Pose estimation of 3D face images using fuzzy nearest distance in fuzzy interpolation line

Authors have developed a novel method to estimate the pose position of an incoming 3D face image. In the learning system, a set of 3D face images of various persons with various face expressions at determined pose is used as a fuzzy reference vector. Instead of using the conventional crisp-vector in conventional crisp-feature space, we develop a pose estimation system using fuzzy-vector as a point in a fuzzy-feature space, by incorporating fuzzy numbers to deal with the fuzziness of the data caused by statistical measurement error directly. A fuzzy-linear interpolation and a fuzzy-spline interpolation which uses fuzzy points are then constructed. To estimate the pose position of an unknown crisp-image vector, it is firstly transformed into a fuzzy-vector and projected onto 3D fuzzy-feature spaces, then calculate the fuzzy-distances to all available fuzzy-points in the designated fuzzy-lines. We also develop fuzzy distance calculation methods for determining the pose position of an unknown 3D face image. Comparisons of the recognition results of the proposed methods with the crispline interpolation methods show that the proposed methods increased the recognition rate by 30%.