvary, Daniel and Harth, Philipp and Macke, Jakob H. and Hege, Hans-Christian and de Kock, Christiaan P. J. and Sakmann, Bert and Oberlaender, Marcel}, title = {The Impact of Neuron Morphology on Cortical Network Architecture}, volume = {39}, journal = {Cell Reports}, number = {2}, doi = {10.1016/j.celrep.2022.110677}, year = {2022}, abstract = {The neurons in the cerebral cortex are not randomly interconnected. This specificity in wiring can result from synapse formation mechanisms that connect neurons depending on their electrical activity and genetically defined identity. Here, we report that the morphological properties of the neurons provide an additional prominent source by which wiring specificity emerges in cortical networks. This morphologically determined wiring specificity reflects similarities between the neurons' axo-dendritic projections patterns, the packing density and cellular diversity of the neuropil. The higher these three factors are the more recurrent is the topology of the network. Conversely, the lower these factors are the more feedforward is the network's topology. These principles predict the empirically observed occurrences of clusters of synapses, cell type-specific connectivity patterns, and nonrandom network motifs. Thus, we demonstrate that wiring specificity emerges in the cerebral cortex at subcellular, cellular and network scales from the specific morphological properties of its neuronal constituents.}, language = {en} } @inproceedings{LuedkeAmiranashviliAmbellanetal.2022, author = {L{\"u}dke, David and Amiranashvili, Tamaz and Ambellan, Felix and Ezhov, Ivan and Menze, Bjoern and Zachow, Stefan}, title = {Landmark-free Statistical Shape Modeling via Neural Flow Deformations}, volume = {13432}, booktitle = {Medical Image Computing and Computer Assisted Intervention - MICCAI 2022}, publisher = {Springer, Cham}, arxiv = {http://arxiv.org/abs/2209.06861}, doi = {10.1007/978-3-031-16434-7_44}, year = {2022}, abstract = {Statistical shape modeling aims at capturing shape variations of an anatomical structure that occur within a given population. Shape models are employed in many tasks, such as shape reconstruction and image segmentation, but also shape generation and classification. Existing shape priors either require dense correspondence between training examples or lack robustness and topological guarantees. We present FlowSSM, a novel shape modeling approach that learns shape variability without requiring dense correspondence between training instances. It relies on a hierarchy of continuous deformation flows, which are parametrized by a neural network. Our model outperforms state-of-the-art methods in providing an expressive and robust shape prior for distal femur and liver. We show that the emerging latent representation is discriminative by separating healthy from pathological shapes. Ultimately, we demonstrate its effectiveness on two shape reconstruction tasks from partial data. Our source code is publicly available (https://github.com/davecasp/flowssm).}, language = {en} } @misc{SagnolHegeWeiser2016, author = {Sagnol, Guillaume and Hege, Hans-Christian and Weiser, Martin}, title = {Using sparse kernels to design computer experiments with tunable precision}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59605}, year = {2016}, abstract = {Statistical methods to design computer experiments usually rely on a Gaussian process (GP) surrogate model, and typically aim at selecting design points (combinations of algorithmic and model parameters) that minimize the average prediction variance, or maximize the prediction accuracy for the hyperparameters of the GP surrogate. In many applications, experiments have a tunable precision, in the sense that one software parameter controls the tradeoff between accuracy and computing time (e.g., mesh size in FEM simulations or number of Monte-Carlo samples). We formulate the problem of allocating a budget of computing time over a finite set of candidate points for the goals mentioned above. This is a continuous optimization problem, which is moreover convex whenever the tradeoff function accuracy vs. computing time is concave. On the other hand, using non-concave weight functions can help to identify sparse designs. In addition, using sparse kernel approximations drastically reduce the cost per iteration of the multiplicative weights updates that can be used to solve this problem.}, language = {en} } @article{LelievreZhang2019, author = {Leli{\`e}vre, Tony and Zhang, Wei}, title = {Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates}, journal = {Multiscale Modeling and Simulation}, number = {17}, arxiv = {http://arxiv.org/abs/1805.01928}, doi = {10.1137/18M1186034}, pages = {1019 -- 1051}, year = {2019}, abstract = {Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Leli{\`e}vre, Nonlinearity, 2010] to approximate the essential dynamics of high-dimensional diffusion processes along a given reaction coordinate. The approximation error of the effective dynamics when it is used to approximate the behavior of the original dynamics has been considered in recent years. As a continuation of the previous work [F. Legoll, T. Leli{\`e}vre, and S. Olla, Stoch. Process. Appl, 2017], in this paper we obtain pathwise estimates for effective dynamics when the reaction coordinate function is either nonlinear or vector-valued.}, language = {en} } @article{Zhang2021, author = {Zhang, Wei}, title = {Some new results on relative entropy production, time reversal, and optimal control of time-inhomogeneous diffusion processes}, volume = {62}, journal = {Journal of Mathematical Physics}, number = {4}, arxiv = {http://arxiv.org/abs/2006.11212}, doi = {10.1063/5.0038740}, pages = {26}, year = {2021}, abstract = {This paper studies time-inhomogeneous nonequilibrium diffusion processes, including both Brownian dynamics and Langevin dynamics. We derive upper bounds of the relative entropy production of the time-inhomogeneous process with respect to the transient invariant probability measures. We also study the time reversal of the reverse process in Crooks' fluctuation theorem. We show that the time reversal of the reverse process coincides with the optimally controlled forward process that leads to zero variance importance sampling estimator based on Jarzynski's equality.}, language = {en} } @article{ZhangKlusConradetal.2019, author = {Zhang, Wei and Klus, Stefan and Conrad, Tim and Sch{\"u}tte, Christof}, title = {Learning chemical reaction networks from trajectory data}, volume = {18}, journal = {SIAM Journal on Applied Dynamical Systems (SIADS)}, number = {4}, arxiv = {http://arxiv.org/abs/1902.04920}, doi = {10.1137/19M1265880}, pages = {2000 -- 2046}, year = {2019}, abstract = {We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed,our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under l^1 sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit.}, language = {en} }