Combining Conformal Deformation and Cook–Torrance Shading for 3-D Reconstruction in Laparoscopy

2014 ◽  
Vol 61 (6) ◽  
pp. 1684-1692 ◽  
Author(s):  
Abed Malti ◽  
Adrien Bartoli
Keyword(s):  
Conformal Deformation

scholarly journals A Polyakov Formula for Sectors

2017 ◽  
Vol 28 (2) ◽  
pp. 1773-1839 ◽  
Author(s):  
Clara L. Aldana ◽  
Julie Rowlett
Keyword(s):  
Heat Kernel ◽  
Explicit Expression ◽  
Unit Area ◽  
Logarithmic Singularity ◽  
Conformal Factor ◽  
Opening Angle ◽  
Conformal Deformation ◽  
Finite Area ◽  
Different Parts

Abstract We consider finite area convex Euclidean circular sectors. We prove a variational Polyakov formula which shows how the zeta-regularized determinant of the Laplacian varies with respect to the opening angle. Varying the angle corresponds to a conformal deformation in the direction of a conformal factor with a logarithmic singularity at the origin. We compute explicitly all the contributions to this formula coming from the different parts of the sector. In the process, we obtain an explicit expression for the heat kernel on an infinite area sector using Carslaw–Sommerfeld’s heat kernel. We also compute the zeta-regularized determinant of rectangular domains of unit area and prove that it is uniquely maximized by the square.

scholarly journals Ricci curvature of conformal deformation on compact 2-manifolds

2020 ◽  
Vol 19 (6) ◽  
pp. 3223-3231
Author(s):  
Yoon-Tae Jung ◽  
◽  
Soo-Young Lee ◽  
Eun-Hee Choi
Keyword(s):  
Ricci Curvature ◽  
Conformal Deformation

scholarly journals Hyperbolization of Euclidean Ornaments

10.37236/78 ◽  
2009 ◽  
Vol 16 (2) ◽  
Author(s):  
Martin von Gagern ◽  
Jürgen Richter-Gebert
Keyword(s):  
Differential Geometry ◽  
Pattern Recognition ◽  
Hyperbolic Plane ◽  
Discrete Differential Geometry ◽  
Fundamental Region ◽  
Symmetry Groups ◽  
Symmetry Detection ◽  
Conformal Deformation ◽  
Optimal Resolution ◽  
Wallpaper Groups

In this article we outline a method that automatically transforms an Euclidean ornament into a hyperbolic one. The necessary steps are pattern recognition, symmetry detection, extraction of a Euclidean fundamental region, conformal deformation to a hyperbolic fundamental region and tessellation of the hyperbolic plane with this patch. Each of these steps has its own mathematical subtleties that are discussed in this article. In particular, it is discussed which hyperbolic symmetry groups are suitable generalizations of Euclidean wallpaper groups. Furthermore it is shown how one can take advantage of methods from discrete differential geometry in order to perform the conformal deformation of the fundamental region. Finally it is demonstrated how a reverse pixel lookup strategy can be used to obtain hyperbolic images with optimal resolution.

scholarly journals Asymptotic analysis of singular solutions of the scalar and mean curvature equations

2005 ◽  
Vol 2005 (5) ◽  
pp. 679-698
Author(s):  
Gonzalo García ◽  
Hendel Yaker
Keyword(s):  
Asymptotic Analysis ◽  
Mean Curvature ◽  
Related Problem ◽  
Singular Solutions ◽  
Conformal Deformation ◽  
Conformal Metric ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Mean Curvature Equations ◽  
Sobolev Critical Exponent

We show that positive solutions of a semilinear elliptic problem in the Sobolev critical exponent with Newmann conditions, related to conformal deformation of metrics inℝ+n, are asymptotically symmetric in a neighborhood of the origin. As a consequence, we prove for a related problem of conformal deformation of metrics inℝ+nthat if a solution satisfies a Kazdan-Warner-type identity, then the conformal metric can be realized as a smooth metric onS+n.

Sign in / Sign up

Export Citation Format

Share Document