Whether it is the geometry of a human face, the boundary of a brain tumor or the decision interface of multivariate financial data, isosurfaces are important objects for understanding and analyzing all types of data. The marching cubes algorithm is a very effective and widely used technique for extracting isosurfaces from scientific data sets. The purpose of this research project is to exploit some special properties of the isosurfaces produced by the marching cubes algorithm in order to develop particularly efficient geometry processing tools for the analysis, manipulation and processing of these surfaces. The intellectual merit of the research project consists of the development of new methods for extracting meaning and understanding from data by new and efficient digital geometry processing tools for the special case of isosurfaces produced by the marching cubes algorithm. Since isosurfaces are widely used in many areas of science, the results of this research will have broad impact on data analysis in general.
It has recently been discovered that the isosurfaces produced by the marching cubes (MC) algorithm have some special properties that allow for the development of particularly efficient geometry processing tools. These properties include (1) some special aspects of a network of orthogonal polygons which allow curve techniques to be lifted to surfaces and (2) a local function property provided by a modification of the original MC method which allows conventional approximation techniques to be applied to these special isosurfaces. This research will concentrate on three aspects of geometry processing for surfaces, namely (1) parameterizations which are necessary for texture mapping, remeshing, compression and many other useful surface operations; (2) methods of estimating curvature and other related surface properties which will serve as the basic tools for many useful higher level surface processing techniques and (3) algorithms for smoothing and fairing surfaces.
