Efficient 4D shape completion from sparse samples via cubic spline fitting in linear rotation-invariant space

Computer animation is frequently produced via interpolating a few sparse samples created by artists or reverse-engineered from physical prototypes, however, existing interpolation techniques fall short in efficiently generating a smooth 4D shape sequence from sparse samples. In this paper, we extend traditional curve fitting technique to 4D shape completion in shape space with novel technical components. In particular, we seek a smooth 4D shape sequence by minimizing the total shape distortion along the sequence trajectory. After embedding the shapes into a linear rotation-invariant feature space, the complex global minimization of shape distortion in shape space can be converted into simple cubic spline fitting problems in feature domains, which can be solved analytically. With cubic splines, we can not only handle in-between shapes interpolation, but also perform extrapolation towards more exciting results. To further improve the computational efficiency, we devise a hierarchical framework, in which the shape space is decomposed into high-frequency and low-frequency domains, the interpolation is only operated on the low-frequency domain, while the high-frequency details are enabled via deformation transfer techniques. We have conducted extensive experiments and comprehensive evaluations that showcase many attractive advantages of our novel method, including smooth interpolation between shapes, plausible extrapolation outside conventional shape domain, robustness under large deformations, and interactive performance for complicated shapes with high-quality details.