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LCLN

LABORATORY FOR COMPUTATIONAL LONGITUDINAL NEUROIMAGING (LCLN)

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Journal Publications

FastSurfer - A fast and accurate deep learning based neuroimaging pipeline. L.Henschel,...M.Reuter. under review 2019. [arXiv].
FatSegNet: A Fully Automated Deep Learning Pipeline for Adipose Tissue Segmentation on Abdominal Dixon MRI. S.Estrada,...M.Reuter. Magn Reson Med. 2019 (open access). [arXiv] [DOI-Link].
Advantages of cortical surface reconstruction using submillimeter 7 T MEMPRAGE. N.Zaretskaya et al.. NeuroImage 165:11-26, 2018. [DOI-Link].
GRAPPA reconstructed wave-CAIPI MP-RAGE at 7 Tesla. JM.Schwarz, ...M.Reuter, T.Stöcker. Magn Reson Med. 80(6):2427-2438, 2018. [DOI-Link].
A Longitudinal Imaging Genetics Study of Neuroanatomical Asymmetry in Alzheimer's Disease. C.Wachinger, ...M.Reuter, A.Riekmann. Biological Psychiatry 84(7):522-530, 2018. [DOI-Link].
Longitudinal MRI data analysis in presence of measurement error but absence of replicates. C.Ranjan et al.. IISE Trans on Healthcare Sys Eng 8(2):117-130, 2018. [DOI-Link].
Object and scene memory are differentially associated with CSF markers of Alzheimer's disease and MRI volumetry. D.Berron et al.. Alzheimer's & Dementia 13(7):P1553-P1554, 2017. [DOI-Link].
DeepNAT: Deep convolutional neural network for segmenting neuroanatomy. C.Wachinger, M.Reuter, T.Klein. NeuroImage 170:434-445, 2017. [DOI-Link].
High-resolution magnetic resonance imaging reveals nuclei of the human amygdala: manual segmentation to automatic atlas. Z.M.Saygin, et al.. NeuroImage 155:370-382, 2017. [DOI-Link].
Mindboggling morphometry of human brains. A.Klein, et al.. PLoS Computational Biology 2017; 13(3):e1005350. [DOI-Link].
Mid-space-independent deformable image registration. I.Aganj, J.E.Iglesias, M.Reuter,.... NeuroImage 152:158-170, 2017. [DOI-Link].
Whole-brain Analysis Reveals Increased Neuroanatomical Asymmetries in Dementia for Hippocampus and Amygdala. C.Wachinger,... M.Reuter. Brain 139(12):3253-3266, 2016. [DOI-Link].
Multidimensional Heritability Analysis of Neuroanatomical Shape. T.Ge, M.Reuter,.... Nature Communications 7:13291, 2016. [DOI-Link].
Bayesian longitudinal segmentation of hippocampal substructures in brain MRI using subject-specific atlases. J.Iglesias,... M.Reuter. NeuroImage 141:542-555, 2016. [DOI-Link].
Domain adaptation for Alzheimer's disease diagnostics. C.Wachinger, M.Reuter. NeuroImage 139:470-479, 2016. [PDF] [DOI-Link] [PubMed]
Joint reconstruction of white-matter pathways from longitudinal diffusion MRI data with anatomical priors. A.Yendiki, M.Reuter.... NeuroImage 127:277-286, 2016. [DOI-Link].
Prospective motion correction with volumetric navigators (vNavs) reduces the bias and variance in brain morphometry induced by subject motion. MD.Tisdall*, M.Reuter* ...(*equal contribution). NeuroImage 127:12-22, 2016. [DOI-Link].
Responses of the human brain to mild de- and rehydration explored in vivo by 1H-MR imaging and spectroscopy. A.Biller, et al.. American Journal of Neuroradiology 36:2277-2284, 2015. [PDF] [DOI-Link] [PubMed] details

This is the first study simultaneously evaluating changes in brain tissue fluid, metabolites, volume, and cortical thickness. Our results reflect cellular volume regulatory mechanisms at a macroscopic level and emphasize that it is essential to control for hydration levels in studies on brain morphometry and metabolism in order to avoid confounding the findings. hide

Assessing atrophy measurement techniques in dementia: Results from the MIRIAD atrophy challenge. D.Cash, et al.. NeuroImage 123:149-164, 2015 [DOI-Link].
BrainPrint: A Discriminative Characterization of Brain Morphology. C.Wachinger, ..., M.Reuter. NeuroImage 109:232-248, 2015. [PDF] [BibTex] [DOI-Link] [PubMed] details

We introduce BrainPrint, a compact and discriminative representation of brain morphology to study the similarity between brains. BrainPrint captures shape information of an ensemble of cortical and subcortical structures by solving the eigenvalue problem of the 2D and 3D Laplace-Beltrami operator on triangular (boundary) and tetrahedral (volumetric) meshes. We highlight four applications for BrainPrint in this article: (i) subject identication, (ii) age and sex prediction, (iii) brain asymmetry analysis, and (iv) potential genetic influences on brain morphology. The properties of BrainPrint require the derivation of new algorithms to account for the heterogeneous mix of brain structures with varying discriminative power. We conduct experiments on three datasets, including over 3000 MRI scans from the ADNI database, 436 MRI scans from the OASIS dataset, and 236 MRI scans from the VETSA twin study. All processing steps for obtaining the compact representation are fully automated, making this processing framework particularly attractive for handling large datasets. hide

Standardized evaluation of algorithms for computer-aided diagnosis of dementia based on structural MRI: the CADDementia challenge. E.Bron, et al.. NeuroImage 111:562-579, 2015 [DOI-Link] [PubMed].
Head Motion during MRI Acquisition Reduces Gray Matter Volume and Thickness Estimates. M.Reuter*, MD.Tisdall* ...(*equal contribution). NeuroImage 107:107-115, 2015. [PDF] [BibTex] [DOI-Link] [PubMed] details

Here we show that cortical gray matter volume and thickness estimates based on MRI (FreeSurfer 5.3, VBM8 SPM, and FSL Siena 5.0.7) are biased by head motion with an average apparent volume loss of roughly 0.7%/mm/min of subject motion. Effects vary across regions and remain significant after excluding scans that fail a rigorous quality check. In view of these results, the interpretation of reported morphometric effects of movement disorders or other conditions with increased motion tendency may need to be revisited: effects may be overestimated when not controlling for head motion. Furthermore, drug studies with hypnotic, sedative, tranquilizing, or neuromuscular-blocking substances may contain spurious effects of reduced atrophy or brain growth simply because they affect motion distinct from true effects of the disease or therapeutic process. hide

Multi-Modal Robust Inverse-Consistent Linear Registration. C.Wachinger, ..., M.Reuter. Human Brain Mapping Journal 36(4):1365-1380, 2015. [PDF] [BibTex] [DOI-Link [PubMed]
Avoiding symmetry-breaking spatial non-uniformity in deformable image registration via a quasi-volume-preserving constraint. I.Aganj, M.Reuter, M.R.Sabuncu, B.Fischl. NeuroImage 106:238-251, 2015 [DOI-Link] [PubMed].
Effects of Sex Chromosome Dosage on Corpus Callosum Morphology in Supernumerary Sex Chromosome Aneuploidies. B.S.C.Wade, S.H.Joshi, M.Reuter, et al. Biology of Sex Differences 5:16, 2014 [DOI-Link].
Cross-validation of serial optical coherence scanning and diffusion tensor imaging: A study on neural fiber maps in human medulla oblongata. H.Wang, J.Zhu, M.Reuter, et al. NeuroImage 100:395-404, 2014. [BibTex] [DOI-Link] [PubMed]
Event Time Analysis of Longitudinal Neuroimage Data. M.R.Sabuncu, J.Bernal-Rusiel, M.Reuter, et al. NeuroImage 97:9-18, 2014. [BibTex] [DOI-Link] [PubMed] details

This paper presents a method for the statistical analysis of the associations between longitudinal neuroimaging measurements, e.g., of cortical thickness, and the timing of a clinical event of interest, e.g., disease onset. The proposed approach consists of two steps: (i) a linear mixed effects (LME) model to capture temporal variation in serial imaging data and (ii) the extended Cox regression model to examine the relationship between time-dependent imaging measurements and the timing of the event of interest. We provide a quantitative and objective empirical evaluation of the statistical performance of the proposed method on longitudinal data from subjects suffering from Mild Cognitive Impairment (MCI) at baseline. hide

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Impact of MRI head placement on glioma response assessment. M.Reuter, et al. Journal of Neuro-Oncology 118(1):123-129, 2014. [PDF] [BibTex] [DOI-Link] [PubMed] details

Diagnosis of progressive disease or (partial) response during tumor treatment is based on manual size estimates of enhancing tumor area. We show that the manual area measure is highly sensitive to changes in head placement in the MRI scanner, with a root mean squared error of 22%. In our simulated study, the majority of subjects would have been incorrectly diagnosed with progressive disease without any true anatomical changes. These results highlight the urgent need for revised and more reliable response assessment criteria such as increased slice resolution, 3D volume analysis and percent change computation with respect to an average of patient specific longitudinal measurements instead of a single measurement to define progression or response. hide

The effect of amyloid pathology and glucose metabolism on cortical volume loss over time in Alzheimer's disease. S.Adriaanse, et al. European Journal of Nuclear Medicine and Molecular Imaging 41(6):1190-1198, 2014. [BibTex] [DOI-Link]
MRI Parcellation of Ex Vivo Medial Temporal Lobe. J.Augustinack, C.Magnain, M.Reuter, et al. NeuroImage 93(2):252-259, 2014. [BibTex] [DOI-Link] [PubMed] details

Brain mapping of mesocortical areas affected with neurofibrillary tangle pathology early in Alzheimer's disease progression provides not only an accurate description for location of these areas but also supplies spherical coordinates that allows comparison between other ex vivo cases and larger in vivo datasets. We have identified several cytoarchitectonic features in the medial temporal lobe with high resolution ex vivo MRI, such as the entorhinal layer II 'islands', perirhinal layer II-III columns as well as lamina of the hippocampus. Localization of Brodmann area's 28 and 35 demonstrates MRI based area boundaries validated with multiple methods and histological stains. Based on our findings, both myelin and Nissl staining relate to contrast in ex vivo MRI. Precise brain mapping serves to create modern atlases for cortical areas, allowing accurate localization with important applications to detecting early disease processes. hide

Whole brain mapping of water pools and molecular dynamics with rotating frame MR relaxation using gradient modulated low-power adiabatic pulses. O.C.Andronesi, H.Bhat, M.Reuter, et al. NeuroImage 89:92-109, 2014. [BibTex] [DOI-Link] [PubMed]
Quantitative comparison of cortical surface reconstructions from MP2RAGE and multi-echo MPRAGE data at 3 and 7 T. K.Fujimoto, et al. NeuroImage 90:60-73, 2014. [BibTex] [DOI-Link] [PubMed]
PRECREST: A Phase II Prevention and Biomarker Trial of Creatine in At-Risk for Huntington's disease. H.D.Rosas, et al. Neurology, online, 2014. [BibTex] [DOI-Link] [PubMed] details

We describe a design that preserves the autonomy of subjects not wanting genetic testing while including controls for assessing the specificity of treatment effects. Our results demonstrate the feasibility of prevention trials for HD and the safety of high-dose creatine, provide possible evidence of disease modification, support future studies of creatine, and illustrate the value of prodromal biomarkers. hide

Blockface histology with optical coherence tomography: A comparison with Nissl staining. C.Magnain, J.Augustinack, M.Reuter, et al. NeuroImage 84:524-533, 2014. [BibTex] [DOI-Link] [PubMed] details

Spectral domain optical coherence tomography (SD-OCT) is a high resolution imaging technique that generates excellent contrast based on intrinsic optical properties of the tissue, such as neurons and fibers. The SD-OCT data acquisition is performed directly on the tissue block, diminishing the need for cutting, mounting and staining and thus excluding related artifacts and distortions. We utilized SD-OCT to visualize the laminar structure of the isocortex and compared cortical cytoarchitecture with the gold standard Nissl staining, both qualitatively and quantitatively. Our results suggest that SD-OCT contains information comparable to standard histological stains such as Nissl in terms of distinguishing cortical layers and architectonic areas. We propose that SD-OCT can be used to reliably generate 3D reconstructions of multiple cubic centimeters of cortex that can be used to accurately and semi-automatically perform standard histological analyses. hide

Spatiotemporal Linear Mixed Effects Modeling for the Mass-univariate Analysis of Longitudinal Neuroimage Data. J.L.Bernal-Rusiel, M.Reuter, et al. NeuroImage 81:358-370, 2013. [BibTex] [DOI-Link] [PubMed] details

We present an extension of the Linear Mixed Effects (LME) modeling approach to be applied to the mass-univariate analysis of longitudinal neuroimaging (LNI) data. The proposed method, called spatiotemporal LME or ST-LME, exploits the spatial structure in image data. We instantiated ST-LME for the analysis of cortical surface measurements (e.g. thickness) computed by FreeSurfer. We validate the proposed ST-LME method and provide a quantitative and objective empirical comparison with alternative methods using (ADNI) and (OASIS) datasets. Our experiments revealed that ST-LME offers a dramatic gain in statistical power and repeatability of findings, while providing good control of the false positive rate. hide

Statistical Analysis of Longitudinal Neuroimage Data with Linear Mixed Effects Models. J.L.Bernal-Rusiel, D.N.Greve, M.Reuter et al. NeuroImage 66:249-260, 2012. [BibTex] [DOI-Link] [PubMed] details

Longitudinal neuroimaging (LNI) studies are rapidly becoming more prevalent and growing in size. However, widely used methods for the statistical analysis are often sub-optimal. Linear Mixed Effects (LME) modeling, a mature approach well known in the statistics community, offers a powerful and versatile framework for analyzing real-life LNI data. This article presents the theory behind LME models, contrasts it with other popular approaches (repeated measures ANOVA or annualized atrophy rates) in the context of LNI, provides empirical evaluation of the performance, and is accompanied with an array of computational tools that will be made freely available through FreeSurfer. hide

A comparison of methods for non-rigid 3D shape retrieval. Z.Lian, A.Godil et al. Pattern Recognition, 46(1):449-461, 2013. [DOI-Link] details

The aim of this paper is to measure and compare the performance of state-of-the-art methods for non-rigid 3D shape retrieval. The paper develops a new benchmark consisting of 600 non-rigid 3D watertight meshes, which are equally classified into 30 categories, to carry out experiments for 11 different algorithms, whose retrieval accuracies are evaluated using 6 commonly-utilized measures. hide

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Within-Subject Template Estimation for Unbiased Longitudinal Image Analysis. M.Reuter, N.J.Schmansky, H.D.Rosas, B.Fischl. NeuroImage 61(4):1402-1418, 2012. [PDF] [BibTex] [DOI-Link] [PubMed] details

Challenges in longitudinal image analysis have been related to the variability that is inherent in the available cross-sectional processing tools, to the introduction of bias in longitudinal processing and to potential over-regularization. In this paper we introduce a novel longitudinal image processing framework for FreeSurfer, based on unbiased, robust, within-subject template creation, for automatic surface reconstruction and segmentation of brain MRI of arbitrarily many time points. The presented results show a significant increase in precision and discrimination power while preserving the ability to detect large anatomical deviations; as such they hold great potential in clinical applications, e.g. allowing for smaller sample sizes or shorter trials to establish disease specific biomarkers or to quantify drug effects. hide

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Volumetric Navigators for Prospective Motion Correction and Selective Reacquisition in Neuroanatomical MRI. M.D.Tisdall, A.T.Hess, M.Reuter et al. Magnetic Resonance in Medicine 68(2):389-399, 2012. [BibTex] [DOI-Link] [PubMed] details

We introduce a novel method of prospectively compensating for subject motion in neuroanatomical imaging. Short 3D EPI volumetric navigators (vNavs) are embedded in a long 3D sequence, and the resulting image volumes registered to provide an estimate of the subject's location in the scanner, giving a motion-corrected sequence with no extra time requirements. We also demonstrate motion-driven selective reacquisition of k-space to further compensate for subject motion. The improved final output and lack of additional hardware requirements make this method suitable for high-throughput environments. hide

A tale of two factors: What determines the rate of progression in Huntington's disease? A longitudinal MRI study. H.D.Rosas, M.Reuter et al. Movement Disorders 26(9):1691-1697, 2011. [BibTex] [DOI-Link] [PubMed] details

We evaluated progression in Huntington's disease using a novel longitudinal magnetic resonance imaging analysis. Patients who developed symptoms earlier demonstrated the most rapid rates of atrophy compared with those who developed symptoms during middle age or more advanced age. Rates of regional brain atrophy seem to be influenced by the age of onset of Huntington's disease symptoms and are only partially explained by CAG repeat length. These findings suggest that other genetic, epigenetic, and environmental factors play important roles in neurodegeneration in Huntington's disease. hide

The dynamics of cortical and hippocampal atrophy in Alzheimer's disease. M.R.Sabuncu et al. Archives of Neurology 68(8):1040-1048, 2011. [BibTex] [PDF] [DOI-Link] [PubMed] details

Measure: We used automated tools to compute annual longitudinal atrophy in the hippocampus and cortical regions targeted in AD. We used Mini-Mental State Examination scores as a measure of cognitive performance. We performed a cross-subject analysis of atrophy rates and acceleration on individuals with an AD-like cerebrospinal fluid molecular profile. Conclusion: Alzheimer disease specific cortical thinning and hippocampal volume loss are consistent with a sigmoidal pattern, with an acceleration phase during the early stages of the disease. Clinical trials should carefully consider the nonlinear behavior of these AD biomarkers. hide

Avoiding Asymmetry-Induced Bias in Longitudinal Image Processing. M.Reuter, B.Fischl. NeuroImage 57(1):19-21, invited comment, 2011. [PDF] [BibTex] [DOI-Link] [PubMed] details

Longitudinal image processing procedures frequently transfer or pool information across time within subject, with the dual goals of reducing the variability and increasing the accuracy of the derived measures. In this note, we discuss common difficulties in longitudinal image processing, focusing on the introduction of bias, and describe the approaches we have taken to avoid them in the FreeSurfer longitudinal processing stream. hide

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Selective Disruption of the Cerebral Neocortex in Alzheimer's Disease. R.S.Desikan, M.R. Sabuncu, N.J. Schmansky, M. Reuter, H.J. Cabral et al. PloS ONE 5(9):e12853, 2010. [BibTex] [PDF] [DOI-Link] [PubMed] details

Alzheimer's disease (AD) and its transitional state mild cognitive impairment (MCI) are characterized by amyloid plaque and tau neurofibrillary tangle (NFT) deposition within the cerebral neocortex and neuronal loss within the hippocampal formation. However, the precise relationship between pathologic changes in neocortical regions and hippocampal atrophy is largely unknown. This longitudinal study combines structural MRI scans and automated image analysis tools (longitudinal FreeSurfer) with change of the above measures. We examined the relationship between the presence of Alzheimer's pathology, gray matter thickness of select neocortical regions, and hippocampal volume in cognitively normal older participants and individuals with MCI and AD (n = 724). Conclusion: Cortical A beta and tau pathology affects gray matter thinning within select neocortical regions and potentially contributes to downstream hippocampal degeneration. Neocortical Alzheimer's pathology is evident even amongst older asymptomatic individuals suggesting the existence of a preclinical phase of dementia. hide

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Highly Accurate Inverse Consistent Registration: A Robust Approach. M. Reuter, H.D. Rosas, B. Fischl. NeuroImage 53(4):1181-1196, 2010. [PDF] [BibTex] [DOI-Link] [PubMed] details

The registration of images is a task that is at the core of many applications in computer vision. In computational neuroimaging where the automated segmentation of brain structures is frequently used to quantify change, a highly accurate registration is necessary for motion correction of images taken in the same session, or across time in longitudinal studies where changes in the images can be expected. This paper, inspired by Nestares and Heeger (2000), presents a method based on robust statistics to register images in the presence of differences, such as jaw movement, differential MR distortions and true anatomical change. The approach we present guarantees inverse consistency (symmetry), can deal with different intensity scales and automatically estimates a sensitivity parameter to detect outlier regions in the images. The resulting registrations are highly accurate due to their ability to ignore outlier regions and show superior robustness with respect to noise, to intensity scaling and outliers when compared to state-of-the-art registration tools such as FLIRT (in FSL) or the coregistration tool in SPM. hide

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Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions. M. Reuter. International Journal of Computer Vision 89(2):287-308, 2010 (online 08/09). [PDF] [BibTex] [DOI-Link] [Pubget] details

This work introduces a method to hierarchically segment articulated shapes into meaningful parts and to register these parts across populations of near-isometric shapes (e.g. head, arms and legs of humans in different body postures). The method exploits the isometry invariance of eigenfunctions of the Laplace-Beltrami operator and uses topological features (level sets at important saddles) for the segmentation. Concepts from persistent homology are employed for a hierarchical representation, for the elimination of topological noise and for the comparison of eigenfunctions. The obtained parts can be registered via their spectral projection across a population of near isometric shapes. This work also presents the highly accurate computation of eigenfunctions and eigenvalues with cubic FEM on triangle meshes and discusses the construction of persistence diagrams from the Morse-Smale complex as well as the relation to size functions. hide

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Discrete Laplace-Beltrami Operators for Shape Analysis and Segmentation. M. Reuter, S. Biasotti, D. Giorgi, G. Patane, M. Spagnuolo. SMI'09, Computers & Graphics 33(3):381-390, 2009. [PDF] [BibTex] [DOI-Link] details

In this paper, we first analyze different common discretizations of the Laplace-Beltrami operator (geometric Laplacians, linear and cubic FEM operators) in terms of the correctness of their eigenfunctions with respect to the continuous case. We then present the family of segmentations induced by the nodal sets of the eigenfunctions, discussing its meaningfulness for shape understanding. hide

reuter-cad09
Laplace-Beltrami Eigenvalues and Topological Features of Eigenfunctions for Statistical Shape Analysis.
Invited Paper:
M. Reuter, F.-E. Wolter, M. Shenton, M. Niethammer. Computer-Aided Design 41(10):739-755, 2009. [PDF] [BibTex] [DOI-Link] [PubMed] [Pubget] details

This paper proposes the use of the surface based Laplace-Beltrami and the volumetric Laplace eigenvalues and -functions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the 2D surface and 3D solid methods is demonstrated at a population of female caudate nuclei (a subcortical gray matter structure of the brain, involved in memory function, emotion processing, and learning) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the Laplace-Beltrami eigenvalues and -functions are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann vs. the Dirichlet spectra in 3D. Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable of localizing geometric properties and detecting shape differences by indirectly registering topological features such as critical points, level sets and integral lines of the gradient field across subjects. The use of these topological features of the Laplace-Beltrami eigenfunctions in 2D and 3D for statistical shape analysis is novel. hide

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Solving Nonlinear Polynomial Systems in the Barycentric Bernstein Basis. M. Reuter, T. Mikkelsen, E. Sherbrooke, T. Maekawa, N. Patrikalakis. The Visual Computer 24(3):187-200, January 2007. [PDF] [BibTex] [DOI-Link] details

We present a method for solving arbitrary systems of N nonlinear polynomials in n variables over an n-dimensional simplicial domain based on polynomial representation in the barycentric Bernstein basis and subdivision. The roots are approximated to arbitrary precision by iteratively constructing a series of smaller bounding simplices. We use geometric subdivision to isolate multiple roots within a simplex. An algorithm implementing this method in rounded interval arithmetic is described and analyzed. We find that when the total order of polynomials is close to the maximum order of each variable, an iteration of this solver algorithm is asymptotically more efficient than the corresponding step in a similar algorithm which relies on polynomial representation in the tensor product Bernstein basis. We also discuss various implementation issues and identify topics for further study. hide

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Laplace Spectra as Fingerprints for Image Recognition. N. Peinecke, F.-E. Wolter and M. Reuter. Computer-Aided Design 39(6):460-476, June 2007. [PDF] [BibTex] [DOI-Link] details

In the area of image retrieval from data bases and for copyright protection of large image collections there is a growing demand for unique but easily computable fingerprints for images. These fingerprints can be used to quickly identify every image within a larger set of possibly similar images. This paper introduces a novel method to automatically obtain such fingerprints from an image. It is based on a re-interpretation of an image as a Riemannian manifold. This representation is feasible for gray value images and color images. We discuss the use of the spectrum of eigenvalues of different variants of the Laplace operator as a fingerprint and show the usability of this approach in several use cases. Contrary to existing works in this area we do not only use the discrete Laplacian, but also with a particular emphasis the underlying continuous operator. This allows better results in comparing the resulting spectra and deeper insights in the problems arising. We show how the well known discrete Laplacian is related to the continuous Laplace-Beltrami operator. Furthermore we introduce the new concept of solid height functions to overcome some potential limitations of the method. hide

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Laplace-Beltrami spectra as "Shape-DNA" of surfaces and solids.
Most Cited Paper Award: [2009_most_cited_cad.pdf]
M. Reuter, F.-E. Wolter and N. Peinecke. Computer-Aided Design 38(4):342-366, 2006. [PDF] [BibTex] [DOI-Link] details

This paper describes in detail a method to extract fingerprints of any surface or solid object by taking the eigenvalues of its respective Laplace-Beltrami operator. Since the spectrum is an isometry invariant it is independent of the objects representation including parametrization, spatial position and of its representation (e.g. NURBS or any parametrized or implicitly represented surface or even for polyhedra). Therefore checking if two objects are isometric needs no prior alignment (registration / localization) of the objects, but only a comparison of their (normalized) spectra, the Shape-DNA. In this paper we describe the computation of the Shape-DNA and their comparison. We also give an overview on implementation issues like meshing, numerics and the used "Atlas" data structure allowing principally to compute eigenvalues of topologically complex objects by gluing surface patches. Exploiting the isometry invariance of the Laplace-Beltrami operator we succeed in computing eigenvalues for smoothly bounded objects without discretization errors caused by approximation of the boundary. Furthermore we show the rapid convergence of the heat trace series and demonstrate that it is computationally feasible to extract geometrical data such as the volume, the boundary length and even the Euler characteristic from the numerically calculated fingerprint data. This fact not only confirms the exactness of our computed eigenvalues, but also underlines the geometrical importance of the spectrum. With the help of the here described Shape-DNA it is possible to support copyright protection, database retrieval and quality assessment of digital data representing surfaces and solids. hide

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Martin Reuter - MIT - Cambridge, MA, USA - EMail: reu...@mit.edu
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