Non-local \(L_{0}\) Gradient Minimization Filter and Its Applications for Depth Image Upsampling

In this work, we propose a non-local \(L_{0}\) gradient minimization filter. The nonlocal idea is to restore an unknown pixel using other similar pixels, and the nonlocal gradient model has been verified for feature and structure-preserving. We introduce the nonlocal idea into a \(L_{0}\) gradient minimization approach, which is effective for preserving major edges while eliminating the low-amplitude structures. An optimization framework is designed for achieving this effort. Many optimized based filters do not have the property of joint filtering, so they can not be used in many problems, such as joint denoising, joint upsampling, while the proposed filter not only inherits the advantages of the \(L_{0}\) gradient minimization filter, but also has the property of the joint filtering. So our filter can be applied to joint super resolution. With the guidance of the high-resolution image, we propose upsampling the low-resolution depth image with the proposed filter. Experimental results demonstrate the effectiveness of our method both qualitatively and quantitatively compared with the state-of-the-art methods.