Gordon and Udupa published a fast boundary-tracking algorithm for 3-dimensional finite binary images and confirmed the soundness of their algorithm by observation of its behavior on numerous experimental images. Higher-dimensional analogs of Gordon and Udupa's algorithm are now being used in medical imaging software. This paper presents a proof that these higher-dimensional boundary-tracking algorithms are also sound.
T. Yung Kong,
"Justification of a type of fast anisotropic boundary tracker for multidimensional binary images", Proc. SPIE 1832, Vision Geometry, (9 April 1993); doi: 10.1117/12.142176; https://doi.org/10.1117/12.142176