This paper proposes an intrinsic decomposition method from a single RGB-D image. To remedy the highly ill-conditioned problem, the reflectance component is regularized by a sparsity term, which is weighted by a bilateral kernel to exploit non-local structural correlation. As shading images are piece-wise smooth and have sparse gradient fields, the sparse-induced ${\ell }_1$-norm is used to regularize the finite difference of the direct irradiance component, which is the most dominant sub-component of shading and describes the light directly received by the surfaces of the objects from the light source. To derive an efficient algorithm, the proposed model is transformed into an unconstrained minimization of the augmented Lagrangian function, which is then optimized via the alternating direction method. The stability of the proposed method with respect to parameter perturbation and its robustness to noise are investigated by experiments. Quantitative and qualitative evaluation demonstrates that our method has better performance than state-of-the-art methods. Our method can also achieve intrinsic decomposition from a single color image by integrating existed depth estimation methods. We also present a depth refinement method based on our intrinsic decomposition method, which obtains more geometry details without texture artifacts. Other application, e.g., texture editing, also demonstrates the effectiveness of our method.

本文提出了一种基于单张RGB-D图像的本征分解方法。为了解决病情严重的问题，反射率分量由稀疏项进行正则化，稀疏项由双边核加权以利用非局部结构相关性。由于阴影图像是逐段平滑的并且具有稀疏的梯度场，因此稀疏引起的${\ell }_{\mathrm{1个}}$-norm用于规范直接辐照度分量的有限差分，直接辐照度分量是阴影的最主要子分量，它描述对象表面从光源直接接收的光。为了获得有效的算法，将提出的模型转换为增强的拉格朗日函数的无约束最小化，然后通过交替方向方法对其进行优化。通过实验研究了该方法在参数摄动方面的稳定性及其对噪声的鲁棒性。定量和定性评估表明，我们的方法比最先进的方法具有更好的性能。通过整合现有的深度估计方法，我们的方法还可以从单色图像中实现固有分解。我们还提出了一种基于我们固有分解方法的深度细化方法，该方法可以获取更多的几何细节，而不会产生纹理伪像。其他应用例如，纹理编辑，也证明了我们方法的有效性。