Two basic methods are commonly used to fit surfaces to binary data. In the first, the binary data is low-pass filtered, and an algorithm such as Marching Cubes is applied, where the surface is built through each surface cube at an iso-surface of the grey-scale data [4]. To remove terracing artifacts and reduce the number of triangles in the model, surface smoothing and decimation algorithms can be applied. However, because these procedures are applied to the surface without reference to the original segmentation, they can result in loss of fine detail.
In the second general method for fitting a surface to binary data, the binary object is enclosed by a parametric or spline surface. Control points on the surface are moved towards the binary data in order to minimize an energy function based on surface curvature and distance between the binary surface and the parametric surface [5]. This approach has two main drawbacks for general applications. First, it is difficult to determine how many control points will be needed to ensure sufficient detail in the final model. Second, this method does not handle complex topologies easily.
Recently, Gibson [2] introduced Constrained Elastic SurfaceNets which fit an elastic net of nodes over the surface of a binary segmented dataset and moved the node positions to reduce the surface curvature while constraining the net to remain within one voxel of the binary surface. This approach produces smooth surface models from binary segmented data that are faithful to the original segmentation.