@inproceedings{HanikHegevonTycowicz, author = {Hanik, Martin and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {Bi-invariant Two-Sample Tests in Lie Groups for Shape Analysis}, series = {Shape in Medical Imaging}, booktitle = {Shape in Medical Imaging}, publisher = {Springer International Publishing}, address = {Cham}, doi = {10.1007/978-3-030-61056-2_4}, pages = {44 -- 54}, abstract = {We propose generalizations of the T²-statistics of Hotelling and the Bhattacharayya distance for data taking values in Lie groups. A key feature of the derived measures is that they are compatible with the group structure even for manifolds that do not admit any bi-invariant metric. This property, e.g., assures analysis that does not depend on the reference shape, thus, preventing bias due to arbitrary choices thereof. Furthermore, the generalizations agree with the common definitions for the special case of flat vector spaces guaranteeing consistency. Employing a permutation test setup, we further obtain nonparametric, two-sample testing procedures that themselves are bi-invariant and consistent. We validate our method in group tests revealing significant differences in hippocampal shape between individuals with mild cognitive impairment and normal controls.}, language = {en} } @inproceedings{HanikHegeHennemuthetal., author = {Hanik, Martin and Hege, Hans-Christian and Hennemuth, Anja and von Tycowicz, Christoph}, title = {Nonlinear Regression on Manifolds for Shape Analysis using Intrinsic B{\´e}zier Splines}, series = {Proc. Medical Image Computing and Computer Assisted Intervention (MICCAI)}, booktitle = {Proc. Medical Image Computing and Computer Assisted Intervention (MICCAI)}, publisher = {Springer International Publishing}, address = {Cham}, doi = {10.1007/978-3-030-59719-1_60}, pages = {617 -- 626}, abstract = {Intrinsic and parametric regression models are of high interest for the statistical analysis of manifold-valued data such as images and shapes. The standard linear ansatz has been generalized to geodesic regression on manifolds making it possible to analyze dependencies of random variables that spread along generalized straight lines. Nevertheless, in some scenarios, the evolution of the data cannot be modeled adequately by a geodesic. We present a framework for nonlinear regression on manifolds by considering Riemannian splines, whose segments are B{\´e}zier curves, as trajectories. Unlike variational formulations that require time-discretization, we take a constructive approach that provides efficient and exact evaluation by virtue of the generalized de Casteljau algorithm. We validate our method in experiments on the reconstruction of periodic motion of the mitral valve as well as the analysis of femoral shape changes during the course of osteoarthritis, endorsing B{\´e}zier spline regression as an effective and flexible tool for manifold-valued regression.}, language = {en} } @article{NavaYazdaniHegeSullivanetal., author = {Nava-Yazdani, Esfandiar and Hege, Hans-Christian and Sullivan, T. J. and von Tycowicz, Christoph}, title = {Geodesic Analysis in Kendall's Shape Space with Epidemiological Applications}, series = {Journal of Mathematical Imaging and Vision}, volume = {62}, journal = {Journal of Mathematical Imaging and Vision}, number = {4}, doi = {10.1007/s10851-020-00945-w}, pages = {549 -- 559}, abstract = {We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall's shape space. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude over common, nonlinear constrained approaches. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As an example application we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative (OAI). Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data alone.}, language = {en} } @article{MahnkeArltBaumetal., author = {Mahnke, Heinz-Eberhard and Arlt, Tobias and Baum, Daniel and Hege, Hans-Christian and Herter, Felix and Lindow, Norbert and Manke, Ingo and Siopi, Tzulia and Menei, Eve and Etienne, Marc and Lepper, Verena}, title = {Virtual unfolding of folded papyri}, series = {Journal of Cultural Heritage}, volume = {41}, journal = {Journal of Cultural Heritage}, publisher = {Elsevier}, doi = {10.1016/j.culher.2019.07.007}, pages = {264 -- 269}, abstract = {The historical importance of ancient manuscripts is unique since they provide information about the heritage of ancient cultures. Often texts are hidden in rolled or folded documents. Due to recent impro- vements in sensitivity and resolution, spectacular disclosures of rolled hidden texts were possible by X-ray tomography. However, revealing text on folded manuscripts is even more challenging. Manual unfolding is often too risky in view of the fragile condition of fragments, as it can lead to the total loss of the document. X-ray tomography allows for virtual unfolding and enables non-destructive access to hid- den texts. We have recently demonstrated the procedure and tested unfolding algorithms on a mockup sample. Here, we present results on unfolding ancient papyrus packages from the papyrus collection of the Mus{\´e}e du Louvre, among them objects folded along approximately orthogonal folding lines. In one of the packages, the first identification of a word was achieved, the Coptic word for "Lord".}, language = {en} } @article{FroehlerElberfeldMoelleretal., author = {Fr{\"o}hler, Bernhard and Elberfeld, Tim and M{\"o}ller, Torsten and Hege, Hans-Christian and De Beenhouwer, Jan and Sijbers, Jan and Kastner, Johann and Heinzl, Christoph}, title = {Analysis and comparison of algorithms for the tomographic reconstruction of curved fibres}, series = {Nondestructive Testing and Evaluation}, volume = {35}, journal = {Nondestructive Testing and Evaluation}, number = {3}, doi = {10.1080/10589759.2020.1774583}, pages = {328 -- 341}, abstract = {We present visual methods for the analysis and comparison of the results of curved fibre reconstruction algorithms, i.e., of algorithms extracting characteristics of curved fibres from X-ray computed tomography scans. In this work, we extend previous methods for the analysis and comparison of results of different fibre reconstruction algorithms or parametrisations to the analysis of curved fibres. We propose fibre dissimilarity measures for such curved fibres and apply these to compare multiple results to a specified reference. We further propose visualisation methods to analyse differences between multiple results quantitatively and qualitatively. In two case studies, we show that the presented methods provide valuable insights for advancing and parametrising fibre reconstruction algorithms, and support in improving their results in characterising curved fibres.}, language = {en} } @article{UdvaryHarthMackeetal., 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 = {A Theory for the Emergence of Neocortical Network Architecture}, series = {BioRxiv}, journal = {BioRxiv}, doi = {https://doi.org/10.1101/2020.11.13.381087}, language = {en} }