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 eigenvec-tors of a Laplacian matrix. Then, taking advantage of the sparsity of these color signals represented in that dic-tionary, 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 op-timization 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.%在实际工作中, 由于扫描设备的局限性等原因易造成3D 模型表面颜色纹理的缺损, 为此, 利用非规则空间信号的稀疏表示提出了一种直接修复3D 模型表面颜色纹理的方法. 首先将3D 网格模型各顶点处的 RGB 值分别视为定义在2D流形曲面上的3个离散信号, 选取3D网格曲面上的拉普拉斯矩阵的特征向量集作为字典; 然后, 利用在此字典中颜色信号表示系数的稀疏性, 对表面颜色有缺失的3D网格曲面, 以待修复颜色信号表示系数的稀疏性作为目标, 以模型完好部分颜色值的保真作为约束建立稀疏优化目标函数; 最后, 求解该优化问题得到修复后的颜色信号. 实验证明, 由于拉普拉斯矩阵的特征向量具有良好的全局性和内蕴性, 使得在缺失部分重建出的颜色信号高度逼近原始的颜色纹理, 且与已知部分整体保持一致.
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