Shape quantification of tissue and biomaterials can be central to many studies and applications in bioengineering and biomechanics. Often, shape is mapped with photogrammetry or projected light techniques that provide XYZ point cloud data, and shape is quantified using derived flexure and curvature calculations based on the point cloud data. Accordingly, the accuracy of the calculated curvature depends on the properties of the point cloud data set. In this study, we present a curvature variability prediction (CVP) software model that predicts the distribution, i.e., the standard deviation, of curvature measurements associated with surface topography point cloud data properties. The CVP model point cloud data input variables include XYZ noise, sampling density, and map extent. The CVP model outputs the curvature variability statistic in order to assess performance in the curvature domain. Representative point cloud data properties are obtained from an automated biological specimen video topographer, the BioSpecVT (ver. 1.02) (Vision Metrics, Inc.,). The BioSpecVT uses a calibrated, structured light pattern to support automated computer vision feature extraction software for precisely converting video images of biological specimens, within seconds, into three dimensional point cloud data. In representative sample point cloud data obtained with the BioSpecVT, sampling density is about 11 pts/mm<sup>2</sup> for an XYZ mapping volume encompassing about 16 mm x 13.5 mm x 18.5 mm, average XY per point variability is about ±2 μm, and Z axis variability is about ±40 μm (50% level) with a Gaussian distribution. A theoretical study with the CVP model shows that for derived point cloud data properties, curvature mapping accuracy increases, i.e. measurement variability decreases, when curvature increases from about 30 m<sup>-1 </sup>to 137 m<sup>-1</sup>. This computed result is consistent with the Z axis noise becoming less significant as the measured depth increases across an approximately fixed XY region.
Elevation mapping corneal topography instruments provide an array of x, y, z data points describing the corneal surface. An advantage of elevation mapping instruments is their ability to calculate the 3D data array strictly from the instrument's geometry and calibration data; no assumptions about the corneal surface itself are needed. However, uncompensated eye movements can affect accuracy. Longitudinal eye movements occur along the z axis, due to pulmonary and cardiac pulsations. Eye rotations due to saccades and drifts are normal occurrences, as are translational body movements. An analysis of eye and body movements at the cornea's surface indicates a nearly linear relationship between data acquisition times of less than 33 msec, and the possible change in elevation at a point referenced to an instrument axis. The proportionality constant is expected to vary by a factor of about six over the range of clinical patients, since eye and body movements are exaggerated in juvenile patients, geriatric patients, and patients with poor vision. The analysis estimates an elevation change due to rotation and longitudinal translation of the eye of up to +/- 285 micrometers in 33 msec within the clinical population. This analysis indicates that when a topographer's acquisition time is greater than 100 microsecond(s) ec (during which an apparent elevation change of up to 1.0 micrometers may occur) testing on static objects may not provide a realistic measure of an instrument's clinical performance.