Quantitative analysis on PCA-based statistical 3D face shape modeling

Principle Component Analysis (PCA)-based statistical 3D face modeling using example faces is a popular technique for modeling 3D faces and has been widely used for 3D face reconstruction and face recognition. The capability of the model to depict a new 3D face depends on the exemplar faces in the training set. Although a few 3D face databases are available to the research community and they have been used for 3D face modeling, there is little work done on rigorous statistical analysis of the models built from these databases. The common factors that are generally concerned are the size of the training set and the different choice of the examples in the training set. In this paper, a case study on USF Human ID 3D database, one of the most popular databases in the field, has been used to study the effect of these factors on the representational power. We found that: 1) the size of the training set increase, the more accurate the model can represent a new face; 2) the increase of the representational power tends to slow down in an exponential manner and achieves saturity when the number of faces is greater than 250. These findings are under assumptions that the 3D faces in the database are randomly chosen and can represent different races and gender with neutral expressions. This analysis can be applied to the database which includes expressions too. A regularized 3D face reconstruction algorithm has also been tested to find out how feature points selection affects the accuracy of the 3D face reconstruction based on the PCA-model.