Robust and Efficient Recovery of Rigid Motion from Subspace Constraints Solved using Recursive Identification of Nonlinear Implicit Systems

The problem of estimating rigid motion from projections may be characterized using a nonlinear dynamical system, composed of the rigid motion transformation and the perspective map. The time derivative of the output of such a system, which is also called the "motion field", is bilinear in the motion parameters, and may be used to specify a subspace constraint on either the direction of translation or the inverse depth of the observed points. Estimating motion may then be formulated as an optimization task constrained on such a subspace. Heeger and Jepson [5], who first introduced this constraint, solve the optimization task using an extensive search over the possible directions of translation. We reformulate the optimization problem in a systems theoretic framework as the the identification of a dynamic system in exterior differential form with parameters on a differentiable manifold, and use techniques which pertain to nonlinear estimation and identification theory to perform the optimization task in a principled manner. The general technique for addressing such identification problems [14] has been used successfully in addressing other problems in computational vision [13, 12]. The application of the general method [14] results in a recursive and pseudo-optimal solution of the motion problem, which has robustness properties far superior to other existing techniques we have implemented. By releasing the constraint that the visible points lie in front of the observer, we may explain some psychophysical effects on the nonrigid percept of rigidly moving shapes. Experiments on real and synthetic image sequences show very promising results in terms of robustness, accuracy and computational efficiency

Learning Rank Reduced Interpolation with Principal Component Analysis

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.Comment: Accepted at Intelligent Vehicles Symposium (IV), Los Angeles, USA, June 201