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a b s t r a c tGeometric modelling using Partial Differential Equations (PDEs) has been gradually recognised due to its smooth instinct, as well as the ability to generate a variety of geometric shapes by intuitively manipulating a relatively small set of PDE boundary curves. In this paper we explore and demonstrate the feasibility of the PDE method in facial geometry parameterisation. The geometry of a generic face is approximated by evaluating spectral solutions to a group of fourth order elliptic PDEs. Our PDE-based parameterisation scheme can produce and animate a high-resolution 3D face with a relatively small number of parameters. By taking advantage of parametric representation, the PDE method can use one fixed animation scheme to manipulate the facial geometry in varying Levels of Detail (LODs), without any further process.

Abstract-An alternative technique for shape morphing using a surface generating method using partial differential equations is outlined throughout this work. The boundaryvalue nature that is inherent to this surface generation technique together with its mathematical properties are hereby exploited for creating intermediate shapes between an initial shape and a final one. Four alternative shape morphing techniques are proposed here. The first one is based on the use of a linear combination of the boundary conditions associated with the initial and final surfaces, the second one consists of varying the Fourier mode for which the PDE is solved whilst the third results from a combination of the first two. The fourth of these alternatives is based on the manipulation of the spine of the surfaces, which is computed as a by-product of the solution. Results of morphing sequences between two topologically nonequivalent surfaces are presented. Thus, it is shown that the PDE based approach for morphing is capable of obtaining smooth intermediate surfaces automatically in most of the methodologies presented in this work and the spine has been revealed as a powerful tool for morphing surfaces arising from the method proposed here.

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