Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map translations. This is not the case for rotations. Global rotation equivariance is typically sought through data augmentation, but patch-wise equivariance is more difficult. We present Harmonic Networks or H-Nets, a CNN exhibiting equivariance to patch-wise translation and 360-rotation. We achieve this by replacing regular CNN filters with circular harmonics, returning a maximal response and orientation for every receptive field patch.H-Nets use a rich, parameter-efficient and fixed computational complexity representation, and we show that deep feature maps within the network encode complicated rotational invariants. We demonstrate that our layers are general enough to be used in conjunction with the latest architectures and techniques, such as deep supervision and batch normalization. We also achieve state-of-the-art classification on rotated-MNIST, and competitive results on other benchmark challenges.

Monocular depth estimators can be trained with various forms of self-supervision from binocular-stereo data to circumvent the need for high-quality laser scans or other ground-truth data. The disadvantage, however, is that the photometric reprojection losses used with selfsupervised learning typically have multiple local minima. These plausible-looking alternatives to ground truth can restrict what a regression network learns, causing it to predict depth maps of limited quality. As one prominent example, depth discontinuities around thin structures are often incorrectly estimated by current state-of-the-art methods.Here, we study the problem of ambiguous reprojections in depth prediction from stereo-based self-supervision, and introduce Depth Hints to alleviate their effects. Depth Hints are complementary depth suggestions obtained from simple off-the-shelf stereo algorithms. These hints enhance an existing photometric loss function, and are used to guide a network to learn better weights. They require no additional data, and are assumed to be right only sometimes. We show that using our Depth Hints gives a substantial boost when training several leading self-supervised-from-stereo models, not just our own. Further, combined with other good practices, we produce state-of-the-art depth predictions on the KITTI benchmark. We demonstrate that our selective training using DepthHints is a general enhancement that can improve multiple leading self-supervised training algorithms, allowing our implementations to reach better minima. The Depth Hints can come from the same stereo image data, via, e.g. OpenCV's stereo estimates [13,14].3. We show that our selective training with Depth Hints, coupled with sensible network design choices, leads us to outperform most other algorithms. We achieve state-of-the-art results on the KITTI dataset [8], outperforming both our baseline model and previously published results.

Deep feature spaces have the capacity to encode complex transformations of their input data. However, understanding the relative feature-space relationship between two transformed encoded images is difficult. For instance, what is the relative feature space relationship between two rotated images? What is decoded when we interpolate in feature space? Ideally, we want to disentangle confounding factors, such as pose, appearance, and illumination, from object identity. Disentangling these is difficult because they interact in very nonlinear ways. We propose a simple method to construct a deep feature space, with explicitly disentangled representations of several known transformations. A person or algorithm can then manipulate the disentangled representation, for example, to re-render an image with explicit control over parameterized degrees of freedom. The feature space is constructed using a transforming encoder-decoder network with a custom feature transform layer, acting on the hidden representations. We demonstrate the advantages of explicit disentangling on a variety of datasets and transformations, and as an aid for traditional tasks, such as classification. *

Supervised deep networks are among the best methods for finding correspondences in stereo image pairs. Like all supervised approaches, these networks require ground truth data during training. However, collecting large quantities of accurate dense correspondence data is very challenging. We propose that it is unnecessary to have such a high reliance on ground truth depths or even corresponding stereo pairs. Inspired by recent progress in monocular depth estimation, we generate plausible disparity maps from single images. In turn, we use those flawed disparity maps in a carefully designed pipeline to generate stereo training pairs. Training in this manner makes it possible to convert any collection of single RGB images into stereo training data. This results in a significant reduction in human effort, with no need to collect real depths or to hand-design synthetic data. We can consequently train a stereo matching network from scratch on datasets like COCO, which were previously hard to exploit for stereo. Through extensive experiments we show that our approach outperforms stereo networks trained with standard synthetic datasets, when evaluated on KITTI, ETH3D, and Middlebury. Code to reproduce our results is available at https://github.com/nianticlabs/stereo-from-mono/.

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