Huckemann, Stephan F.

[["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","563"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","Journal of the Royal Statistical Society: Series B (Statistical Methodology)"],["dc.bibliographiccitation.lastpage","587"],["dc.bibliographiccitation.volume","78"],["dc.contributor.author","Hartmann, Alexander K."],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Dannemann, Jörn"],["dc.contributor.author","Laitenberger, Oskar"],["dc.contributor.author","Geisler, Claudia"],["dc.contributor.author","Egner, Alexander"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2017-09-07T11:44:53Z"],["dc.date.available","2017-09-07T11:44:53Z"],["dc.date.issued","2016"],["dc.description.abstract","A major challenge in many modern superresolution fluorescence microscopy techniques at the nanoscale lies in the correct alignment of long sequences of sparse but spatially and temporally highly resolved images. This is caused by the temporal drift of the protein structure, e.g. due to temporal thermal inhomogeneity of the object of interest or its supporting area during the observation process. We develop a simple semiparametric model for drift correction in single-marker switching microscopy. Then we propose an M-estimator for the drift and show its asymptotic normality. This is used to correct the final image and it is shown that this purely statistical method is competitive with state of the art calibration techniques which require the incorporation of fiducial markers in the specimen. Moreover, a simple bootstrap algorithm allows us to quantify the precision of the drift estimate and its effect on the final image estimation. We argue that purely statistical drift correction is even more robust than fiducial tracking, rendering the latter superfluous in many applications. The practicability of our method is demonstrated by a simulation study and by a single-marker switching application. This serves as a prototype for many other typical imaging techniques where sparse observations with high temporal resolution are blurred by motion of the object to be reconstructed."],["dc.identifier.doi","10.1111/rssb.12128"],["dc.identifier.gro","3141679"],["dc.identifier.isi","000376150200002"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/8562"],["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","1467-9868"],["dc.relation.issn","1369-7412"],["dc.title","Drift estimation in sparse sequential dynamic imaging, with application to nanoscale fluorescence microscopy"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.subtype","original"],["dspace.entity.type","Publication"]]

[["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2017-09-07T11:48:02Z"],["dc.date.available","2017-09-07T11:48:02Z"],["dc.date.issued","2009"],["dc.identifier.gro","3146829"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4634"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.relation.conference","57th Session of the ISI"],["dc.relation.eventend","2009-08-22"],["dc.relation.eventlocation","Durban, South Africa"],["dc.relation.eventstart","2009-08-16"],["dc.relation.ispartof","Proceedings of the ISI 2009"],["dc.title","Intrinsic two-way MANOVA for shape spaces"],["dc.type","conference_paper"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dc.type.version","unpublished"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","2113"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Bernoulli"],["dc.bibliographiccitation.lastpage","2142"],["dc.bibliographiccitation.volume","22"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Kim, Kwang-Rae"],["dc.contributor.author","Munk, Axel"],["dc.contributor.author","Rehfeldt, Florian"],["dc.contributor.author","Sommerfeld, Max"],["dc.contributor.author","Weickert, Joachim"],["dc.contributor.author","Wollnik, Carina"],["dc.date.accessioned","2020-12-10T18:43:58Z"],["dc.date.available","2020-12-10T18:43:58Z"],["dc.date.issued","2016"],["dc.description.abstract","We generalize the SiZer of Chaudhuri and Marron (J. Amer. Statist. Assoc. 94 (1999) 807-823; Ann. Statist. 28 (2000) 408-428) for the detection of shape parameters of densities on the real line to the case of circular data. It turns out that only the wrapped Gaussian kernel gives a symmetric, strongly Lipschitz semi-group satisfying \"circular\" causality, that is, not introducing possibly artificial modes with increasing levels of smoothing. Some notable differences between Euclidean and circular scale space theory are highlighted. Based on this, we provide an asymptotic theory to make inference about the persistence of shape features. The resulting circular mode persistence diagram is applied to the analysis of early mechanically-induced differentiation in adult human stem cells from their actin-myosin filament structure. As a consequence, the circular SiZer based on the wrapped Gaussian kernel (WiZer) allows the verification at a controlled error level of the observation reported by Zemel et al. (Nat. Phys. 6 (2010) 468-473): Within early stem cell differentiation, polarizations of stem cells exhibit preferred directions in three different micro-environments."],["dc.identifier.doi","10.3150/15-BEJ722"],["dc.identifier.gro","3141600"],["dc.identifier.isi","000376814400007"],["dc.identifier.issn","1350-7265"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/78282"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.intern","DOI-Import GROB-394"],["dc.notes.status","final"],["dc.notes.submitter","PUB_WoS_Import"],["dc.relation","RTG 2088: Research Training Group 2088 Discovering structure in complex data: Statistics meets Optimization and Inverse Problems"],["dc.relation.eissn","1573-9759"],["dc.relation.issn","1350-7265"],["dc.title","The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["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","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","2465"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Annals of statistics"],["dc.bibliographiccitation.lastpage","2498"],["dc.bibliographiccitation.volume","38"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Kim, Peter T."],["dc.contributor.author","Koo, Ja-Yong"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2017-09-07T11:45:20Z"],["dc.date.available","2017-09-07T11:45:20Z"],["dc.date.issued","2010"],["dc.description.abstract","In this paper we consider a novel statistical inverse problem on the Poincare, or Lobachevsky, upper (complex) half plane. Here the Riemannian structure is hyperbolic and a transitive group action comes from the space of 2 x 2 real matrices of determinant one via Mobius transformations. Our approach is based on a deconvolution technique which relies on the Helgason-Fourier calculus adapted to this hyperbolic space. This gives a minimax nonparametric density estimator of a hyperbolic density that is corrupted by a random Mains transform. A motivation for this work comes from the reconstruction of impedances of capacitors where the above scenario on the Poincare plane exactly describes the physical system that is of statistical interest."],["dc.identifier.doi","10.1214/09-AOS783"],["dc.identifier.gro","3142876"],["dc.identifier.isi","000280359400017"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/7233"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/328"],["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.issn","0090-5364"],["dc.rights","Goescholar"],["dc.rights.uri","https://goescholar.uni-goettingen.de/licenses"],["dc.title","Moebius deconvolution on the hyperbolic plane with application to impedance density estimation"],["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"]]