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 crisp-line interpolation methods show that the proposed methods increased the recognition rate by 30%.