A team of researchers working at the Institute of Communication and Computer Systems (ICCS), located at the National Technical University of Athens (NTUA), has designed a whole new implementation of the standard Marching Cubes (MC) algorithm. The innovative method will enable doctors to optimize reconstruction of anatomical structures from 3D medical images. The newly developed algorithm is able to reproduce all 15 predefined cases of cube configurations, established with the standard MC, as well as additional ones, which can be found in specialized literature. The process of extracting triangulated surfaces from volumetric data doesn't suffer from the recurrent type A "hole problem" in the standard MC. The new solution has been implemented in Java in order to create files in Virtual Reality Modelling Language (VRML) format from real 3D medical data. The algorithm thus can be used in telemedicine applications which are platform independent.
In today's clinical practice, doctors use 3D patient data to obtain anatomical structures by segmenting and identifying the latter as a stack of intersections with parallel planes matching the number of 3D image slices. These are not sufficient though to fully grasp the extent of the object's shape and morphology. Advanced visualization and manipulation techniques form necessary tools to acquire an acceptable anatomical reconstruction. In fact, there are different approaches to the problem, such as the use of De Launey triangulation, Voronoi diagrams or graph techniques, as to generate optimal contours of the required object. Or a functional minimization procedure may be applied. In the two cases however, the grey scale image should produce closed, non-intersecting contours. The third method, known as the Marching Cubes technique, makes use of cubic neighbourhoods of 8 voxels in order to create adequate triangles.
In the standard MC algorithm, one has to find a match in the 15 predefined cube configurations for each specimen encountered in the image in order to determine the surface triangles. As a result, the cubes are all extracted and rotated to yield a large number of triangles, requiring a lot of computational power. To reduce the amount of cube configurations, there is a tendency to use symmetry which might cause incoherent surfaces or "holes" in cases where two adjacent cubes occur. If at least one cube face is showing an intersection point in each of its four edges, you are dealing with the type A "hole problem". The novel MC algorithm, designed by the ICCS team, is able to generate polygons instead of triangles for every possible cube configuration, without referring to any predefined cases. It is even possible to handle cases in which more than one polygon is present in the same cube.
The new solution has several advantages to offer. It is no longer necessary to rotate and compare the cubes encountered in the image, with the predefined cases. This results in computational speed-up. No complementary symmetry is required anymore. Therefore the type A "hole problem" is being eliminated automatically. Previously, this critical issue has been tackled by introducing a set of additional configurations which the novel MC algorithm is able to generate without any difficulty in the user-friendly World Wide Web compliant VRML 2.0 format. Multiple users from remote sites are allowed to rotate and scale the 3D structures in real time on a standard PC. The VRML viewers are integrated into most Internet browsers and support co-planar as well as non-planar polygon rendering. They are equally able to interact with Java programmes.
The first experimental results present detailed anatomical structures, which originate both from full resolution Computed Tomography (CT) and Magnetic Resonance (MR) images of human heads. In the near future, the ICCS research team from NTUA plans to concentrate its efforts on minimizing the amount of triangles, generated by the novel MC algorithm. For further technical details about the ongoing work, you can contact Dr. George K. Matsopoulos.