Depth images play an important role and are prevalently used in many computer vision and computational imaging tasks. However, due to the limitation of active sensing technology, the captured depth images in practice usually suffer from low resolution and noise, which prevents its further applications. To remedy this problem, in this paper, we first propose an adaptive data fidelity formulation to optimally generate each depth pixel from a mixture probability distribution, characterizing the similarity both in the depth map and the corresponding high-resolution guided color image. The proposed method is able to fit the distribution of the input depth signal as an optimization problem by maximizing the mixture probability. Furthermore, to promote the piecewise property that depth images exhibit, we propose a transferred graph Laplacian model as a regularization term, which is general and able to handle various depth recovery tasks such as super-resolution and denoising well. Specifically, each pixel within the recovered depth image is represented as a vertex in a graph with weights in connected edges representing the similarity between vertices. By minimizing the squared variations of the image signal, the task of depth image recovery can be converted to the problem of graph-based image filtering. Since the proposed graph Laplacian regularization model is able to fully exploit a priori information about the depth image, a much more accurate and robust estimation of the underlying depth can be obtained. Extensive experiment evaluations verify that the proposed method obtains recovered depth with higher quality in terms of both objective and subjective criteria, compared with most of the state-of-the-art methods.

中文翻译：

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具有自适应数据保真度和转移图拉普拉斯正则化的颜色引导深度图像恢复

深度图像起着重要作用，广泛用于许多计算机视觉和计算成像任务。然而，由于主动传感技术的限制，在实践中捕获的深度图像通常会受到低分辨率和噪声的影响，从而阻碍了其进一步应用。为了解决这个问题，在本文中，我们首先提出了一种自适应数据保真度公式，以从混合概率分布中最优地生成每个深度像素，表征深度图和相应的高分辨率引导彩色图像中的相似性。所提出的方法能够通过最大化混合概率来拟合输入深度信号的分布作为优化问题。此外，为了促进深度图像展示的分段特性，我们提出了一个转移图拉普拉斯模型作为正则化项，它是通用的，能够很好地处理各种深度恢复任务，例如超分辨率和去噪。具体来说，恢复的深度图像中的每个像素都表示为图中的一个顶点，连接边中的权重表示顶点之间的相似性。通过最小化图像信号的平方变化，深度图像恢复的任务可以转换为基于图的图像滤波问题。由于所提出的图拉普拉斯正则化模型能够充分利用关于深度图像的先验信息，因此可以获得对潜在深度的更准确和稳健的估计。