Modified SurfaceNets Smoothing a Marching Cubes Mesh

Modified SurfaceNets Smoothing a Marching Cubes Mesh

Modified SurfaceNets:

Smoothing a Marching Cubes Mesh

Virginia Holmstrom

1 Introduction

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. [2]

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.

2 Modified SurfaceNets

2.1

Marching Cubes Mesh.

Both Marching Cubes and SurfaceNets take binary imagery

data as input and output a triangular mesh. For SurfaceNets

to smooth a Marching Cubes mesh it would have to be

imagery slices. Similar to Marching Cubes, SurfaceNets

defines a cube from 8 voxels, with 4 voxels each taken from

(meaning at least one of the voxels has a different binary

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