Capturing data from three-dimensional surfaces using fuzzy landmarks

Anatomical landmarks are defined as biologically meaningful loci that can be unambiguously defined and repeatedly located with a high degree of accuracy and precision. The neurocranial surface is characteristically void of such loci. We define a new class of landmarks, termed fuzzy landmarks, that will allow us to represent the form of the neurocranium. A fuzzy landmark represents the position of a biological structure that is precisely delineated, but occupies an area that is larger than a single point in the observer's reference system. In this study, we present a test case in which the cranial bosses are evaluated as fuzzy landmarks. Five fuzzy landmarks (the cranial bosses) and three traditional landmarks were placed repeatedly by a single observer on three-dimensional (3D) computed tomography (CT) surface reconstructions of pediatric dry skulls and skulls of pediatric patients, and directly on four of the same dry skulls using a 3Space digitizer. Thirty landmark digitizing trials from CT scans show an average error of 1.15 mm local to each fuzzy landmark, while the average error for the last ten trials was 0.75 mm, suggesting a learning curve. Data collected with the 3Space digitizer was comparable. Measurement error of fuzzy landmarks is larger than that of traditional landmarks, but is acceptable, especially since fuzzy landmarks allow inclusion of areas that would otherwise go unsampled. The information obtained is valuable in growth studies, clinical evaluation, and volume measurements. Our method of fuzzy landmarking is not limited to cranial bosses, and can be applied to any other anatomical features with fuzzy boundaries.