Objective: To compare three-dimensional nasal measurements directly made on subjects to those made on plaster casts, and nasal dimensions obtained with a surface-based approach to values obtained with a landmark representation. Methods: Soft-tissue nasal landmarks were directly digitized on 20 healthy adults. Stone casts of their noses were digitized and mathematically reconstructed using nonuniform rational B-splines (NURBS) curves. Linear distances, angles, volumes and surface areas were computed using facial landmarks and NURBS-reconstructed models (surface-based approach). Results: Measurements on the stone casts were somewhat smaller than values obtained directly from subjects (differences between −0.05 and −1.58 mm). Dahlberg's statistic ranged between 0.73 and 1.47 mm. Significant (p < .05) t values were found for 4 of 15 measurements. The surface-based approach gave values 3.5 (volumes) and 2.1 (surface area) times larger than those computed with the landmark-based method. The two values were significantly related (volume, r = 0.881; surface, r = 0.924; p < .001), the resulting equations estimated actual values well (mean difference, volume −0.01 mm3, SD 1.47, area 0.05 cm2, SD 1.44); limits of agreement between −2.89 and 2.87 mm3 (volume); −2.88 and 2.78 cm2 (area). Conclusions: Considering the characteristics of the two methods, and for practical purposes, nasal distances and angles obtained on plaster models were comparable to digital data obtained directly from subjects. Surface areas and volumes were best obtained using a surface-based approach, but could be estimated using data provided by the landmark representation.
Efficient matrix computation for isogeometric discretizations with hierarchical B-splines in any dimension
