Analysis of planar curves: A new approach to the analysis of facial profiles

The aim of this work is to study the human facial profiles by using new techniques applied to the analysis of planar curves. This involves establishing a method of segmentation, description and classification of profiles, not being restricted to whether the analysis is done on a single profile or a set of them. The particular problems of quantifying changes in facial morphology are investigated. Mathematical techniques, based on scale space filtering and curvature approaches, are used to describe the changes on the profiles. Special emphasis is given to the analysis of the shape of segments rather than to the movement of points, landmarks or vectors, although these are also explored. Qualitative descriptions are derived providing a unique representation of the facial profiles, allowing the changes in shape as a result of the treatment, to be visually observed and assessed. Based on these descriptions, the profile is automatically and objectively divided into a number of regions considered suitable for analysis, which are seen to correspond to parts of the face of interest to the clinician (e.g. nose, chin, upper lip, etc.).Quantitative descriptions are also derived for the various segments, through curvature and bending energy plots, and other complementary measures such as length, compactness, roundness and skew. These allow the segments to be classified in terms of their concavity. The data used are two-dimensional cross sections (profiles) that are a representation of a three-dimensional (3D) model of the human head. Possible sources of data are: traces from lateral radiographs, profiles obtained from 3D data sets generated from Computerized Tomography scans and or from Optical Surface scans. Computer programs were developed for the analysis of the data on a PC-based Transputer system. Possible areas of applications would be: psychology, pattern recognition, orthodontic and surgical treatments, forensic science and computer vision