Is Appearance Free Action Recognition Possible?

Intuition might suggest that motion and dynamic information are key to video-based action recognition. In contrast, there is evidence that state-of-the-art deep-learning video understanding architectures are biased toward static information available in single frames. Presently, a methodology and corresponding dataset to isolate the effects of dynamic information in video are missing. Their absence makes it difficult to understand how well contemporary architectures capitalize on dynamic vs. static information. We respond with a novel Appearance Free Dataset (AFD) for action recognition. AFD is devoid of static information relevant to action recognition in a single frame. Modeling of the dynamics is necessary for solving the task, as the action is only apparent through consideration of the temporal dimension. We evaluated 11 contemporary action recognition architectures on AFD as well as its related RGB video. Our results show a notable decrease in performance for all architectures on AFD compared to RGB. We also conducted a complimentary study with humans that shows their recognition accuracy on AFD and RGB is very similar and much better than the evaluated architectures on AFD. Our results motivate a novel architecture that revives explicit recovery of optical flow, within a contemporary design for best performance on AFD and RGB.

Computed Tomography Reconstruction using Generative Energy-Based Priors

In the past decades, Computed Tomography (CT) has established itself as one of the most important imaging techniques in medicine. Today, the applicability of CT is only limited by the deposited radiation dose, reduction of which manifests in noisy or incomplete measurements. Thus, the need for robust reconstruction algorithms arises. In this work, we learn a parametric regularizer with a global receptive field by maximizing it's likelihood on reference CT data. Due to this unsupervised learning strategy, our trained regularizer truly represents higher-level domain statistics, which we empirically demonstrate by synthesizing CT images. Moreover, this regularizer can easily be applied to different CT reconstruction problems by embedding it in a variational framework, which increases flexibility and interpretability compared to feed-forward learning-based approaches. In addition, the accompanying probabilistic perspective enables experts to explore the full posterior distribution and may quantify uncertainty of the reconstruction approach. We apply the regularizer to limited-angle and few-view CT reconstruction problems, where it outperforms traditional reconstruction algorithms by a large margin.

Learning atrial fiber orientations and conductivity tensors from intracardiac maps using physics-informed neural networks

Electroanatomical maps are a key tool in the diagnosis and treatment of atrial fibrillation. Current approaches focus on the activation times recorded. However, more information can be extracted from the available data. The fibers in cardiac tissue conduct the electrical wave faster, and their direction could be inferred from activation times. In this work, we employ a recently developed approach, called physics informed neural networks, to learn the fiber orientations from electroanatomical maps, taking into account the physics of the electrical wave propagation. In particular, we train the neural network to weakly satisfy the anisotropic eikonal equation and to predict the measured activation times. We use a local basis for the anisotropic conductivity tensor, which encodes the fiber orientation. The methodology is tested both in a synthetic example and for patient data. Our approach shows good agreement in both cases and it outperforms a state of the art method in the patient data. The results show a first step towards learning the fiber orientations from electroanatomical maps with physics-informed neural networks.

Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction

Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less frequently systematically analyzed. In this work, we introduce a Bayesian variational framework to quantify the epistemic uncertainty. To this end, we solve the linear inverse problem of undersampled MRI reconstruction in a variational setting. The associated energy functional is composed of a data fidelity term and the total deep variation (TDV) as a learned parametric regularizer. To estimate the epistemic uncertainty we draw the parameters of the TDV regularizer from a multivariate Gaussian distribution, whose mean and covariance matrix are learned in a stochastic optimal control problem. In several numerical experiments, we demonstrate that our approach yields competitive results for undersampled MRI reconstruction. Moreover, we can accurately quantify the pixelwise epistemic uncertainty, which can serve radiologists as an additional resource to visualize reconstruction reliability.

Shared Prior Learning of Energy-Based Models for Image Reconstruction

We propose a novel learning-based framework for image reconstruction particularly designed for training without ground truth data, which has three major building blocks: energy-based learning, a patch-based Wasserstein loss functional, and shared prior learning. In energy-based learning, the parameters of an energy functional composed of a learned data fidelity term and a data-driven regularizer are computed in a mean-field optimal control problem. In the absence of ground truth data, we change the loss functional to a patch-based Wasserstein functional, in which local statistics of the output images are compared to uncorrupted reference patches. Finally, in shared prior learning, both aforementioned optimal control problems are optimized simultaneously with shared learned parameters of the regularizer to further enhance unsupervised image reconstruction. We derive several time discretization schemes of the gradient flow and verify their consistency in terms of Mosco convergence. In numerous numerical experiments, we demonstrate that the proposed method generates state-of-the-art results for various image reconstruction applications--even if no ground truth images are available for training.

BP-MVSNet: Belief-Propagation-Layers for Multi-View-Stereo

In this work, we propose BP-MVSNet, a convolutional neural network (CNN)-based Multi-View-Stereo (MVS) method that uses a differentiable Conditional Random Field (CRF) layer for regularization. To this end, we propose to extend the BP layer and add what is necessary to successfully use it in the MVS setting. We therefore show how we can calculate a normalization based on the expected 3D error, which we can then use to normalize the label jumps in the CRF. This is required to make the BP layer invariant to different scales in the MVS setting. In order to also enable fractional label jumps, we propose a differentiable interpolation step, which we embed into the computation of the pairwise term. These extensions allow us to integrate the BP layer into a multi-scale MVS network, where we continuously improve a rough initial estimate until we get high quality depth maps as a result. We evaluate the proposed BP-MVSNet in an ablation study and conduct extensive experiments on the DTU, Tanks and Temples and ETH3D data sets. The experiments show that we can significantly outperform the baseline and achieve state-of-the-art results.

Total Deep Variation: A Stable Regularizer for Inverse Problems

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and a regularizer. Classically, handcrafted regularizers are used, which are commonly outperformed by state-of-the-art deep learning approaches. In this work, we combine the variational formulation of inverse problems with deep learning by introducing the data-driven general-purpose total deep variation regularizer. In its core, a convolutional neural network extracts local features on multiple scales and in successive blocks. This combination allows for a rigorous mathematical analysis including an optimal control formulation of the training problem in a mean-field setting and a stability analysis with respect to the initial values and the parameters of the regularizer. In addition, we experimentally verify the robustness against adversarial attacks and numerically derive upper bounds for the generalization error. Finally, we achieve state-of-the-art results for numerous imaging tasks.

Belief Propagation Reloaded: Learning BP-Layers for Labeling Problems

It has been proposed by many researchers that combining deep neural networks with graphical models can create more efficient and better regularized composite models. The main difficulties in implementing this in practice are associated with a discrepancy in suitable learning objectives as well as with the necessity of approximations for the inference. In this work we take one of the simplest inference methods, a truncated max-product Belief Propagation, and add what is necessary to make it a proper component of a deep learning model: We connect it to learning formulations with losses on marginals and compute the backprop operation. This BP-Layer can be used as the final or an intermediate block in convolutional neural networks (CNNs), allowing us to design a hierarchical model composing BP inference and CNNs at different scale levels. The model is applicable to a range of dense prediction problems, is well-trainable and provides parameter-efficient and robust solutions in stereo, optical flow and semantic segmentation.

Total Deep Variation for Linear Inverse Problems

Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent architectural design patterns from deep learning. We cast the learning problem as a discrete sampled optimal control problem, for which we derive the adjoint state equations and an optimality condition. By exploiting the variational structure of our approach, we perform a sensitivity analysis with respect to the learned parameters obtained from different training datasets. Moreover, we carry out a nonlinear eigenfunction analysis, which reveals interesting properties of the learned regularizer. We show state-of-the-art performance for classical image restoration and medical image reconstruction problems.