Journal ArticleDOI
The eikonal equation: some results applicable to computer vision
TLDR
In this article, the relationship between the light reflected from a surface and its shape was investigated, and it was shown that a special type of eikonal equation has only one convex and positive C2 solution in some neighborhood of a singular point.Abstract:
In this paper we investigate certain first order partial differential equations which formulate the relationship between the light reflected from a surface and its shape. Particular emphasis is given to eikonal equations. Two results are presented. First, we prove that a special type of eikonal equation has only one convex and positive C2 solution in some neighborhood of a singular point. Using this result, we show that a restricted form of this equation has exactly two solutions. These results have application in scanning electron microscopy.read more
Citations
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Journal ArticleDOI
Shape-from-shading: a survey
TL;DR: Six well-known SFS algorithms are implemented and compared, and the performance of the algorithms was analyzed on synthetic images using mean and standard deviation of depth error, mean of surface gradient error, and CPU timing.
Journal ArticleDOI
Height and gradient from shading
TL;DR: In this paper, the shape-from-shading problem is solved by linearization of the reflectance map about the current estimate of the surface orientation at each picture cell, which can find an exact solution of a given shape from shading problem even though a regularizing term is included.
Book ChapterDOI
Shape From Shading
Emmanuel Prados,Olivier Faugeras +1 more
TL;DR: This chapter describes the main difficulties of the Shape From Shading problem and the most recent theoretical results and gives some examples of realistic modeling and of rigorous numerical methods.
Height and gradient from shading
TL;DR: In this paper, the shape-from-shading problem is solved by linearization of the reflectance map about the current estimate of the surface orientation at each picture cell, which can find an exact solution of a given shape from shading problem even though a regularizing term is included.
Journal ArticleDOI
Numerical methods for shape-from-shading: A new survey with benchmarks
TL;DR: This paper provides a brief description of each method, highlighting its basic assumptions and mathematical properties, and proposes some numerical benchmarks in order to compare the methods in terms of their efficiency and accuracy in the reconstruction of surfaces corresponding to synthetic, as well as to real images.
References
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Book
Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Book
Theory of Ordinary Differential Equations
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.
Book
Foundations of mechanics
TL;DR: In this article, Ratiu and Cushman introduce differential theory calculus on manifolds and derive an overview of qualitative and topological properties of differentiable properties of topological dynamics.
Book
Taschenbuch der Mathematik
I N Bronstein,K A Semendjajew +1 more
TL;DR: This paper presents a meta-analyses of the statistical methods used to estimate the Boltzmann inequality, a measure of the uncertainty in the solutions to the inequality of the discrete-time equations.