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Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector corresponding to the smallest, or zero, eigenvalue of a matrix representing a linear system. Incorporating this in deep learning frameworks would allow us to explicitly encode known notions of geometry, instead of having the network implicitly learn them from data. However, performing eigendecomposition within a network requires the ability to differentiate this operation. While theoretically doable, this introduces numerical instability in the optimization process in practice. In this paper, we introduce an eigendecomposition-free approach to training a deep network whose loss depends on the eigenvector corresponding to a zero eigenvalue of a matrix predicted by the network. We demonstrate that our approach is much more robust than explicit differentiation of the eigendecomposition using two general tasks, outlier rejection and denoising, with several practical examples including wide-baseline stereo, the perspective-n-point problem, and ellipse fitting. Empirically, our method has better convergence properties and yields state-of-the-art results., Comment: 16 pages, Accepted by TPAMI. arXiv admin note: substantial text overlap with arXiv:1803.08071

Active Learning for discriminative models has largely been studied with the focus on individual samples, with less emphasis on how classes are distributed or which classes are hard to deal with. In this work, we show that this is harmful. We propose a method based on the Bayes' rule, that can naturally incorporate class imbalance into the Active Learning framework. We derive that three terms should be considered together when estimating the probability of a classifier making a mistake for a given sample; i) probability of mislabelling a class, ii) likelihood of the data given a predicted class, and iii) the prior probability on the abundance of a predicted class. Implementing these terms requires a generative model and an intractable likelihood estimation. Therefore, we train a Variational Auto Encoder (VAE) for this purpose. To further tie the VAE with the classifier and facilitate VAE training, we use the classifiers' deep feature representations as input to the VAE. By considering all three probabilities, among them especially the data imbalance, we can substantially improve the potential of existing methods under limited data budget. We show that our method can be applied to classification tasks on multiple different datasets -- including one that is a real-world dataset with heavy data imbalance -- significantly outperforming the state of the art.

We introduce a comprehensive benchmark for local features and robust estimation algorithms, focusing on the downstream task -- the accuracy of the reconstructed camera pose -- as our primary metric. Our pipeline's modular structure allows easy integration, configuration, and combination of different methods and heuristics. This is demonstrated by embedding dozens of popular algorithms and evaluating them, from seminal works to the cutting edge of machine learning research. We show that with proper settings, classical solutions may still outperform the perceived state of the art. Besides establishing the actual state of the art, the conducted experiments reveal unexpected properties of Structure from Motion (SfM) pipelines that can help improve their performance, for both algorithmic and learned methods. Data and code are online https://github.com/vcg-uvic/image-matching-benchmark, providing an easy-to-use and flexible framework for the benchmarking of local features and robust estimation methods, both alongside and against top-performing methods. This work provides a basis for the Image Matching Challenge https://vision.uvic.ca/image-matching-challenge., Comment: Added: KeyNet-SOSNet, AffNet-HardNet, TFeat, MKD from kornia

Voronoi diagrams are highly compact representations that are used in various Graphics applications. In this work, we show how to embed a differentiable version of it -- via a novel deep architecture -- into a generative deep network. By doing so, we achieve a highly compact latent embedding that is able to provide much more detailed reconstructions, both in 2D and 3D, for various shapes. In this tech report, we introduce our representation and present a set of preliminary results comparing it with recently proposed implicit occupancy networks.

We aim to reduce the tedious nature of developing and evaluating methods for aligning PET-CT scans from multiple patient visits. Current methods for registration rely on correspondences that are created manually by medical experts with 3D manipulation, or assisted alignments done by utilizing mutual information across CT scans that may not be consistent when transferred to the PET images. Instead, we propose to label multiple key points across several 2D slices, which we then fit a key curve to. This removes the need for creating manual alignments in 3D and makes the labelling process easier. We use these key curves to define an error metric for the alignments that can be computed efficiently. While our metric is non-differentiable, we further show that we can utilize it during the training of our deep model via a novel method. Specifically, instead of relying on detailed geometric labels -- e.g., manual 3D alignments -- we use synthetically generated deformations of real data. To incorporate robustness to changes that occur between visits other than geometric changes, we enforce consistency across visits in the deep network's internal representations. We demonstrate the potential of our method via qualitative and quantitative experiments.

In the current era of stellar spectroscopic surveys, synthetic spectral libraries are the basis for the derivation of stellar parameters and chemical abundances. In this paper, we compare the stellar parameters determined using five popular synthetic spectral grids (INTRIGOSS, FERRE, AMBRE, PHOENIX, and MPIA/1DNLTE) with our convolutional neural network (CNN, $\texttt{StarNet}$). The stellar parameters are determined for six physical properties (effective temperature, surface gravity, metallicity, [$\alpha$/Fe], radial velocity, and rotational velocity) given the spectral resolution, signal-to-noise, and wavelength range of optical FLAMES-UVES spectra from the Gaia-ESO Survey. Both CNN modelling and epistemic uncertainties are incorporated through training an ensemble of networks. $\texttt{StarNet}$ training was also adapted to mitigate differences between the synthetic grids and observed spectra by augmenting with realistic observational signatures (i.e. resolution matching, wavelength sampling, Gaussian noise, zeroing flux values, rotational and radial velocities, continuum removal, and masking telluric regions). Using the FLAMES-UVES spectra for FGK type dwarfs and giants as a test set, we quantify the accuracy and precision of the stellar label predictions from $\texttt{StarNet}$. We find excellent results over a wide range of parameters when $\texttt{StarNet}$ is trained on the MPIA/1DNLTE synthetic grid, and acceptable results over smaller parameter ranges when trained on the 1DLTE grids. These tests also show that our CNN pipeline is highly adaptable to multiple simulation grids., Comment: 20 pages, 17 figures, published by MNRAS. Code for StarNet available at https://github.com/Spiffical/StarNet

We propose an optimization-based framework to register sports field templates onto broadcast videos. For accurate registration we go beyond the prevalent feed-forward paradigm. Instead, we propose to train a deep network that regresses the registration error, and then register images by finding the registration parameters that minimize the regressed error. We demonstrate the effectiveness of our method by applying it to real-world sports broadcast videos, outperforming the state of the art. We further apply our method on a synthetic toy example and demonstrate that our method brings significant gains even when the problem is simplified and unlimited training data is available.

The dominant approach for learning local patch descriptors relies on small image regions whose scale must be properly estimated a priori by a keypoint detector. In other words, if two patches are not in correspondence, their descriptors will not match. A strategy often used to alleviate this problem is to "pool" the pixel-wise features over log-polar regions, rather than regularly spaced ones. By contrast, we propose to extract the "support region" directly with a log-polar sampling scheme. We show that this provides us with a better representation by simultaneously oversampling the immediate neighbourhood of the point and undersampling regions far away from it. We demonstrate that this representation is particularly amenable to learning descriptors with deep networks. Our models can match descriptors across a much wider range of scales than was possible before, and also leverage much larger support regions without suffering from occlusions. We report state-of-the-art results on three different datasets.

Many problems in computer vision require dealing with sparse, unordered data in the form of point clouds. Permutation-equivariant networks have become a popular solution-they operate on individual data points with simple perceptrons and extract contextual information with global pooling. This can be achieved with a simple normalization of the feature maps, a global operation that is unaffected by the order. In this paper, we propose Attentive Context Normalization (ACN), a simple yet effective technique to build permutation-equivariant networks robust to outliers. Specifically, we show how to normalize the feature maps with weights that are estimated within the network, excluding outliers from this normalization. We use this mechanism to leverage two types of attention: local and global-by combining them, our method is able to find the essential data points in high-dimensional space to solve a given task. We demonstrate through extensive experiments that our approach, which we call Attentive Context Networks (ACNe), provides a significant leap in performance compared to the state-of-the-art on camera pose estimation, robust fitting, and point cloud classification under noise and outliers. Source code: https://github.com/vcg-uvic/acne., Comment: CVPR 2020

We propose a novel image sampling method for differentiable image transformation in deep neural networks. The sampling schemes currently used in deep learning, such as Spatial Transformer Networks, rely on bilinear interpolation, which performs poorly under severe scale changes, and more importantly, results in poor gradient propagation. This is due to their strict reliance on direct neighbors. Instead, we propose to generate random auxiliary samples in the vicinity of each pixel in the sampled image, and create a linear approximation with their intensity values. We then use this approximation as a differentiable formula for the transformed image. We demonstrate that our approach produces more representative gradients with a wider basin of convergence for image alignment, which leads to considerable performance improvements when training networks for classification tasks. This is not only true under large downsampling, but also when there are no scale changes. We compare our approach with multi-scale sampling and show that we outperform it. We then demonstrate that our improvements to the sampler are compatible with other tangential improvements to Spatial Transformer Networks and that it further improves their performance.

We propose to simultaneously learn to sample and reconstruct magnetic resonance images (MRI) to maximize the reconstruction quality given a limited sample budget, in a self-supervised setup. Unlike existing deep methods that focus only on reconstructing given data, thus being passive, we go beyond the current state of the art by considering both the data acquisition and the reconstruction process within a single deep-learning framework. As our network learns to acquire data, the network is active in nature. In order to do so, we simultaneously train two neural networks, one dedicated to reconstruction and the other to progressive sampling, each with an automatically generated supervision signal that links them together. The two supervision signals are created through Monte Carlo tree search (MCTS). MCTS returns a better sampling pattern than what the current sampling network can give and, thus, a better final reconstruction. The sampling network is trained to mimic the MCTS results using the previous sampling network, thus being enhanced. The reconstruction network is trained to give the highest reconstruction quality, given the MCTS sampling pattern. Through this framework, we are able to train the two networks without providing any direct supervision on sampling.

We propose a deep network that can be trained to tackle image reconstruction and classification problems that involve detection of multiple object instances, without any supervision regarding their whereabouts. The network learns to extract the most significant top-K patches, and feeds these patches to a task-specific network -- e.g., auto-encoder or classifier -- to solve a domain specific problem. The challenge in training such a network is the non-differentiable top-K selection process. To address this issue, we lift the training optimization problem by treating the result of top-K selection as a slack variable, resulting in a simple, yet effective, multi-stage training. Our method is able to learn to detect recurrent structures in the training dataset by learning to reconstruct images. It can also learn to localize structures when only knowledge on the occurrence of the object is provided, and in doing so it outperforms the state-of-the-art.

We present a novel deep architecture and a training strategy to learn a local feature pipeline from scratch, using collections of images without the need for human supervision. To do so we exploit depth and relative camera pose cues to create a virtual target that the network should achieve on one image, provided the outputs of the network for the other image. While this process is inherently non-differentiable, we show that we can optimize the network in a two-branch setup by confining it to one branch, while preserving differentiability in the other. We train our method on both indoor and outdoor datasets, with depth data from 3D sensors for the former, and depth estimates from an off-the-shelf Structure-from-Motion solution for the latter. Our models outperform the state of the art on sparse feature matching on both datasets, while running at 60+ fps for QVGA images., Comment: NIPS 2018

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be solved by finding the eigenvector corresponding to the smallest, or zero, eigenvalue of a matrix representing a linear system. Incorporating this in deep learning frameworks would allow us to explicitly encode known notions of geometry, instead of having the network implicitly learn them from data. However, performing eigendecomposition within a network requires the ability to differentiate this operation. Unfortunately, while theoretically doable, this introduces numerical instability in the optimization process in practice. In this paper, we introduce an eigendecomposition-free approach to training a deep network whose loss depends on the eigenvector corresponding to a zero eigenvalue of a matrix predicted by the network. We demonstrate on several tasks, including keypoint matching and 3D pose estimation, that our approach is much more robust than explicit differentiation of the eigendecomposition, It has better convergence properties and yields state-of-the-art results on both tasks., Comment: 25 pages

We develop a deep architecture to learn to find good correspondences for wide-baseline stereo. Given a set of putative sparse matches and the camera intrinsics, we train our network in an end-to-end fashion to label the correspondences as inliers or outliers, while simultaneously using them to recover the relative pose, as encoded by the essential matrix. Our architecture is based on a multi-layer perceptron operating on pixel coordinates rather than directly on the image, and is thus simple and small. We introduce a novel normalization technique, called Context Normalization, which allows us to process each data point separately while imbuing it with global information, and also makes the network invariant to the order of the correspondences. Our experiments on multiple challenging datasets demonstrate that our method is able to drastically improve the state of the art with little training data., Comment: CVPR 2018 (Oral)

We propose an automatic method for generating high-quality annotations for depth-based hand segmentation, and introduce a large-scale hand segmentation dataset. Existing datasets are typically limited to a single hand. By exploiting the visual cues given by an RGBD sensor and a pair of colored gloves, we automatically generate dense annotations for two hand segmentation. This lowers the cost/complexity of creating high quality datasets, and makes it easy to expand the dataset in the future. We further show that existing datasets, even with data augmentation, are not sufficient to train a hand segmentation algorithm that can distinguish two hands. Source and datasets will be made publicly available.

Authoring location-based experiences involving multiple participants, collaborating or competing in both indoor and outdoor mixed realities, is extremely complex and bound to serious technical challenges. In this work, we present the first results of the MAGELLAN European project and how these greatly simplify this creative process using novel authoring, augmented reality (AR) and indoor geolocalisation techniques.

We introduce a novel Deep Network architecture that implements the full feature point handling pipeline, that is, detection, orientation estimation, and feature description. While previous works have successfully tackled each one of these problems individually, we show how to learn to do all three in a unified manner while preserving end-to-end differentiability. We then demonstrate that our Deep pipeline outperforms state-of-the-art methods on a number of benchmark datasets, without the need of retraining., Comment: Accepted to ECCV 2016 (spotlight)

We show how to train a Convolutional Neural Network to assign a canonical orientation to feature points given an image patch centered on the feature point. Our method improves feature point matching upon the state-of-the art and can be used in conjunction with any existing rotation sensitive descriptors. To avoid the tedious and almost impossible task of finding a target orientation to learn, we propose to use Siamese networks which implicitly find the optimal orientations during training. We also propose a new type of activation function for Neural Networks that generalizes the popular ReLU, maxout, and PReLU activation functions. This novel activation performs better for our task. We validate the effectiveness of our method extensively with four existing datasets, including two non-planar datasets, as well as our own dataset. We show that we outperform the state-of-the-art without the need of retraining for each dataset., Comment: Accepted as Oral presentation in Computer Vision and Pattern Recognition, 2016

We introduce a learning-based approach to detect repeatable keypoints under drastic imaging changes of weather and lighting conditions to which state-of-the-art keypoint detectors are surprisingly sensitive. We first identify good keypoint candidates in multiple training images taken from the same viewpoint. We then train a regressor to predict a score map whose maxima are those points so that they can be found by simple non-maximum suppression. As there are no standard datasets to test the influence of these kinds of changes, we created our own, which we will make publicly available. We will show that our method significantly outperforms the state-of-the-art methods in such challenging conditions, while still achieving state-of-the-art performance on the untrained standard Oxford dataset.