Reconstruction of 3D faces by shape estimation and texture interpolation

This paper aims to address the ill-posed problem of reconstructing 3D faces from single 2D face images. An extended Tikhonov regularization method is connected with the standard 3D morphable model in order to reconstruct the 3D face shapes from a small set of 2D facial points. Further, by interpolating the input 2D texture with the model texture and warping the interpolated texture to the reconstructed face shapes, 3D face reconstruction is achieved. For the texture warping, the 2D face deformation has been learned from the model texture using a set of facial landmarks. Our experimental results justify the robustness of the proposed approach with respect to the reconstruction of realistic 3D face shapes

Mobility and asymmetry effects in one-dimensional rock-paper-scissors games

As the behavior of a system composed of cyclically competing species is strongly influenced by the presence of fluctuations, it is of interest to study cyclic dominance in low dimensions where these effects are the most prominent. We here discuss rock-paper-scissors games on a one-dimensional lattice where the interaction rates and the mobility can be species dependent. Allowing only single site occupation, we realize mobility by exchanging individuals of different species. When the interaction and swapping rates are symmetric, a strongly enhanced swapping rate yields an increased mixing of the species, leading to a mean-field like coexistence even in one-dimensional systems. This coexistence is transient when the rates are asymmetric, and eventually only one species will survive. Interestingly, in our spatial games the dominating species can differ from the species that would dominate in the corresponding nonspatial model. We identify different regimes in the parameter space and construct the corresponding dynamical phase diagram.Comment: 6 pages, 5 figures, to appear in Physical Review

Surface Structural Disordering in Graphite upon Lithium Intercalation/Deintercalation

We report on the origin of the surface structural disordering in graphite anodes induced by lithium intercalation and deintercalation processes. Average Raman spectra of graphitic anodes reveal that cycling at potentials that correspond to low lithium concentrations in LixC (0 \leq x < 0.16) is responsible for most of the structural damage observed at the graphite surface. The extent of surface structural disorder in graphite is significantly reduced for the anodes that were cycled at potentials where stage-1 and stage-2 compounds (x > 0.33) are present. Electrochemical impedance spectra show larger interfacial impedance for the electrodes that were fully delithiated during cycling as compared to electrodes that were cycled at lower potentials (U < 0.15 V vs. Li/Li+). Steep Li+ surface-bulk concentration gradients at the surface of graphite during early stages of intercalation processes, and the inherent increase of the LixC d-spacing tend to induce local stresses at the edges of graphene layers, and lead to the breakage of C-C bonds. The exposed graphite edge sites react with the electrolyte to (re)form the SEI layer, which leads to gradual degradation of the graphite anode, and causes reversible capacity loss in a lithium-ion battery.Comment: 12 pages, 5 figure

Rank-Sparsity Incoherence for Matrix Decomposition

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of applications in model and system identification, and is NP-hard in general. In this paper we consider a convex optimization formulation to splitting the specified matrix into its components, by minimizing a linear combination of the $\ell_1$ norm and the nuclear norm of the components. We develop a notion of \emph{rank-sparsity incoherence}, expressed as an uncertainty principle between the sparsity pattern of a matrix and its row and column spaces, and use it to characterize both fundamental identifiability as well as (deterministic) sufficient conditions for exact recovery. Our analysis is geometric in nature, with the tangent spaces to the algebraic varieties of sparse and low-rank matrices playing a prominent role. When the sparse and low-rank matrices are drawn from certain natural random ensembles, we show that the sufficient conditions for exact recovery are satisfied with high probability. We conclude with simulation results on synthetic matrix decomposition problems