Geometrical descriptors for human face morphological analysis and recognition

The human eye, connected to the brain, gives people the possibility to immediately, automatically and exactly recognize one person from another. A main aim is obviously to “copy” this recognition mechanism of the brain and to use it as a means for face recognition. Since the human recognition happens through an automatic “authentication” of facial shape and features, this face study is totally Geometry-based. In order to formalize the anatomical facial features, many strategies may be used. This work collects various solutions. Particularly, a geometrical description of human face is here proposed as a survey. Some elements of Differential Geometry, such as the Coefficients of the Fundamental Forms, the Principal Curvatures, Mean and Gaussian Curvatures, the derivatives and the Shape and Curvedness Indexes introduced by Koenderink and VanDoorn are briefly defined and explained, and then used as descriptors for three-dimensional facial surface. Their behaviour on faces is classified according to some feedback parameters: similarity between different faces, sensitivity to noise, completeness and smoothness. Face is the most important part of human anatomy, and its study has many scopes. This survey may be used as a starting point for elaborating and implementing an algorithm for 3D facial recognition.