Geometry meets semantics for semi-supervised monocular depth estimation

Depth estimation from a single image represents a very exciting challenge in computer vision. While other image-based depth sensing techniques leverage on the geometry between different viewpoints (e.g., stereo or structure from motion), the lack of these cues within a single image renders ill-posed the monocular depth estimation task. For inference, state-of-the-art encoder-decoder architectures for monocular depth estimation rely on effective feature representations learned at training time. For unsupervised training of these models, geometry has been effectively exploited by suitable images warping losses computed from views acquired by a stereo rig or a moving camera. In this paper, we make a further step forward showing that learning semantic information from images enables to improve effectively monocular depth estimation as well. In particular, by leveraging on semantically labeled images together with unsupervised signals gained by geometry through an image warping loss, we propose a deep learning approach aimed at joint semantic segmentation and depth estimation. Our overall learning framework is semi-supervised, as we deploy groundtruth data only in the semantic domain. At training time, our network learns a common feature representation for both tasks and a novel cross-task loss function is proposed. The experimental findings show how, jointly tackling depth prediction and semantic segmentation, allows to improve depth estimation accuracy. In particular, on the KITTI dataset our network outperforms state-of-the-art methods for monocular depth estimation.Comment: 16 pages, Accepted to ACCV 201

Partial Sum Minimization of Singular Values in Robust PCA: Algorithm and Applications

Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known that the underlying structure of clean data is low-rank, but the exact rank of clean data is also known. Yet, when applying conventional rank minimization for those problems, the objective function is formulated in a way that does not fully utilize a priori target rank information about the problems. This observation motivates us to investigate whether there is a better alternative solution when using rank minimization. In this paper, instead of minimizing the nuclear norm, we propose to minimize the partial sum of singular values, which implicitly encourages the target rank constraint. Our experimental analyses show that, when the number of samples is deficient, our approach leads to a higher success rate than conventional rank minimization, while the solutions obtained by the two approaches are almost identical when the number of samples is more than sufficient. We apply our approach to various low-level vision problems, e.g. high dynamic range imaging, motion edge detection, photometric stereo, image alignment and recovery, and show that our results outperform those obtained by the conventional nuclear norm rank minimization method.Comment: Accepted in Transactions on Pattern Analysis and Machine Intelligence (TPAMI). To appea