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Group Classification of Generalized Eikonal Equations
Ukrainian Mathematical Journal, 2001The goal of the paper is to obtain the group classification of the equation \[ \sum_{i=0}^{n}u^2_{x_i}=F(t,u,u_t) \quad(x_0:=t)\tag{1} \] for a scalar unknown function \(u(t,x_1,\ldots,x_n)\). In this equation, the function \(F:\mathbb R^3 \mapsto \mathbb R\) is regarded as an ``arbitrary element''.
Popovych, R. O., Ehorchenko, I. A.
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A Hamiltonian Approach to the Eikonal Equation
1999The eikonal equation and variants of it are of significant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shape-from-shading and for recent dynamic theories of shape.
Kaleem Siddiqi +2 more
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Smooth solutions of the eikonal equation and the behaviour of local minima of the distance function
Izvestiya: Mathematics, 2019We study smooth solutions of the eikonal equation. To do this, we investigate the problem of geometric-topological properties of the singularities of the distance function and the regular set.
I. G. Tsar'kov
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A parallel algorithm for solving the Eikonal equation
2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)., 2003A large variety of methods based on partial differential equations (PDE) use the interface propagation. For their flexibility these methods are being more and more applied to various problems ranging from physics, fluid mechanics to control theory and computer vision.
Eva Dejnozková, Petr Dokládal
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Ordered Line Integral Methods for Solving the Eikonal Equation
Journal of Scientific Computing, 2019We present a family of fast and accurate Dijkstra-like solvers for the eikonal equation and factored eikonal equation which compute solutions on a regular grid by solving local variational minimization problems.
S. Potter, M. Cameron
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A geometric idea to solve the eikonal equation
Proceedings of the 21st Spring Conference on Computer Graphics, 2005Given a closed plane curve c(t) = (c1,c2) (t) ∈ e R2 and associated function values g(t) we present a geometric idea and an algorithm to solve the equation ||∇f|| = a = const. with respect to the boundary values g(t) along the boundary c(t). This is equivalent to finding a developable surface D of constant slope a = tan α through the spatial curve C ...
Martin Peternell, Tibor Steiner
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Automatic Difference Operators for the Eikonal Equation
SIAM Journal on Scientific ComputingzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alex Kleb +2 more
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1999
The problem is to find a complex function $$ w(x,y) = u(x,y) + iv(x,y) $$ such that $$ \left\{ {\begin{array}{*{20}{c}} {w_x^2 + w_y^2 + {f^2} = 0,a.ein\Omega } \\ {w = \varphi on\partial \Omega ,} \end{array}} \right. $$ Where \( f:\Omega \times {\mathbb{R}^2} \to \mathbb{R}(f = f(x,y,u,v)) \) is continuous and \( \Omega \subset {\mathbb{
Bernard Dacorogna, Paolo Marcellini
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The problem is to find a complex function $$ w(x,y) = u(x,y) + iv(x,y) $$ such that $$ \left\{ {\begin{array}{*{20}{c}} {w_x^2 + w_y^2 + {f^2} = 0,a.ein\Omega } \\ {w = \varphi on\partial \Omega ,} \end{array}} \right. $$ Where \( f:\Omega \times {\mathbb{R}^2} \to \mathbb{R}(f = f(x,y,u,v)) \) is continuous and \( \Omega \subset {\mathbb{
Bernard Dacorogna, Paolo Marcellini
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On the construction of pseudo-Finsler eikonal equations
2020Summary: In this study, we have generalized pseudo-Finsler map by introducing the concept of semi-Riemannian map and have found pseudo-Finsler eikonal equations using pseudo-Finsler map. After that, we have obtained some sufficient theorems on pseudo-Finsler manifolds for the existence of solutions to the eikonal equation.
Çimdiker, Muradiye, Ekici, Cumali
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Eikonal approximation and the parabolic equation
The Journal of the Acoustical Society of America, 1976We discuss two aspects of the general problem of sound propagation in an ocean characterized by a range-dependent profile. We first consider a normal-mode formalism for describing a situation in which the eikonal approximation can be applied in the horizontal plane.
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