Kinect depth map inpainting using spline approximation

Image inpainting consists in reconstructing missing parts of a given image. In this work, we propose to use an approximation method based on splines and finite elements approximation to recover missing depth values in images acquired with a Kinect 3D sensor. Neighboring pixels in the depth map may contain very different distance values. The considered surface approximation problem therefore involves rapidly varying data which can lead to oscillations (Gibbs phenomenon). To address this issue, we propose to apply two scale transformations to dampen these oscillations near steep gradients implied by the data. The algorithm is presented with some numerical examples of inpainting. Our approach also permits to get a finer resolution of the 3D depth map.