Hotz, Thomas

[["dc.bibliographiccitation.firstpage","593"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","IEEE Transactions on Pattern Analysis and Machine Intelligence"],["dc.bibliographiccitation.lastpage","603"],["dc.bibliographiccitation.volume","32"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2017-09-07T11:46:05Z"],["dc.date.available","2017-09-07T11:46:05Z"],["dc.date.issued","2010"],["dc.description.abstract","We propose an intrinsic multifactorial model for data on Riemannian manifolds that typically occur in the statistical analysis of shape. Due to the lack of a linear structure, linear models cannot be defined in general; to date only one-way MANOVA is available. For a general multifactorial model, we assume that variation not explained by the model is concentrated near elements defining the effects. By determining the asymptotic distributions of respective sample covariances under parallel transport, we show that they can be compared by standard MANOVA. Often in applications manifolds are only implicitly given as quotients, where the bottom space parallel transport can be expressed through a differential equation. For Kendall's space of planar shapes, we provide an explicit solution. We illustrate our method by an intrinsic two-way MANOVA for a set of leaf shapes. While biologists can identify genotype effects by sight, we can detect height effects that are otherwise not identifiable."],["dc.identifier.doi","10.1109/TPAMI.2009.117"],["dc.identifier.gro","3142944"],["dc.identifier.isi","000274548800003"],["dc.identifier.pmid","20224117"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/404"],["dc.language.iso","en"],["dc.notes.intern","WoS Import 2017-03-10"],["dc.notes.status","final"],["dc.notes.submitter","PUB_WoS_Import"],["dc.relation.issn","0162-8828"],["dc.title","Intrinsic MANOVA for Riemannian Manifolds with an Application to Kendall's Space of Planar Shapes"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.subtype","original"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.journal","Statistica Sinica"],["dc.bibliographiccitation.lastpage","100"],["dc.bibliographiccitation.volume","20"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2019-07-10T08:13:39Z"],["dc.date.available","2019-07-10T08:13:39Z"],["dc.date.issued","2010"],["dc.description.abstract","In this paper, we illustrate a new approach for applying classical statistical methods to multivariate non-linear data. In two examples occurring in the statistical study of shape of three dimensional geometrical objects, we illustrate that the current methods of PCA by linear Euclidean approximation are unsuitable if such data in non-linear spaces fall into regions of high curvature, or if they have a large spread. In the following we give an overview of the background of relevant previous work, and an introduction to the building blocks of our work."],["dc.identifier.fs","582259"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/7238"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/61303"],["dc.language.iso","en"],["dc.notes.intern","Merged from goescholar"],["dc.relation.orgunit","Fakultät für Mathematik und Informatik"],["dc.rights","Goescholar"],["dc.rights.uri","https://goescholar.uni-goettingen.de/licenses"],["dc.subject.ddc","510"],["dc.title","Intrinsic shape analysis: Geodesic PCA for Riemannian manifolds modulo isometric lie group actions"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1507"],["dc.bibliographiccitation.issue","9"],["dc.bibliographiccitation.journal","IEEE Transactions on Pattern Analysis and Machine Intelligence"],["dc.bibliographiccitation.lastpage","1519"],["dc.bibliographiccitation.volume","30"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2017-09-07T11:48:14Z"],["dc.date.available","2017-09-07T11:48:14Z"],["dc.date.issued","2008"],["dc.description.abstract","Quadratic differentials naturally define analytic orientation fields on planar surfaces. We propose to model orientation fields of fingerprints by specifying quadratic differentials. Models for all fingerprint classes such as arches, loops, and whorls are laid out. These models are parameterized by a few geometrically interpretable parameters that are invariant under euclidean motions. We demonstrate their ability in adapting to given observed orientation fields, and we compare them to existing models using the fingerprint images of the NIST Special Database 4. We also illustrate that these models allow for extrapolation into unobserved regions. This goes beyond the scope of earlier models for the orientation field as those are restricted to the observed planar fingerprint region. Within the framework of quadratic differentials, we are able to analytically verify Penrose's formula for the singularities on a palm [19]. Potential applications of these models are the use of their parameters as indexes of large fingerprint databases, as well as the definition of intrinsic coordinates for single fingerprint images."],["dc.identifier.doi","10.1109/TPAMI.2007.70826"],["dc.identifier.gro","3143245"],["dc.identifier.isi","000257504400001"],["dc.identifier.pmid","18617711"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/738"],["dc.notes.intern","WoS Import 2017-03-10"],["dc.notes.status","final"],["dc.notes.submitter","PUB_WoS_Import"],["dc.publisher","Ieee Computer Soc"],["dc.relation.issn","0162-8828"],["dc.title","Global models for the orientation field of fingerprints: An approach based on quadratic differentials"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.subtype","original"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","2255"],["dc.bibliographiccitation.issue","16"],["dc.bibliographiccitation.journal","Bioinformatics"],["dc.bibliographiccitation.lastpage","2262"],["dc.bibliographiccitation.volume","30"],["dc.contributor.author","Futschik, Andreas"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Munk, Axel"],["dc.contributor.author","Sieling, Hannes"],["dc.date.accessioned","2017-09-07T11:45:36Z"],["dc.date.available","2017-09-07T11:45:36Z"],["dc.date.issued","2014"],["dc.description.abstract","Motivation: DNA segmentation, i.e. the partitioning of DNA in compositionally homogeneous segments, is a basic task in bioinformatics. Different algorithms have been proposed for various partitioning criteria such as Guanine/Cytosine (GC) content, local ancestry in population genetics or copy number variation. A critical component of any such method is the choice of an appropriate number of segments. Some methods use model selection criteria and do not provide a suitable error control. Other methods that are based on simulating a statistic under a null model provide suitable error control only if the correct null model is chosen. Results: Here, we focus on partitioning with respect to GC content and propose a new approach that provides statistical error control: as in statistical hypothesis testing, it guarantees with a user-specified probability 1 - alpha that the number of identified segments does not exceed the number of actually present segments. The method is based on a statistical multiscale criterion, rendering this as a segmentation method that searches segments of any length (on all scales) simultaneously. It is also accurate in localizing segments: under benchmark scenarios, our approach leads to a segmentation that is more accurate than the approaches discussed in the comparative review of Elhaik et al. In our real data examples, we find segments that often correspond well to features taken from standard University of California at Santa Cruz (UCSC) genome annotation tracks."],["dc.identifier.doi","10.1093/bioinformatics/btu180"],["dc.identifier.gro","3142071"],["dc.identifier.isi","000342746000003"],["dc.identifier.pmid","24753487"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4222"],["dc.language.iso","en"],["dc.notes.intern","WoS Import 2017-03-10"],["dc.notes.status","final"],["dc.notes.submitter","PUB_WoS_Import"],["dc.relation.eissn","1460-2059"],["dc.relation.issn","1367-4803"],["dc.title","Multiscale DNA partitioning: statistical evidence for segments"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.subtype","original"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","11"],["dc.bibliographiccitation.lastpage","20"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Gottschlich, Carsten"],["dc.contributor.author","Lorenz, Robert"],["dc.contributor.author","Bernhardt, Stefanie"],["dc.contributor.author","Hantschel, Michael"],["dc.contributor.author","Munk, Axel"],["dc.contributor.editor","Brömme, Arslan"],["dc.contributor.editor","Busch, Christoph"],["dc.date.accessioned","2018-02-05T09:43:18Z"],["dc.date.available","2018-02-05T09:43:18Z"],["dc.date.issued","2011"],["dc.description.abstract","We study the effect of growth on the fingerprints of adolescents, based on which we suggest a simple method to adjust for growth when trying to retrieve an adolescent's fingerprint in a database years later. Here, we focus on the statistical analyses used to determine how fingerprints grow: Procrustes analysis allows us to establish that fingerprints grow isotropically, an appropriate mixed effects model shows that fingerprints essentially grow proportionally to body height. The resulting growth model is validated by showing that it brings points of interest as close as if both fingerprints were taken from an adult. Further details on this study, in particular results when applying our growth model in verification and identification tests, can be found in C. Gottschlich, T. Hotz, R. Lorenz, S. Bernhardt, M. Hantschel and A. Munk: Modeling the Growth of Fingerprints Improves Matching for Adolescents, IEEE Transations on Information Forensics and Security, 2011"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/11949"],["dc.language.iso","en"],["dc.notes.status","fcwi-famis"],["dc.publisher","Gesellschaft für Informatik"],["dc.publisher.place","Bonn"],["dc.relation.eventend","09.09.2011"],["dc.relation.eventlocation","Darmstadt"],["dc.relation.eventstart","08.09.2011"],["dc.relation.ispartof","BIOSIG 2011 Proceedings - international conference of the biometrics special interest group"],["dc.title","Statistical analyses of fingerprint growth"],["dc.type","conference_paper"],["dc.type.internalPublication","unknown"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","543"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","Computational Statistics & Data Analysis"],["dc.bibliographiccitation.lastpage","558"],["dc.bibliographiccitation.volume","56"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Marnitz, Philipp"],["dc.contributor.author","Stichtenoth, Rahel"],["dc.contributor.author","Davies, Laurie"],["dc.contributor.author","Kabluchko, Zakhar"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2017-09-07T11:48:58Z"],["dc.date.available","2017-09-07T11:48:58Z"],["dc.date.issued","2012"],["dc.description.abstract","It is shown how to choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, an efficient method for locally adaptive image denoising is presented. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples together with applications in confocal microscopy illustrate the usefulness of the approach. (C) 2011 Elsevier B.V. All rights reserved."],["dc.identifier.doi","10.1016/j.csda.2011.08.018"],["dc.identifier.gro","3142576"],["dc.identifier.isi","000298122600009"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/8942"],["dc.language.iso","en"],["dc.notes.intern","WoS Import 2017-03-10"],["dc.notes.status","final"],["dc.notes.submitter","PUB_WoS_Import"],["dc.relation.eissn","1872-7352"],["dc.relation.issn","0167-9473"],["dc.title","Locally adaptive image denoising by a statistical multiresolution criterion"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.subtype","original"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","84"],["dc.bibliographiccitation.journal","Statistica Sinica"],["dc.bibliographiccitation.lastpage","100"],["dc.bibliographiccitation.volume","20"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2017-09-07T11:48:02Z"],["dc.date.available","2017-09-07T11:48:02Z"],["dc.date.issued","2010"],["dc.description.abstract","A general framework is laid out for principal component analysis (PCA) on quotient spaces that result from an isometric Lie group action on a complete Riemannian manifold. If the quotient is a manifold, geodesics on the quotient can be lifted to horizontal geodesics on the original manifold. Thus, PCA on a manifold quotient can be pulled back to the original manifold. In general, however, the quotient space may no longer carry a manifold structure. Still, horizontal geodesics can be well-defined in the general case. This allows for the concept of generalized geodesics and orthogonal projection on the quotient space as the key ingredients for PCA. Generalizing a result of Bhattacharya and Patrangenaru (2003), geodesic scores can be defined outside a null set. Building on that, an algorithmic method to perform PCA on quotient spaces based on generalized geodesics is developed. As a typical example where non-manifold quotients appear, this framework is applied to Kendall’s shape spaces. In fact, this work has been motivated by an application occurring in forest biometry where the current method of Euclidean linear approximation is unsuitable for performing PCA. This is illustrated by a data example of individual tree stems whose Kendall shapes fall into regions of high curvature of shape space: PCs obtained by Euclidean approximation fail to reflect between-data distances and thus cannot correctly explain data variation. Similarly, for a classical archeological data set with a large spread in shape space, geodesic PCA allows new insights that have not been available under PCA by Euclidean approximation. We conclude by reporting challenges, outlooks, and possible perspectives of intrinsic shape analysis."],["dc.identifier.fs","582260"],["dc.identifier.gro","3146828"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/7496"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4632"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.rights.access","openAccess"],["dc.subject","Extrinsic mean; forest biometry; geodesics; intrinsic mean; Lie group actions; non-linear multivariate statistics; orbifolds; orbit spaces; principal component analysis; Riemannian manifolds; shape analysis"],["dc.subject.ddc","510"],["dc.title","Rejoinder - Intrinsic shape analysis: Geodesic PCA for Riemannian manifolds modulo isometric lie group actions"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","376"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","IEEE Transactions on NanoBioscience"],["dc.bibliographiccitation.lastpage","386"],["dc.bibliographiccitation.volume","12"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Schütte, Ole M."],["dc.contributor.author","Sieling, Hannes"],["dc.contributor.author","Polupanow, Tatjana"],["dc.contributor.author","Diederichsen, Ulf"],["dc.contributor.author","Steinem, Claudia"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2017-09-07T11:47:00Z"],["dc.date.available","2017-09-07T11:47:00Z"],["dc.date.issued","2013"],["dc.description.abstract","Based on a combination of jump segmentation and statistical multiresolution analysis for dependent data, a new approach called J-SMURF to idealize ion channel recordings has been developed. It is model-free in the sense that no a-priori assumptions about the channel's characteristics have to be made; it thus complements existing methods which assume a model for the channel's dynamics, like hidden Markov models. The method accounts for the effect of an analog filter being applied before the data analysis, which results in colored noise, by adapting existing muliresolution statistics to this situation. J-SMURF's ability to denoise the signal without missing events even when the signal-to-noise ratio is low is demonstrated on simulations as well as on ion current traces obtained from gramicidin A channels reconstituted into solvent-free planar membranes. When analyzing a newly synthesized acylated system of a fatty acid modified gramicidin channel, we are able to give statistical evidence for unknown gating characteristics such as subgating."],["dc.identifier.doi","10.1109/TNB.2013.2284063"],["dc.identifier.gro","3142239"],["dc.identifier.isi","000330226400014"],["dc.identifier.pmid","24235310"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/10112"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/6076"],["dc.language.iso","en"],["dc.notes.intern","WoS Import 2017-03-10"],["dc.notes.intern","Merged from goescholar"],["dc.notes.status","final"],["dc.notes.submitter","PUB_WoS_Import"],["dc.relation.eissn","1558-2639"],["dc.relation.issn","1536-1241"],["dc.rights","Goescholar"],["dc.rights.uri","https://goescholar.uni-goettingen.de/licenses"],["dc.title","Idealizing Ion Channel Recordings by a Jump Segmentation Multiresolution Filter"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.subtype","original"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","127"],["dc.bibliographiccitation.journal","Journal of the Royal Statistical Society. Series C, Applied statistics"],["dc.bibliographiccitation.lastpage","143"],["dc.bibliographiccitation.volume","59"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Munk, Axel"],["dc.contributor.author","Gaffrey, D."],["dc.contributor.author","Sloboda, Branislav"],["dc.date.accessioned","2017-09-07T11:46:42Z"],["dc.date.available","2017-09-07T11:46:42Z"],["dc.date.issued","2010"],["dc.description.abstract","We analyse the shapes of star-shaped objects which are prealigned. This is motivated from two examples studying the growth of leaves, and the temporal evolution of tree rings. In the latter case measurements were taken at fixed angles whereas in the former case the angles were free. Subsequently, this leads to different shape spaces, related to different concepts of size, for the analysis. Whereas several shape spaces already existed in the literature when the angles are fixed, a new shape space for free angles, called spherical shape space, needed to be introduced. We compare these different shape spaces both regarding their mathematical properties and in their adequacy to the data at hand; we then apply suitably defined principal component analysis on these. In both examples we find that the shapes evolve mainly along the first principal component during growth; this is the 'geodesic hypothesis' that was formulated by Le and Kume. Moreover, we could link change-points of this evolution to significant changes in environmental conditions."],["dc.identifier.gro","3142997"],["dc.identifier.isi","000273320300007"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/463"],["dc.notes.intern","WoS Import 2017-03-10"],["dc.notes.status","final"],["dc.notes.submitter","PUB_WoS_Import"],["dc.publisher","Wiley-blackwell Publishing, Inc"],["dc.relation.issn","0035-9254"],["dc.title","Shape spaces for prealigned star-shaped objects-studying the growth of plants by principal components analysis"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.subtype","original"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","84"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Statistica Sinica"],["dc.bibliographiccitation.lastpage","100"],["dc.bibliographiccitation.volume","20"],["dc.contributor.author","Huckemann, Stephan F."],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2018-11-07T08:48:37Z"],["dc.date.available","2018-11-07T08:48:37Z"],["dc.date.issued","2010"],["dc.identifier.isi","000275034100008"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/21258"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Statistica Sinica"],["dc.relation.issn","1017-0405"],["dc.title","Intrinsic Shape Analysis: Geodesic PCA for Riemannian Manifolds Modulo Isometric Lie Group Actions Rejoinder"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dc.type.subtype","letter_note"],["dspace.entity.type","Publication"]]