A GPU Rendering Algorithm for Discrete Optimal Mass Transportation

To solve the problem of difficulty in implementing the discrete optimal transportation algorithm,this paper presents a simple algorithm that solve the problem by rendering quadrilateral with the help of GPU rendering pipeline. Firstly, a series of 3D plane was built from the preimage of optimal mass transportation map. In order to obtain the vertical projection, these planes were rendered using orthographic camera.Current measure can be computed from it. Then, gradient descent was used to adjust the planes’ position so as to let current measure be equal to target measure, obtaining the results of optimal mass transportation.Finally, an equiareal parameterization for topological disk was constructed based on the algorithm The algorithm was evaluated on the models of Maxplanck, Alexraw, Lion, Totoro and Buddaha. Compared with the numerical method, the iteration speed of this algorithm is improved by 8 times and compared with other similar methods, taking the logarithm of ratio of area as evaluation criteria, our algorithm is more area-preserving.