Color Texture Inpainting for 3D Shape Based on Signal Sparse Optimization

In practices,many causes such as the technical limitations of scanning devices usually lead to the damage of color textures on a 3D model surface.To deal with this problem,a method about directly inpainting color textures on a 3D surface is presented,based on the sparse representation of signals defined on an irregular space.Firstly,in this method,the RGB values at each vertex of a 3D model are treated as three discrete color signals defined on a 2D manifold respectively,and a dictionary is defined which is comprised of the eigenvectors of a Laplacian matrix.Then,taking advantage of the sparsity of these color signals represented in that dictionary,for those 3D model surfaces with damaged color textures,it constructs an objective function by setting the sparsity of the representation coefficients as the goal and the data fidelity with the undamaged part as the constraints.Lastly,the missing parts of the color signals can be estimated efficiently by solving the sparse optimization problem.The experiment results show that,the global and the intrinsic properties of the eigenvectors of Laplacian matrix will guarantee that the reconstructed parts are highly approximate to the original ones and consistent to the undamaged parts.