In this work we present a self-supervised learning framework to simultaneously train two Convolutional Neural Networks (CNNs) to predict depth and surface normals from a single image. In contrast to most existing frameworks which represent outdoor scenes as fronto-parallel planes at piece-wise smooth depth, we propose to predict depth with surface orientation while assuming that natural scenes have piece-wise smooth normals. We show that a simple depth-normal consistency as a soft-constraint on the predictions is sufficient and effective for training both these networks simultaneously. The trained normal network provides state-of-the-art predictions while the depth network, relying on much realistic smooth normal assumption, outperforms the traditional self-supervised depth prediction network by a large margin on the KITTI benchmark. Demo video: this https URL
While most of the self supervised approaches have mainly focused on getting accurate depth-maps, little attention has been devoted to use other scene representations. We are aware of two recent works @cite_27 @cite_44 which incorporate the surface orientation (normal) estimation for single view geometric understanding. Similar to @cite_4 , @cite_27 @cite_44 learn depth from monocular sequences using a self-supervised photometric loss but additionally they compute surface normals from the predicted depths using a weighted mean cross product @cite_41 . They propose to regularize the inverse depths and the normals computed from the depth predictions simultaneously. We believe that this is redundant and a separate normal prediction is beneficial then relying on the normals to be computed from predicted depth. The differences between our work and @cite_27 @cite_44 is detailed in section and a extensive comparison of the proposed work with these methods is described in section .
@cite_44 @cite_41 @cite_27 @cite_4
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Learning to estimate 3D geometry in a single image by watching unlabeled videos via deep convolutional network is attracting significant attention. In this paper, we introduce a "3D as-smooth-as-possible (3D-ASAP)" prior inside the pipeline, which enables joint estimation of edges and 3D scene, yielding results with significant improvement in accuracy for fine detailed structures. Specifically, we define the 3D-ASAP prior by requiring that any two points recovered in 3D from an image should lie on an existing planar surface if no other cues provided. We design an unsupervised framework that Learns Edges and Geometry (depth, normal) all at Once (LEGO). The predicted edges are embedded into depth and surface normal smoothness terms, where pixels without edges in-between are constrained to satisfy the prior. In our framework, the predicted depths, normals and edges are forced to be consistent all the time. We conduct experiments on KITTI to evaluate our estimated geometry and CityScapes to perform edge evaluation. We show that in all of the tasks, i.e. depth, normal and edge, our algorithm vastly outperforms other state-of-the-art (SOTA) algorithms, demonstrating the benefits of our approach. This paper concerns accurate computation of the singular value decomposition (SVD) of an (m n ) matrix (A ). As is well known, cross-product matrix based SVD algorithms compute large singular values accurately but generally deliver poor small singular values. A new novel cross-product matrix based SVD method is proposed: (a) Use a backward stable algorithm to compute the eigenpairs of (A^ T A ) and take the square roots of the large eigenvalues of it as the large singular values of (A ) ; (b) form the Rayleigh quotient of (A^ T A ) with respect to the matrix consisting of the computed eigenvectors associated with the computed small eigenvalues of (A^ T A ) ; (c) compute the eigenvalues of the Rayleigh quotient and take the square roots of them as the small singular values of (A ). A detailed quantitative error analysis is conducted on the method. It is proved that if small singular values are well separated from the large ones then the method can compute the small ones accurately up to the order of the unit roundoff ( ). An algorithm is developed that is not only cheaper than the standard Golub–Reinsch and Chan SVD algorithms but also can update or downdate a new SVD by adding or deleting a row and compute certain refined Ritz vectors for large matrix eigenproblems at very low cost. Several variants of the algorithm are proposed that compute some or all parts of the SVD. Typical numerical examples confirm the high accuracy of our algorithm. We present an unsupervised learning framework for the task of monocular depth and camera motion estimation from unstructured video sequences. In common with recent work [10, 14, 16], we use an end-to-end learning approach with view synthesis as the supervisory signal. In contrast to the previous work, our method is completely unsupervised, requiring only monocular video sequences for training. Our method uses single-view depth and multiview pose networks, with a loss based on warping nearby views to the target using the computed depth and pose. The networks are thus coupled by the loss during training, but can be applied independently at test time. Empirical evaluation on the KITTI dataset demonstrates the effectiveness of our approach: 1) monocular depth performs comparably with supervised methods that use either ground-truth pose or depth for training, and 2) pose estimation performs favorably compared to established SLAM systems under comparable input settings.