Mandible shape modeling using the second eigenfunction of the Laplace-Beltrami operator

2011 ◽  
Author(s):  
Seongho Seo ◽  
Moo K. Chung ◽  
Brian J. Whyms ◽  
Houri K. Vorperian
Keyword(s):  
Beltrami Operator ◽  
Shape Modeling ◽  
Mandible Shape

Parametric blends for shape modeling

2003 ◽  
Author(s):  
M.A. Sanglikar ◽  
P. Koparkar ◽  
V.N. Joshi
Keyword(s):  
Shape Modeling

scholarly journals Random Assignment Problems on 2d Manifolds

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
D. Benedetto ◽  
E. Caglioti ◽  
S. Caracciolo ◽  
M. D’Achille ◽  
G. Sicuro ◽  
...  
Keyword(s):  
Assignment Problem ◽  
Unit Area ◽  
Constant Term ◽  
Beltrami Operator ◽  
Explicit Calculation ◽  
Dimensional Manifold ◽  
Two Dimensional ◽  
Random Assignment ◽  
Assignment Problems ◽  
Theoretical Formulation

AbstractWe consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold $$\Omega $$ Ω of unit area. It is known that the average cost scales as $$E_{\Omega }(N)\sim {1}/{2\pi }\ln N$$ E Ω ( N ) ∼ 1 / 2 π ln N with a correction that is at most of order $$\sqrt{\ln N\ln \ln N}$$ ln N ln ln N . In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first $$\Omega $$ Ω -dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace–Beltrami operator on $$\Omega $$ Ω . We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics.

scholarly journals Integration and Modularity of Quantitative Trait Locus Effects on Geometric Shape in the Mouse Mandible

Genetics ◽  
2004 ◽  
Vol 166 (4) ◽  
pp. 1909-1921
Author(s):  
Christian Peter Klingenberg ◽  
Larry J Leamy ◽  
James M Cheverud
Keyword(s):  
Quantitative Trait ◽  
Parametric Bootstrap ◽  
Interval Mapping ◽  
Procrustes Analysis ◽  
Bootstrap Test ◽  
Mandible Shape ◽  
Trait Locus ◽  
F2 Generation ◽  
Analysis Interval ◽  
Qtl Effects

Abstract The mouse mandible has long served as a model system for complex morphological structures. Here we use new methodology based on geometric morphometrics to test the hypothesis that the mandible consists of two main modules, the alveolar region and the ascending ramus, and that this modularity is reflected in the effects of quantitative trait loci (QTL). The shape of each mandible was analyzed by the positions of 16 morphological landmarks and these data were analyzed using Procrustes analysis. Interval mapping in the F2 generation from intercrosses of the LG/J and SM/J strains revealed 33 QTL affecting mandible shape. The QTL effects corresponded to a variety of shape changes, but ordination or a parametric bootstrap test of clustering did not reveal any distinct groups of QTL that would affect primarily one module or the other. The correlations of landmark positions between the two modules tended to be lower than the correlations between arbitrary subsets of landmarks, indicating that the modules were relatively independent of each other and confirming the hypothesized location of the boundary between them. While these results are in agreement with the hypothesis of modularity, they also underscore that modularity is a question of the relative degrees to which QTL contribute to different traits, rather than a question of discrete sets of QTL contributing to discrete sets of traits.

scholarly journals Approximating pointwise products of quasimodes

2020 ◽  
Vol 32 (3) ◽  
pp. 541-552
Author(s):  
Mei Ling Jin
Keyword(s):  
Vector Space ◽  
Harmonic Analysis ◽  
Riemannian Manifolds ◽  
Spectral Projection ◽  
Beltrami Operator ◽  
Singular Potentials ◽  
Link Type ◽  
Right Hand ◽  
Low Degree ◽  
The Right

AbstractWe obtain approximation bounds for products of quasimodes for the Laplace–Beltrami operator on compact Riemannian manifolds of all dimensions without boundary. We approximate the products of quasimodes uv by a low-degree vector space {B_{n}}, and we prove that the size of the space {\dim(B_{n})} is small. In this paper, we first study bilinear quasimode estimates of all dimensions {d=2,3}, {d=4,5} and {d\geq 6}, respectively, to make the highest frequency disappear from the right-hand side. Furthermore, the result of the case {\lambda=\mu} of bilinear quasimode estimates improves {L^{4}} quasimodes estimates of Sogge and Zelditch in [C. D. Sogge and S. Zelditch, A note on L^{p}-norms of quasi-modes, Some Topics in Harmonic Analysis and Applications, Adv. Lect. Math. (ALM) 34, International Press, Somerville 2016, 385–397] when {d\geq 8}. And on this basis, we give approximation bounds in {H^{-1}}-norm. We also prove approximation bounds for the products of quasimodes in {L^{2}}-norm using the results of {L^{p}}-estimates for quasimodes in [M. Blair, Y. Sire and C. D. Sogge, Quasimode, eigenfunction and spectral projection bounds for Schrodinger operators on manifolds with critically singular potentials, preprint 2019, https://arxiv.org/abs/1904.09665]. We extend the results of Lu and Steinerberger in [J. F. Lu and S. Steinerberger, On pointwise products of elliptic eigenfunctions, preprint 2018, https://arxiv.org/abs/1810.01024v2] to quasimodes.

scholarly journals Robust and Accurate Mandible Segmentation on Dental CBCT Scans Affected by Metal Artifacts Using a Prior Shape Model

2021 ◽  
Vol 11 (5) ◽  
pp. 364
Author(s):  
Bingjiang Qiu ◽  
Hylke van der van der Wel ◽  
Joep Kraeima ◽  
Haye Hendrik Glas ◽  
Jiapan Guo ◽  
...  
Keyword(s):  
State Of The Art ◽  
Maxillofacial Surgery ◽  
Cone Beam ◽  
Oral And Maxillofacial Surgery ◽  
Metal Artifacts ◽  
Shape Model ◽  
High Attenuation ◽  
Mandible Shape ◽  
Prior Shape ◽  
Segmentation Models

Accurate mandible segmentation is significant in the field of maxillofacial surgery to guide clinical diagnosis and treatment and develop appropriate surgical plans. In particular, cone-beam computed tomography (CBCT) images with metal parts, such as those used in oral and maxillofacial surgery (OMFS), often have susceptibilities when metal artifacts are present such as weak and blurred boundaries caused by a high-attenuation material and a low radiation dose in image acquisition. To overcome this problem, this paper proposes a novel deep learning-based approach (SASeg) for automated mandible segmentation that perceives overall mandible anatomical knowledge. SASeg utilizes a prior shape feature extractor (PSFE) module based on a mean mandible shape, and recurrent connections maintain the continuity structure of the mandible. The effectiveness of the proposed network is substantiated on a dental CBCT dataset from orthodontic treatment containing 59 patients. The experiments show that the proposed SASeg can be easily used to improve the prediction accuracy in a dental CBCT dataset corrupted by metal artifacts. In addition, the experimental results on the PDDCA dataset demonstrate that, compared with the state-of-the-art mandible segmentation models, our proposed SASeg can achieve better segmentation performance.

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