Volume Data Visualization Using Fractal Interpolation Surfaces

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. We present a method for isosurface approximation that uses the vertex extraction phase of the MC algorithm, but subsequently represents the data by fractal interpolation surfaces instead of a polygon mesh. 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 fractal interpolation surfaces are particularly good at representing detailed, irregular or self-similar structures. Thus for many cases the resulting isosurface is more accurate and more compact. The multiresolution extension of the method is also straightforward. Experimental data verify the practical usefulness of the proposed method.