  In computer vision most iterative optimization algorithms, both sparse and
dense, rely on a coarse and reliable dense initialization to bootstrap their
optimization procedure. For example, dense optical flow algorithms profit
massively in speed and robustness if they are initialized well in the basin of
convergence of the used loss function. The same holds true for methods as
sparse feature tracking when initial flow or depth information for new features
at arbitrary positions is needed. This makes it extremely important to have
techniques at hand that allow to obtain from only very few available
measurements a dense but still approximative sketch of a desired 2D structure
(e.g. depth maps, optical flow, disparity maps, etc.). The 2D map is regarded
as sample from a 2D random process. The method presented here exploits the
complete information given by the principal component analysis (PCA) of that
process, the principal basis and its prior distribution. The method is able to
determine a dense reconstruction from sparse measurement. When facing
situations with only very sparse measurements, typically the number of
principal components is further reduced which results in a loss of
expressiveness of the basis. We overcome this problem and inject prior
knowledge in a maximum a posterior (MAP) approach. We test our approach on the
KITTI and the virtual KITTI datasets and focus on the interpolation of depth
maps for driving scenes. The evaluation of the results show good agreement to
the ground truth and are clearly better than results of interpolation by the
nearest neighbor method which disregards statistical information.
