Volume Data Visualization Using Fractal Interpolation Surfaces

Abstract

Visualization of medical or experimental data is often achieved by extracting an intermediate geometric representation of the data. One such popular method for extracting an isosurface from volume data is the Marching Cubes (MC) algorithm, which creates a polygon mesh by sampling the data at the vertices of the cubes of a 3D grid. A method that uses the vertex extraction phase of the MC algorithm and represents the data by fractal interpolation surfaces (FISs) instead of a polygon mesh is presented. The proposed method is appropriate for isosurfaces that are not locally flat, such as natural structures. Another advantage is that a coarser grid resolution can typically be used, since FISs are particularly good at representing detailed, irregular or self-similar structures. Thus for many cases the resulting isosurface is more accurate or more compact. The multiresolution extension of the method is also straightforward. Experimental data verify the practical usefulness of the proposed method.