Nasal similarity measure of 3D faces based on curve shape space

We propose a novel method for measuring the nasal similarity among 3D faces. Firstly, we construct a representation for the nose shape, which is composed of a set of geodesic curves, each crosses the bridge of the nose. Next, using these geodesic curves, we formulate a similarity measure to compare among noses in the curve shape space. Under the Riemannian framework, the shape space is a quotient space for which the scaling, translation and rotation are removed. Since the nose similarity measure is based on the shape comparison, the proposed method has the following advantages: (1) the similarity measure is robust to facial expressions since the nose is not affected by facial expressions; (2) the geometric features of the nose shape match well with the human perception; (3) the similarity measure is independent of the mesh grid because the chosen nose curves are not sensitive to the triangular mesh model. We construct a nasal hierarchical structure for noses organization which is based on nose similarity measure results. In our experiments, we evaluate the performance of the proposed method and compare it with competing methods on three public face databases namely, FRGC2.0, Texas3D and BosphorusDB. The results show superiority of the proposed method in terms of both the speed and the accuracy when the nasal measurements are processed in the nasal hierarchical structure and the nasal samples with low sampling rate (5%-25% of original point cloud).