Issue No. 03 - May/June (2010 vol. 16)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2009.64
Ayelet Dominitz , Technion, Haifa
Allen Tannenbaum , Georgia Institute of Technology, Atlanta and Technion, Haifa
In this paper, we present a novel method for texture mapping of closed surfaces. Our method is based on the technique of optimal mass transport (also known as the “earth-mover's metric”). This is a classical problem that concerns determining the optimal way, in the sense of minimal transportation cost, of moving a pile of soil from one site to another. In our context, the resulting mapping is area preserving and minimizes angle distortion in the optimal mass sense. Indeed, we first begin with an angle-preserving mapping (which may greatly distort area) and then correct it using the mass transport procedure derived via a certain gradient flow. In order to obtain fast convergence to the optimal mapping, we incorporate a multiresolution scheme into our flow. We also use ideas from discrete exterior calculus in our computations.
Texture mapping, optimal mass transport, parametrization, spherical wavelets.
A. Tannenbaum and A. Dominitz, "Texture Mapping via Optimal Mass Transport," in IEEE Transactions on Visualization & Computer Graphics, vol. 16, no. , pp. 419-433, 2009.