Linear Inequality Constraints for Neural Network Activations

We propose a method to impose linear inequality constraints on neural network activations. The proposed method allows a data-driven training approach to be combined with modeling prior knowledge about the task. Our algorithm computes a suitable parameterization of the feasible set at initialization and uses standard variants of stochastic gradient descent to find solutions to the constrained network. Thus, the modeling constraints are always satisfied during training. Crucially, our approach avoids to solve a sub-optimization problem at each training step or to manually trade-off data and constraint fidelity with additional hyperparameters. We consider constrained generative modeling as an important application domain and experimentally demonstrate the proposed method by constraining a variational autoencoder.

Probabilistic Discriminative Learning with Layered Graphical Models

Probabilistic graphical models are traditionally known for their successes in generative modeling. In this work, we advocate layered graphical models (LGMs) for probabilistic discriminative learning. To this end, we design LGMs in close analogy to neural networks (NNs), that is, they have deep hierarchical structures and convolutional or local connections between layers. Equipped with tensorized truncated variational inference, our LGMs can be efficiently trained via backpropagation on mainstream deep learning frameworks such as PyTorch. To deal with continuous valued inputs, we use a simple yet effective soft-clamping strategy for efficient inference. Through extensive experiments on image classification over MNIST and FashionMNIST datasets, we demonstrate that LGMs are capable of achieving competitive results comparable to NNs of similar architectures, while preserving transparent probabilistic modeling.

The Double Sphere Camera Model

Vision-based motion estimation and 3D reconstruction, which have numerous applications (e.g., autonomous driving, navigation systems for airborne devices and augmented reality) are receiving significant research attention. To increase the accuracy and robustness, several researchers have recently demonstrated the benefit of using large field-of-view cameras for such applications. In this paper, we provide an extensive review of existing models for large field-of-view cameras. For each model we provide projection and unprojection functions and the subspace of points that result in valid projection. Then, we propose the Double Sphere camera model that well fits with large field-of-view lenses, is computationally inexpensive and has a closed-form inverse. We evaluate the model using a calibration dataset with several different lenses and compare the models using the metrics that are relevant for Visual Odometry, i.e., reprojection error, as well as computation time for projection and unprojection functions and their Jacobians. We also provide qualitative results and discuss the performance of all models.

Deep Depth From Focus

Depth from focus (DFF) is one of the classical ill-posed inverse problems in computer vision. Most approaches recover the depth at each pixel based on the focal setting which exhibits maximal sharpness. Yet, it is not obvious how to reliably estimate the sharpness level, particularly in low-textured areas. In this paper, we propose `Deep Depth From Focus (DDFF)' as the first end-to-end learning approach to this problem. One of the main challenges we face is the hunger for data of deep neural networks. In order to obtain a significant amount of focal stacks with corresponding groundtruth depth, we propose to leverage a light-field camera with a co-calibrated RGB-D sensor. This allows us to digitally create focal stacks of varying sizes. Compared to existing benchmarks our dataset is 25 times larger, enabling the use of machine learning for this inverse problem. We compare our results with state-of-the-art DFF methods and we also analyze the effect of several key deep architectural components. These experiments show that our proposed method `DDFFNet' achieves state-of-the-art performance in all scenes, reducing depth error by more than 75% compared to the classical DFF methods.

q-Space Novelty Detection with Variational Autoencoders

In machine learning, novelty detection is the task of identifying novel unseen data. During training, only samples from the normal class are available. Test samples are classified as normal or abnormal by assignment of a novelty score. Here we propose novelty detection methods based on training variational autoencoders (VAEs) on normal data. Since abnormal samples are not used during training, we define novelty metrics based on the (partially complementary) assumptions that the VAE is less capable of reconstructing abnormal samples well; that abnormal samples more strongly violate the VAE regularizer; and that abnormal samples differ from normal samples not only in input-feature space, but also in the VAE latent space and VAE output. These approaches, combined with various possibilities of using (e.g. sampling) the probabilistic VAE to obtain scalar novelty scores, yield a large family of methods. We apply these methods to magnetic resonance imaging, namely to the detection of diffusion-space (q-space) abnormalities in diffusion MRI scans of multiple sclerosis patients, i.e. to detect multiple sclerosis lesions without using any lesion labels for training. Many of our methods outperform previously proposed q-space novelty detection methods. We also evaluate the proposed methods on the MNIST handwritten digits dataset and show that many of them are able to outperform the state of the art.

Divergence-Free Shape Interpolation and Correspondence

We present a novel method to model and calculate deformation fields between shapes embedded in $\mathbb{R}^D$. Our framework combines naturally interpolating the two input shapes and calculating correspondences at the same time. The key idea is to compute a divergence-free deformation field represented in a coarse-to-fine basis using the Karhunen-Lo\`eve expansion. The advantages are that there is no need to discretize the embedding space and the deformation is volume-preserving. Furthermore, the optimization is done on downsampled versions of the shapes but the morphing can be applied to any resolution without a heavy increase in complexity. We show results for shape correspondence, registration, inter- and extrapolation on the TOSCA and FAUST data sets.

Deep Perm-Set Net: Learn to predict sets with unknown permutation and cardinality using deep neural networks

Many real-world problems, e.g. object detection, have outputs that are naturally expressed as sets of entities. This creates a challenge for traditional deep neural networks which naturally deal with structured outputs such as vectors, matrices or tensors. We present a novel approach for learning to predict sets with unknown permutation and cardinality using deep neural networks. Specifically, in our formulation we incorporate the permutation as unobservable variable and estimate its distribution during the learning process using alternating optimization. We demonstrate the validity of this new formulation on two relevant vision problems: object detection, for which our formulation outperforms state-of-the-art detectors such as Faster R-CNN and YOLO, and a complex CAPTCHA test, where we observe that, surprisingly, our set based network acquired the ability of mimicking arithmetics without any rules being coded.

Modular Vehicle Control for Transferring Semantic Information Between Weather Conditions Using GANs

Even though end-to-end supervised learning has shown promising results for sensorimotor control of self-driving cars, its performance is greatly affected by the weather conditions under which it was trained, showing poor generalization to unseen conditions. In this paper, we show how knowledge can be transferred using semantic maps to new weather conditions without the need to obtain new ground truth data. To this end, we propose to divide the task of vehicle control into two independent modules: a control module which is only trained on one weather condition for which labeled steering data is available, and a perception module which is used as an interface between new weather conditions and the fixed control module. To generate the semantic data needed to train the perception module, we propose to use a generative adversarial network (GAN)-based model to retrieve the semantic information for the new conditions in an unsupervised manner. We introduce a master-servant architecture, where the master model (semantic labels available) trains the servant model (semantic labels not available). We show that our proposed method trained with ground truth data for a single weather condition is capable of achieving similar results on the task of steering angle prediction as an end-to-end model trained with ground truth data of 15 different weather conditions.

Photometric Depth Super-Resolution

This study explores the use of photometric techniques (shape-from-shading and uncalibrated photometric stereo) for upsampling the low-resolution depth map from an RGB-D sensor to the higher resolution of the companion RGB image. A single-shot variational approach is first put forward, which is effective as long as the target's reflectance is piecewise-constant. It is then shown that this dependency upon a specific reflectance model can be relaxed by focusing on a specific class of objects (e.g., faces), and delegate reflectance estimation to a deep neural network. A multi-shots strategy based on randomly varying lighting conditions is eventually discussed. It requires no training or prior on the reflectance, yet this comes at the price of a dedicated acquisition setup. Both quantitative and qualitative evaluations illustrate the effectiveness of the proposed methods on synthetic and real-world scenarios.

The TUM VI Benchmark for Evaluating Visual-Inertial Odometry

Visual odometry and SLAM methods have a large variety of applications in domains such as augmented reality or robotics. Complementing vision sensors with inertial measurements tremendously improves tracking accuracy and robustness, and thus has spawned large interest in the development of visual-inertial (VI) odometry approaches. In this paper, we propose the TUM VI benchmark, a novel dataset with a diverse set of sequences in different scenes for evaluating VI odometry. It provides camera images with 1024x1024 resolution at 20 Hz, high dynamic range and photometric calibration. An IMU measures accelerations and angular velocities on 3 axes at 200 Hz, while the cameras and IMU sensors are time-synchronized in hardware. For trajectory evaluation, we also provide accurate pose ground truth from a motion capture system at high frequency (120 Hz) at the start and end of the sequences which we accurately aligned with the camera and IMU measurements. The full dataset with raw and calibrated data is publicly available. We also evaluate state-of-the-art VI odometry approaches on our dataset.