Representation and comparison of shapes is a problem with many applications in computer vision and imaging, including object recognition and medical diagnosis. We will discuss some constructions from the theory of conformal mapping which provide ways to represent and compare planar shapes. It is a remarkable fact that conformal maps from the unit disk to a planar domain encode the geometry of t...

Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace’s equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection-diffusion equations for potential flows, and...

Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace’s equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection–diffusion equations for potential flows, and...

Conformal geometry has deep roots in pure mathematics. It is the intersection of complex analysis, Riemann surface theory, algebraic geometry, differential geometry and algebraic topology. Computational conformal geometry plays an important role in digital geometry processing. Recently, theory of discrete conformal geometry and algorithms of computational conformal geometry have been developed....

Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace’s equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection-diffusion equations for potential flows, and...

Abstract- In this article, the design of conformal antennas has been discussed using the characteristic modes (CM) method. For this purpose, the vector wave function(VWF) has been utilized to achieve a two-dimensional mapping of the conformal antenna. In designing and analyzing of cone-shaped antennas applicable for multi-input multi-output (MIMO) systems, the most important goal is to achieve ...

Recently, various conformal geometric methods have been presented for non-rigid surface matching and registration. This work proposes to improve the robustness of conformal geometric methods to the boundaries by incorporating the symmetric information of the input surface. We presented two symmetric conformal mapping methods, which are based on solving Riemann-Cauchy equation and curvature flow...

The Riemann mapping theorem asserts that the open unit disk D = {z| |z| < 1} is conformally equivalent to each simply connected domain G in the complex plane, whose boundary consists of at least two points, i.e., there exists a function f , analytic and univalent function on D , such that f maps D onto G . More precisely, if do is an arbitrary point in D and go is an arbitrary point in G, then ...