Abstract: We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.
Abstract: We present a new method to reconstruct a temporally
coherent 3D animation from single or multi-view RGB-D video data
using unbiased feature point sampling. Given RGB-D video data, in
form of a 3D point cloud sequence, our method first extracts feature
points using both color and depth information. In the subsequent
steps, these feature points are used to match two 3D point clouds in
consecutive frames independent of their resolution. Our new motion
vectors based dynamic alignement method then fully reconstruct
a spatio-temporally coherent 3D animation. We perform extensive
quantitative validation using novel error functions to analyze the
results. We show that despite the limiting factors of temporal and
spatial noise associated to RGB-D data, it is possible to extract
temporal coherence to faithfully reconstruct a temporally coherent
3D animation from RGB-D video data.