Abstract
In this paper, we propose a depth-aided color image inpainting method in the quaternion domain, called depth-aided low-rank quaternion matrix completion (D-LRQMC). In conventional quaternion-based inpainting techniques, the color image is expressed as a quaternion matrix by using the three imaginary parts as the color channels, whereas the real part is set to zero and has no information. Our approach incorporates depth information as the real part of the quaternion representations, leveraging the correlation between color and depth to improve the result of inpainting. In the proposed method, we first restore the observed image with the conventional LRQMC and estimate the depth of the restored result. We then incorporate the estimated depth into the real part of the observed image and perform LRQMC again. Simulation results demonstrate that the proposed D-LRQMC can improve restoration accuracy and visual quality for various images compared to the conventional LRQMC. These results suggest the effectiveness of the depth information for color image processing in quaternion domain.
Abstract (translated)
在这篇论文中，我们提出了一种基于四元数域的深度辅助颜色图像修复方法，称为深度辅助低秩四元数矩阵补全（D-LRQMC）。在传统的基于四元数的修复技术中，彩色图像是通过将三个虚部部分用作色彩通道来表示为一个四元数矩阵，并且实部被设置为零且不携带信息。我们的方法则利用深度信息作为四元数表示中的实部，借助颜色和深度之间的相关性来提高图像修补的效果。 在提出的方法中，我们首先使用传统的LRQMC（低秩四元数矩阵补全）技术恢复观察到的图像，并估计该修复结果的深度。然后将估算出的深度信息整合进原始图像的实部部分，并再次执行LRQMC操作。模拟结果显示，与传统方法相比，我们的D-LRQMC方法能够提升各种图像的复原准确性和视觉质量。这些结果表明，在四元数域中使用深度信息对于彩色图象处理的有效性。
URL
https://arxiv.org/abs/2503.16818
