## Saturday, July 26, 2008

### a starting point for building 3D surface meshes or true volumetric tetrahedral grids

"nanosecond history":

__________1987

Since William Lorensen and Harvey Cline’s publication of Marching Cubes: A High
Resolution 3D Surface Construction Algorithm in 1987 Marching Cubes has become the
defining algorithm for the creation of 3D surface meshes.

Yet despite the success of Marching Cubes the resulting mesh exhibits several weaknesses, including aliasing and terracing artifacts, less-than-optimal triangle quality, and large numbers of triangles.  A
multitude of techniques have been introduced to address these issues, including surface
smoothing and triangle decimation algorithms. Beyond reducing artifacts, smoothing
improves the effectiveness of triangle decimation algorithms and reduces errors during
finite element analysis. However, many smoothing techniques fail to eliminate terracing
because their local filter neighborhood does not encompass the width of the terrace.
Additionally, smoothing a mesh without consideration of the original data may smooth
away crucial fine details as well as mesh generation artifacts.

___________1998

In 1998 Sarah F. F. Gibson published Constrained Elastic Surface Nets: Generating
Smooth Surfaces from Binary Segmented Data. Her work attempts to preserve the fine
detail present in the original data by applying smoothing directly to the binary data and
introduces the concept of a constraint to limit the deviation of the smoothed data from the
original.
Modified SurfaceNets attempts to apply Gibson’s SurfaceNet technique to the
problem of smoothing a Marching Cubes mesh. By defining SurfaceNet nodes on the
Marching Cubes mesh and constraining their movement to their Voronoi regions,
Modified SurfaceNets aims to reduce terracing while preserving the fine detail of the
original image.
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see http://en.wikipedia.org/wiki/Marching_cubes

and see this present bog : http://stef2cnrs.wordpress.com

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This class of Surface Reconstruction methods is OK for immerged SURFACE and only for SURFACE.

If you want to generate not only surface models from your data but also to create true
volumetric tetrahedral grids suitable for advanced 3D ﬁnite-element simulations, then open your mind... Usually, these grids are constructed using a ﬂexible advancing-front algorithm. Again, special care is taken to obtain meshes of high quality, i.e., tetrahedra with bad aspect ratio are avoided...

see a commercial software (with a quite good link with matlab): http://www.comsol.com/

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In biophotonics, we have this process:

1/produce your images (exactly a stack of 2D images)

2/perform many image cleaning and many img processes with or without informations from the other images in the stack (often it is only a process for each image with imageJ)

3/the final step is segmentation & binarisation also with or without informations from the other images in the stack

4/generation of surface ( a/isosurface for rendering; b/ 3D surface mesh)

5/generation true  3D volumetric tetrahedral grids suitable for advanced 3D ﬁnite-element simulations

6/a 4D solver with time

7/statistics and comparison between biology, medical and multiphysics data and 4D simulations