Scientific and technical visualization: A new course offering that integrates mathematics, science, and technology.
Segmentation of MRI data by means of nonlinear diffusion
The article focuses on the application of the segmentation algorithm based on the numerical solution of the Allen-Cahn non-linear diffusion partial differential equation. This equation is related to the motion of curves by mean curvature. It exhibits several suitable mathematical properties including stable solution profile. This allows the user to follow accurately the position of the segmentation curve by bringing it quickly to the vicinity of the segmented object and by approaching the details...
Segmenting colour images on the basis of a fuzzy hierarchical approach.
In this paper we deal with two problems related to imprecision in colour image segmentation processes: to decide whether a set of pixels verify the property to be homogeneously coloured, and to represent the set of possible segmentations of an image at different precision levels. In order to solve the first problem we introduce a measure of distance between colours in the CIE L*a*b* space, that allows us to measure the degree of homogeneity of two pixels p and q on the basis of the maximum distance...
Self-avoiding walks on the lattice ℤ² with the 8-neighbourhood system
This paper deals with the properties of self-avoiding walks defined on the lattice with the 8-neighbourhood system. We compute the number of walks, bridges and mean-square displacement for N=1 through 13 (N is the number of steps of the self-avoiding walk). We also estimate the connective constant and critical exponents, and study finite memory and generating functions. We show applications of this kind of walk. In addition, we compute upper bounds for the number of walks and the connective constant....
Shape Descriptors for Image Analysis
Shape-from-Shading, viscosity solutions and edges.
Skeletonization on quadtree represented images.
Software for visualisation of small objects.
Solutions of fourth-order partial differential equations in a noise removal model.
Some applications of parabolic differential equations of Allen-Cahn type in image processing
Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation
We show stability and consistency of the linear semi-implicit complementary volume numerical scheme for solving the regularized, in the sense of Evans and Spruck, mean curvature flow equation in the level set formulation. The numerical method is based on the finite volume methodology using the so-called complementary volumes to a finite element triangulation. The scheme gives the solution in an efficient and unconditionally stable way.
Strategies for seeing.
Strong minimizers of Blake & Zisserman functional
Subjective surfaces and Riemannian mean curvature flow of graphs.
Summaries of certain spatial patterns retrieved from multidate remote-sensing data.
Symbol Declarations in Mathematical Writing
We present three corpus-based studies on symbol declaration in mathematical writing. We focus on simple object denoting symbols which may be part of larger expressions. We look into whether the symbols are explicitly introduced into the discourse and whether the information on once interpreted symbols can be used to interpret structurally related symbols. Our goal is to support fine-grained semantic interpretation of simple and complex mathematical expressions. The results of our analysis empirically...