Cleaning Up Meshes.

A new implicit modeling technique reconstructs surfaces from incomplete meshes and noisy point clouds

Three-dimensional scanning technologies give designers and engineers a fast, easy means for digitally representing physical objects. What they typically don't give are smooth surfaces. To digitally re-create a physical object, 3D scanners convert the object's surface to point clouds comprising hundreds of thousands of 3D coordinates. The 3D points must then be connected in some manner to create a mesh from which a surface can be extrapolated. Unfortunately, the resulting mesh can be inaccurate or incomplete--either because the shape is highly complex with details that are difficult for the scanner to capture or because of arbitrary "noise" in the resultant point cloud. Reducing or repairing the surface damage can be a painstaking process, but it's an absolutely necessary one for some applications, particularly manufacturing, which requires smoothly blended, manifold surfaces.

In an effort to take the pain out of the conversion process and to provide better results than those that can be achieved using existing surface-reconstruction techniques, researchers at Applied Research Associates and the University of Canterbury in New Zealand have developed an automated system that not only reconstructs surfaces from 3D point clouds, but also fills holes in 3D meshes and smoothes surface distortions caused by noisy point data.

At the heart of the technique is an implicit-modeling system based on a mathematical concept called Radial Basis Functions (RBFs), which are analytical functions that interpolate between known coordinates. The new RBF-based approach, called FastRBF, models the surface using a function that represents the distance from any point in space to the nearest point on the surface.

The reliance on RBFs for implicit modeling is significant because they provide the smallest energy value of the known interpolation functions, and thus are considered the smoothest interpolants. After the data interpolation, the system forms triangular faces along the resulting isosurface to create a mesh representation of the surface.

Fast, Smooth Operators

The chief advantage of using RBFs for implicit modeling is that, unlike parametric surfaces or implicit patches, they rely on a single, continuous analytical function to represent the entire surface of an object, the value and gradient of which can be calculated anywhere in space. It has only been recently, however, that mathematics and algorithms have been developed to perform RBF calculations for large or complex objects. "In the past, it has been generally accepted that, although RBFs are the smoothest interpolants, they were computationally impractical for anything more than a ...