@inproceedings{HanikHegevonTycowicz2020, author = {Hanik, Martin and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {Bi-invariant Two-Sample Tests in Lie Groups for Shape Analysis}, booktitle = {Shape in Medical Imaging}, publisher = {Springer International Publishing}, address = {Cham}, arxiv = {http://arxiv.org/abs/2008.12195}, doi = {10.1007/978-3-030-61056-2_4}, pages = {44 -- 54}, year = {2020}, 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} } @article{HanikHegevonTycowicz2022, author = {Hanik, Martin and Hege, Hans-Christian and von Tycowicz, Christoph}, title = {Bi-invariant Dissimilarity Measures for Sample Distributions in Lie Groups}, volume = {4}, journal = {SIAM Journal on Mathematics of Data Science}, number = {4}, arxiv = {http://arxiv.org/abs/2402.12901}, doi = {10.1137/21M1410373}, pages = {1223 -- 1249}, year = {2022}, abstract = {Data sets sampled in Lie groups are widespread, and as with multivariate data, it is important for many applications to assess the differences between the sets in terms of their distributions. Indices for this task are usually derived by considering the Lie group as a Riemannian manifold. Then, however, compatibility with the group operation is guaranteed only if a bi-invariant metric exists, which is not the case for most non-compact and non-commutative groups. We show here that if one considers an affine connection structure instead, one obtains bi-invariant generalizations of well-known dissimilarity measures: a Hotelling \$T^2\$ statistic, Bhattacharyya distance and Hellinger distance. Each of the dissimilarity measures matches its multivariate counterpart for Euclidean data and is translation-invariant, so that biases, e.g., through an arbitrary choice of reference, are avoided. We further derive non-parametric two-sample tests that are bi-invariant and consistent. We demonstrate the potential of these dissimilarity measures by performing group tests on data of knee configurations and epidemiological shape data. Significant differences are revealed in both cases.}, language = {en} } @inproceedings{SeimKainmuellerHelleretal.2008, author = {Seim, Heiko and Kainm{\"u}ller, Dagmar and Heller, Markus O. and Lamecker, Hans and Zachow, Stefan and Hege, Hans-Christian}, title = {Automatic Segmentation of the Pelvic Bones from CT Data Based on a Statistical Shape Model}, booktitle = {Eurographics Workshop on Visual Computing for Biomedicine (VCBM)}, address = {Delft, Netherlands}, pages = {93 -- 100}, year = {2008}, language = {en} } @inproceedings{LameckerLangeSeebassetal.2003, author = {Lamecker, Hans and Lange, Thomas and Seebaß, Martin and Eulenstein, Sebastian and Westerhoff, Malte and Hege, Hans-Christian}, title = {Automatic Segmentation of the Liver for Preoperative Planning of Resections}, booktitle = {Proc. MMVR 2003}, publisher = {IOS press}, address = {Newport Beach, CA}, pages = {171 -- 173}, year = {2003}, language = {en} } @article{LameckerZachowWittmersetal.2006, author = {Lamecker, Hans and Zachow, Stefan and Wittmers, Antonia and Weber, Britta and Hege, Hans-Christian and Elsholtz, Barbara and Stiller, Michael}, title = {Automatic segmentation of mandibles in low-dose CT-data}, volume = {1(1)}, journal = {Int. J. Computer Assisted Radiology and Surgery}, pages = {393 -- 395}, year = {2006}, language = {en} } @inproceedings{SeimKainmuellerHelleretal.2009, author = {Seim, Heiko and Kainm{\"u}ller, Dagmar and Heller, Markus O. and Zachow, Stefan and Hege, Hans-Christian}, title = {Automatic Extraction of Anatomical Landmarks from Medical Image Data: An Evaluation of Different Methods}, booktitle = {Proc. of IEEE Int. Symposium on Biomedical Imaging (ISBI)}, address = {Boston, MA, USA}, pages = {538 -- 541}, year = {2009}, language = {en} } @inproceedings{DercksenWeberGuentheretal.2009, author = {Dercksen, Vincent J. and Weber, Britta and G{\"u}nther, David and Oberlaender, Marcel and Prohaska, Steffen and Hege, Hans-Christian}, title = {Automatic alignment of stacks of filament data}, booktitle = {Proc. IEEE International Symposium on Biomedical Imaging}, publisher = {IEEE press}, address = {Boston, USA}, pages = {971 -- 974}, year = {2009}, language = {en} } @article{WeberGreenanProhaskaetal.2012, author = {Weber, Britta and Greenan, Garrett and Prohaska, Steffen and Baum, Daniel and Hege, Hans-Christian and M{\"u}ller-Reichert, Thomas and Hyman, Anthony and Verbavatz, Jean-Marc}, title = {Automated tracing of microtubules in electron tomograms of plastic embedded samples of Caenorhabditis elegans embryos}, volume = {178}, journal = {Journal of Structural Biology}, number = {2}, doi = {10.1016/j.jsb.2011.12.004}, pages = {129 -- 138}, year = {2012}, language = {en} } @article{OberlaenderDercksenEggeretal.2009, author = {Oberlaender, Marcel and Dercksen, Vincent J. and Egger, Robert and Gensel, Maria and Sakmann, Bert and Hege, Hans-Christian}, title = {Automated three-dimensional detection and counting of neuron somata}, volume = {180}, journal = {Journal of Neuroscience Methods}, number = {1}, doi = {10.1016/j.jneumeth.2009.03.008}, pages = {147 -- 160}, year = {2009}, language = {en} } @article{RigortGuentherHegerletal.2012, author = {Rigort, Alexander and G{\"u}nther, David and Hegerl, Reiner and Baum, Daniel and Weber, Britta and Prohaska, Steffen and Medalia, Ohad and Baumeister, Wolfgang and Hege, Hans-Christian}, title = {Automated segmentation of electron tomograms for a quantitative description of actin filament networks}, volume = {177}, journal = {Journal of Structural Biology}, doi = {10.1016/j.jsb.2011.08.012}, pages = {135 -- 144}, year = {2012}, language = {en} }