Balanced Infinity Laplacian Models for Depth Completion with Variable Metric and Convolutional Stage

Inpainting is the process of filling in missing or corrupted parts of an image using the information that is present in the rest of the picture. One application of inpainting is the recovery of incomplete depth maps. Depth maps represent the distance from a sensor to each point in the scene. They are becoming increasingly important in applications such as 3D object reconstruction, depth map completion for control of autonomous vehicles, and others. This paper presents three models for inpainting incomplete depth maps and an anisotropic metric. Our inpainting model is the solution of a second-order degenerate partial differential equation. The three used models are variations of the infinity Laplacian: the biased infinity Laplacian, the balanced biased infinity Laplacian, and the double-balanced infinity Laplacian. The contribution of this paper is threefold. First, we propose two new models that are variations of the infinity Laplacian. Second, we evaluate these models on the public data set KITTI Depth Completion Suite. Results show that the considered biased infinity Laplacian and the anisotropic metric perform better than the other proposed models and contemporary models.