Shape-from-Shading (SfS) is a fundamental problem in Computer Vision. Its goal is to solve the image irradiance equation. One prominent solution is the Fast Marching Method of Kimmel & Sethian. When the light source is oblique, Kimmel & Sethian proposed to rotate the image to the light source coordinate system and then solve an ‘almost’ Eikonal equation. This paper presents a new iterative vari...

For a photonic crystal (PhC) of finite size, it is important to calculate its transmission and reflection spectra. For two-dimensional (2-D) PhCs composed of a square lattice of circular cylinders, the problem can be solved by an efficient method based on the Dirichletto-Neumann (DtN) map of the unit cell and a marching scheme using a pair of operators. In this paper, the DtN operator marching ...

We discuss the performance of three numerical methods for the fully nonlinear Monge-Ampère equation. The first two are pseudo time continuation methods while the third is a pure pseudo time marching algorithm. The pseudo time continuation methods are shown to converge for smooth data on a uniformly convex domain. We give numerical evidence that they perform well for the nondegenerate Monge-Ampè...

A survey of the development of the marching cubes algorithm [W. Lorensen, H. Cline, Marching cubes: a high resolution 3D surface construction algorithm. Computer Graphics 1987; 21(4):163–9], a well-known cell-by-cell method for extraction of isosurfaces from scalar volumetric data sets, is presented. The paper’s primary aim is to survey the development of the algorithm and its computational pro...