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

Learning Rank Reduced Interpolation with Principal Component Analysis