Reconstruction of a fluttering flag from a single image

Reconstructing a 3 D object from a single image is a challenging task because determining useful geometric structure information from a single image is difficult. In this paper, we propose a novel method to extract the 3 D mesh of a flag from a single image and drive the flag model to flutter with virtual wind. A deep convolutional neural fields model is first used to generate a depth map of a single image. Based on the Alpha Shape, a coarse 2 D mesh of flag is reconstructed by sampling at different depth regions. Then, we optimize the mesh to generate a mesh with depth based on Restricted Frontal-Delaunay. We transform the Delaunay mesh with depth into a simple spring model and use a velocity-based solver to calculate the moving position of the virtual flag model. The experiments demonstrate that the proposed method can construct a realistic fluttering flag video from a single image.

On the Kelvin Transformation in Finite Difference Implementations

Finite difference operators were applied on a Delaunay mesh. This way it is possible to discretize a radial boundary that is used to perform a Kelvin mapping of an additional outer domain to virtually extend the computation domain to infinity. With an example two-wire problem, the performance of this approach is shown in comparison with a conventional calculation domain and with the analytical solution, respectively. The presented implementation delivers a more precise approximation to the real values and at the same time requires a smaller system of equations—i.e., allows for faster computations.