scholarly journals Reversible Harmonic Maps between Discrete Surfaces

2019 ◽  
Vol 38 (2) ◽  
pp. 1-12 ◽  
Author(s):  
Danielle Ezuz ◽  
Justin Solomon ◽  
Mirela Ben-Chen
Keyword(s):  
Harmonic Maps ◽  
Discrete Surfaces

Practical Computation of the Cut Locus on Discrete Surfaces

2021 ◽  
Vol 40 (5) ◽  
pp. 261-273
Author(s):  
C. Mancinelli ◽  
M. Livesu ◽  
E. Puppo
Keyword(s):  
Cut Locus ◽  
Practical Computation ◽  
Discrete Surfaces

scholarly journals The Adjunction Inequality for Weyl-Harmonic Maps

2020 ◽  
Vol 7 (1) ◽  
pp. 129-140
Author(s):  
Robert Ream
Keyword(s):  
Minimal Surfaces ◽  
Twistor Space ◽  
Harmonic Maps ◽  
Holomorphic Curves ◽  
Weyl Connection ◽  
Almost Kähler ◽  
Conformal Manifolds

AbstractIn this paper we study an analog of minimal surfaces called Weyl-minimal surfaces in conformal manifolds with a Weyl connection (M4, c, D). We show that there is an Eells-Salamon type correspondence between nonvertical 𝒥-holomorphic curves in the weightless twistor space and branched Weyl-minimal surfaces. When (M, c, J) is conformally almost-Hermitian, there is a canonical Weyl connection. We show that for the canonical Weyl connection, branched Weyl-minimal surfaces satisfy the adjunction inequality\chi \left( {{T_f}\sum } \right) + \chi \left( {{N_f}\sum } \right) \le \pm {c_1}\left( {f*{T^{\left( {1,0} \right)}}M} \right).The ±J-holomorphic curves are automatically Weyl-minimal and satisfy the corresponding equality. These results generalize results of Eells-Salamon and Webster for minimal surfaces in Kähler 4-manifolds as well as their extension to almost-Kähler 4-manifolds by Chen-Tian, Ville, and Ma.

scholarly journals Fast Nonsupervised 3D Registration of PET and MR Images of the Brain

1994 ◽  
Vol 14 (5) ◽  
pp. 749-762 ◽  
Author(s):  
Jean-François Mangin ◽  
Vincent Frouin ◽  
Isabelle Bloch ◽  
Bernard Bendriem ◽  
Jaime Lopez-Krahe
Keyword(s):  
Three Dimensional ◽  
Magnetic Resonance Images ◽  
Surface Matching ◽  
3D Registration ◽  
Matching Algorithm ◽  
Distance Map ◽  
Brain Surface ◽  
Discrete Surfaces ◽  
Positron Emission ◽  
The Brain

We propose a fully nonsupervised methodology dedicated to the fast registration of positron emission tomography (PET) and magnetic resonance images of the brain. First, discrete representations of the surfaces of interest (head or brain surface) are automatically extracted from both images. Then, a shape-independent surface-matching algorithm gives a rigid body transformation, which allows the transfer of information between both modalities. A three-dimensional (3D) extension of the chamfer-matching principle makes up the core of this surface-matching algorithm. The optimal transformation is inferred from the minimization of a quadratic generalized distance between discrete surfaces, taking into account between-modality differences in the localization of the segmented surfaces. The minimization process is efficiently performed via the precomputation of a 3D distance map. Validation studies using a dedicated brain-shaped phantom have shown that the maximum registration error was of the order of the PET pixel size (2 mm) for the wide variety of tested configurations. The software is routinely used today in a clinical context by the physicians of the Service Hospitalier Frédéric Joliot (>150 registrations performed). The entire registration process requires ∼5 min on a conventional workstation.

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