# Depth Image Super Resolution Based on Edge-Guided Method
## 1 Introduction and Related Works  
In recent years, with the rapid development of computer vision technology, the depth information of scenes becomes increasingly essential for many applications, such as 3D Reconstruction [1; 2], Augmented Reality [3], Robot Navigation [4] and so on. Some active sensors [5], such as Kinect and PMD (Photonic Mixer Device), can easily acquire depth information of scenes. Then, this information will be used to create a depth image. However, due to the theoretical and practical limitations, the achievable resolution of any depth imaging device is usually too low to meet the needs of many practical applications. How to improve depth image resolution is an urgent problem that needs to be solved. One way to solve this problem is to apply some sophisticated vision sensors. However, these sensors are usually very expensive. Another way is to use super-resolution (SR) algorithm. Compared with expensive sensors, SR algorithm, not relying on hardware configuration, is evidently a low-cost approach. Inspired by the idea of color image SR, researchers have proposed many promising depth image SR methods [6; 7; 8] in recent years, which can improve the resolution of depth image effectively. According to the difference of referenced information, depth SR can be mainly divided into four categories: (1) interpolation; (2) SR from LR depth image frames; (3) SR through fusing depth image and HR color image; and (4) example-based SR.  
(1) Interpolation: There are many analytic methods for image interpolation, including nearest neighbor interpolation, bilinear and cubic interpolation [9]. However, when interpolation is done by a large factor, these analytic methods can cause image edge to be ragged and blurred because of the big value difference of pixels across edges. To solve the problem, [PERSON] [10] presents an SR method based on bilinear interpolation and adaptive sharpening filter. This method can suppress effectively theedge-blurred effect. [PERSON] [11] proposes an improved cubic interpolation algorithm, which uses cubic interpolation to compute the pixels in smooth areas and uses edge-vector interpolation to compute the pixels near edges. [PERSON] [8] presents an edge-guided approach. This method reconstructs sharp HR edges through Markov random field at first, and then an SR depth image can be interpolated under the guidance of these edges. With the help of edge-guided information, the sharpness of edges can be well preserved in the final SR image. At the same time, some bilateral filtering methods [12; 13] can also preserve edge well. (2) SR from LR depth image frames: The HR image can be reconstructed by fusing the complementary information among a few LR depth images captured from the same scene. [PERSON] [14] uses an optimization framework with a bilateral total-variation regularization term to solve such a SR problem. [PERSON] [15] constructs an energy function through the Markov Random Field, and minimizes the energy function to get the HR image. [PERSON] [16] proposes a dynamic-scene SR method for depth image to deal with the problem of non-rigid body motion between LR images. [PERSON] [17] uses convex projection method to construct the imaging model of depth image sequence for depth image SR.  
(3) SR through fusing depth image and HR color image: Most commercial depth cameras can get a depth image and a color image about the same scene simultaneously, and usually the resolution of the color image is higher than that of the depth image. Thus, the HR depth image can be reconstructed with the help of HR color image. [PERSON] [18] calculates an anisotropic total variation diffusion tensor from HR color image, and then the tensor is used to reconstruct the SR depth image. [PERSON] [19] combines bilateral filter with median filter to compute adaptively weights from the HR image, and then the depth image is interpolated according to these weights. [PERSON] [20] proposes a depth image SR method based on joint trilateral filter.