Tuesday, October 4, 2011

Reaction: Marching Cubes: A High Resolution 3D Surface Construction Algorithm

The paper makes an interesting reading. Author has systematically led the reader through information flow in 3D medical algorithms, interconnecting surface construction as the theme of the paper. The algorithm is a based on 14 possible triangulated cubes - cubes being intersected by surface. Normal to the triangle of the vertices is interpolated using mathematical density function.

The paper is sourced way back in 1987 when computational powers were far more limited, hence, the simplicity of the algorithm seems to be apt. Author has achieved the computations with C programming in very old operating systems like VAX/VMS.

The paper has a number of citations or references on account of its approach, simplicity and superiority to Contour Algorithm. Further reading, like the one presented on “Dual Marching Cubes: Primal Contouring of Dual Grids by Scott Schaefer and Joe Warren” somewhere during 2003, presents more efficient algorithm. Here the author abstracts the ability “to reproduce thin features
of the extracted surface without excessive subdivision required by methods such as Marching Cubes...”, Dual Marching Cubes producing “a crackfree, adaptive polygonalization of the surface that reproduces sharp features”. The current paper is a good run through of surface-cube intersection through triangulation to mathematical interpolation of vertices for 3D Surface Construction.

Question: Can we have an explanation of Gradient Vector and Density Function which is the
mathematical basis of this paper?

What are other algorithms used for surface mapping in the medical field in the context of today’s
computational technology?