Abstract

Our work tackles the problem of anisotropic data interpolation in the context of depth computation in large regions of an image. Usually, depth data present areas without depth data due to low confidence in the data. We consider the image endowed with an anisotropic metric gij taking spatial and the geometry information. Our proposal is a numerical implementation based on “eikonal” operators to compute the solution of the biased Infinity Laplacian or biased Absolutely Minimizing Lipschitz Extension (bAMLE). The infinity Laplacian operator interpolates creating cones. The biased infinity Laplacian interpolates creating exponential cones, making it more adapted to real scenes that, in general, present smooth surfaces. Thus, the biased Infinity Laplacian properties make this interpolator able of completing depth data to large image areas. We performed an experimental evaluation comparing our numerical model comparing Infinity Laplacian, biased Infinity Laplacian, and bilateral filter in two databases: Middlebury2014 and KITTI (for depth completion). In Middlebury2014 biased infinity Laplacian outperforms Infinity Laplacian in the up-sampling depth data task, and in KITTI dataset, completing depth images, biased Infinity Laplacian exceeds both bilateral and Infinity Laplacian. The simplicity of our practical implementation makes biased Infinity Laplacian a low-cost-implementation alternative for many computer vision community interpolation problems.