Article
Mathematics, Applied
Alexander Effland, Behrend Heeren, Martin Rumpf, Benedikt Wirth
Summary: The study successfully approximates the Riemann curvature tensor and sectional curvatures by extending the variational time discretization of geodesic calculus. Experimental validation confirms the effectiveness of the method in practical applications and provides a basis for further research.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2022)
Article
Computer Science, Software Engineering
Taner Cevik, Fatih Sahin
Summary: This study proposes a high-discriminative facial recognition method that incorporates shape and grey-level features of faces, utilizing spatial relationships of facial landmark-points and mean grey-level values for recognition. The comprehensive simulations demonstrate the remarkable performance of the method in terms of recognition accuracy and robustness.
Article
Computer Science, Artificial Intelligence
Jun Wan, Zhihui Lai, Jing Li, Jie Zhou, Can Gao
Summary: This article proposes a multiorder multiconstraint deep network (MMDN) for learning more powerful feature correlations and shape constraints, including an implicit multiorder correlating geometry-aware (IMCG) model and an explicit probability-based boundary-adaptive regression (EPBR) method. Experimental results demonstrate the superior performance of MMDN on challenging benchmark data sets.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Chemistry, Multidisciplinary
Xintong Wan, Yifan Wu, Xiaoqiang Li
Summary: The study introduces a facial landmark detection algorithm called Sparse-To-Dense Network (STDN), which utilizes a lightweight network to detect sparse facial landmarks and a group-relational module to enhance shape constraint, effectively addressing challenges posed by large poses and occlusions.
APPLIED SCIENCES-BASEL
(2022)
Article
Computer Science, Artificial Intelligence
Jun Wan, Jun Liu, Jie Zhou, Zhihui Lai, Linlin Shen, Hang Sun, Ping Xiong, Wenwen Min
Summary: Facial landmark detection methods often predict landmarks by mapping input facial appearance features to landmark heatmaps, but they struggle with large poses, occlusions, and varied illuminations. To address this, we propose a novel Reference Heatmap Transformer (RHT) that utilizes reference heatmap information for more accurate detection of facial landmarks. Experimental results on benchmark datasets show that our method outperforms existing state-of-the-art techniques.
IEEE TRANSACTIONS ON IMAGE PROCESSING
(2023)
Article
Optics
Shuwen Wei, Michael Kam, Yaning Wang, Justin D. Opfermann, Hamed Saeidi, Michael H. Hsieh, Axel Krieger, Jin U. Kang
Summary: A numerical landmark localization algorithm based on CNN and CRF is proposed in this study to address the complexity and safety issues caused by fluorescent fiducials in robotic surgery.
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION
(2022)
Article
Multidisciplinary Sciences
Hiroshi Noguchi
Summary: The shapes of biomembrane in living cells are influenced by curvature-inducing proteins. However, the impact of membrane deformation on signal transductions, such as chemical waves, has not been adequately studied. This research demonstrates that membrane deformation can modify the propagation of excitable reaction-diffusion waves through advanced simulations. Reaction waves can induce significant shape transformations and affect wave propagation depending on curvature, feedback, and reaction-deformation time ratio. Furthermore, the occasional disappearance of waves can alter the pathway of wave propagation. These findings highlight the joint regulation of signal transductions by membrane deformation and reaction waves.
SCIENTIFIC REPORTS
(2023)
Article
Computer Science, Artificial Intelligence
Ali Pourramezan Fard, Mohammad H. Mahoor
Summary: Facial landmark detection is a crucial step in facial image analysis. This paper presents a novel loss function and utilizes knowledge distillation to train a lightweight student network for this task, achieving high accuracy by combining two teacher networks and a student network with defined assistive loss functions.
COMPUTER VISION AND IMAGE UNDERSTANDING
(2022)
Article
Computer Science, Software Engineering
K. Karciauskas, J. Peters
Summary: Point-Augmented Subdivision (PAS) is a subdivision method that replaces complex geometry-dependent guided subdivision with explicit subdivision formulas. It can generate high-quality surfaces and is suitable for high-end geometric design, eliminating shape artifacts near extraordinary points.
COMPUTER GRAPHICS FORUM
(2022)
Article
Mathematics
Xingwang Xu, Jian Ye
Summary: This article focuses on the study of closed vacuum static spaces. By using the maximum principle argument, we demonstrate that three-dimensional closed vacuum static spaces with a scalar curvature of 6 must be isometric to either the standard unit sphere S-3 (1) or a finite quotient of the torus S-1 (root 1/3) x S-2 (root 1/3).
INVENTIONES MATHEMATICAE
(2023)
Article
Engineering, Multidisciplinary
Seyed Majid Hosseini Pooya, Ali Massumi
Summary: The paper presents a new damage detection method for beam-like structures that does not require data from the undamaged structure, using the difference between mode shape curvature and mode shape curvature estimation as an indicator for identifying the damage location. The introduced index in magnifying the location of damage is as capable and efficient as the classical mode shape curvature method.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Mathematics
Jintang Li
Summary: This paper introduces the definition of a weak Einstein manifold and proves that if (M, F) is a weak Einstein manifold, then the flag curvature is constant.
ACTA MATHEMATICA SCIENTIA
(2023)
Article
Computer Science, Artificial Intelligence
Riddhish Bhalodia, Shireen Elhabian, Ladislav Kavan, Ross Whitaker
Summary: This paper proposes a self-supervised deep learning approach for discovering landmarks from images that can be directly used as a shape descriptor. The method circumvents segmentation and preprocessing, producing a usable shape descriptor using just 2D or 3D images. Additionally, two variants on the training loss function are proposed to integrate prior shape information into the model.
MEDICAL IMAGE ANALYSIS
(2021)
Article
Mathematics, Applied
Matthias Erbar, Chiara Rigoni, Karl-Theodor Sturm, Luca Tamanini
Summary: We develop the theory of tamed spaces, which are Dirichlet spaces with distribution-valued lower bounds on the Ricci curvature, and investigate them from an Eulerian point of view. We analyze the singular perturbations of Dirichlet form in detail using a broad class of distributions. The distributional Ricci bound is formulated in terms of an integrated version of the Bochner inequality, generalizing the well-known Bakry-Emery curvature-dimension condition. We show the equivalence of distributional Ricci bounds to gradient estimates for the heat semigroup and discuss the consequences in terms of functional inequalities. We provide various examples of tamed spaces, including Riemannian manifolds with interior singularities and singular boundary behavior.
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2022)
Article
Mathematics
Anand Dessai, David Gonzalez-Alvaro
Summary: In our study, we found that the moduli space of metrics on certain homotopy spaces can have multiple path components with distinct properties. The existence of such examples was previously known only in higher dimensions.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Mathematics, Applied
Andreas Kriegl, Peter W. Michor, Armin Rainer
REVISTA MATEMATICA COMPLUTENSE
(2015)
Article
Mathematics
Martin Bauer, Martins Bruveris, Peter W. Michor
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
(2016)
Article
Mathematics, Applied
Martin Bauer, Peter W. Michor, Olaf Mueller
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
(2016)
Article
Mathematics
Andreas Kriegl, Peter W. Michor, Armin Rainer
INDAGATIONES MATHEMATICAE-NEW SERIES
(2016)
Editorial Material
Mathematics, Applied
Martin Bauer, Martins Bruveris, Peter W. Michor
JOURNAL OF GEOMETRIC MECHANICS
(2017)
Article
Physics, Mathematical
Piotr T. Chrusciel, Erwann Delay, Paul Klinger, Andreas Kriegl, Peter W. Michor, Armin Rainer
LETTERS IN MATHEMATICAL PHYSICS
(2018)
Article
Mathematics, Applied
Martins Bruveris, Peter W. Michor, Adam Parusinski, Armin Rainer
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2018)
Article
Mathematics
Andreas Kriegl, Peter W. Michor, Armin Rainer
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
(2015)
Article
Mathematics, Applied
Giuseppe Marmo, Peter W. Michor, Yury A. Neretin
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
(2014)
Article
Mathematics
Martins Bruvcris, Peter W. Michor
MATHEMATISCHE NACHRICHTEN
(2019)
Article
Mathematics, Applied
Martin Bauer, Philipp Harms, Peter W. Michor
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2020)
Article
Physics, Mathematical
Martin Bauer, Martins Bruveris, Philipp Harms, Peter W. Michor
Summary: We prove the holomorphy of the functional calculus A bar right arrow f (A) for a certain class of operators A and holomorphic functions f. Using this result, we demonstrate the real analytic dependence of fractional Laplacians (1 + Delta(g))(p) on the metric g in suitable Sobolev topologies. As an application, we establish the local well-posedness of the geodesic equation for fractional Sobolev metrics on the space of all Riemannian metrics.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Philipp Harms, Peter W. Michor, Xavier Pennec, Stefan Sommer
Summary: This paper develops a geometric perspective on statistics by defining the sample space in the context of independent, identically distributed random samples. The orbifold and path-metric structure of the sample space are fully described, and the infinite sample space is shown to coincide with the Wasserstein space of probability distributions. Metric projections onto 1-skeleta or k-skeleta in Wasserstein space are used to characterize Frechet means and k-means, and a new notion of polymeans is introduced.
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
(2023)
Article
Mathematics
Eric Klassen, Peter W. Michor
ARCHIVUM MATHEMATICUM
(2020)
Article
Mathematics, Applied
Martin Bauer, Martins Bruveris, Philipp Harms, Peter W. Michor
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2018)