Mathematical analysis of “SpiderWeb” surface construction algorithm

"SpiderWeb" is an algorithm to build continuous triangle mesh surfaces embedded in noisy voxel data. This paper outlines a complete proof of the algorithm properties. The main feature of "SpiderWeb" is that its response to noise is the creation of non-manifold closed bubbles. Extremely noisy volume data produces a surface that has the consistency of closed-cell foam rubber. Despite this, the internal and external surfaces are continuous (closed and unbounded) and consistent (oriented). Its main application is surface construction in noisy MRI and Ultrasound data without preflltering.