Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview

This paper attempts to provide an overview of current approaches for solving inverse problems in imaging using variational methods and machine learning. A special focus lies on point estimators and their robustness against adversarial perturbations. In this context results of numerical experiments for a one-dimensional toy problem are provided, showing the robustness of different approaches and empirically verifying theoretical guarantees. Another focus of this review is the exploration of the subspace of data consistent solutions through explicit guidance to satisfy specific semantic or textural properties.

Evaluating Adversarial Robustness of Low dose CT Recovery

Low dose computed tomography (CT) acquisition using reduced radiation or sparse angle measurements is recommended to decrease the harmful effects of X-ray radiation. Recent works successfully apply deep networks to the problem of low dose CT recovery on bench-mark datasets. However, their robustness needs a thorough evaluation before use in clinical settings. In this work, we evaluate the robustness of different deep learning approaches and classical methods for CT recovery. We show that deep networks, including model-based networks encouraging data consistency, are more susceptible to untargeted attacks. Surprisingly, we observe that data consistency is not heavily affected even for these poor quality reconstructions, motivating the need for better regularization for the networks. We demonstrate the feasibility of universal attacks and study attack transferability across different methods. We analyze robustness to attacks causing localized changes in clinically relevant regions. Both classical approaches and deep networks are affected by such attacks leading to changes in the visual appearance of localized lesions, for extremely small perturbations. As the resulting reconstructions have high data consistency with the original measurements, these localized attacks can be used to explore the solution space of the CT recovery problem.

Temporal Action Localization for Inertial-based Human Activity Recognition

A persistent trend in Deep Learning has been the applicability of machine learning concepts to other areas than originally introduced for. As of today, state-of-the-art activity recognition from wearable sensors relies on classifiers being trained on fixed windows of data. Contrarily, video-based Human Activity Recognition has followed a segment-based prediction approach, localizing activity occurrences from start to end. This paper is the first to systematically demonstrate the applicability of state-of-the-art TAL models for wearable Human Activity Recongition (HAR) using raw inertial data as input. Our results show that state-of-the-art TAL models are able to outperform popular inertial models on 4 out of 6 wearable activity recognition benchmark datasets, with improvements ranging as much as 25% in F1-score. Introducing the TAL community's most popular metric to inertial-based HAR, namely mean Average Precision, our analysis shows that TAL models are able to produce more coherent segments along with an overall higher NULL-class accuracy across all datasets. Being the first to provide such an analysis, the TAL community offers an interesting new perspective to inertial-based HAR with yet to be explored design choices and training concepts, which could be of significant value for the inertial-based HAR community.

SIGMA: Scale-Invariant Global Sparse Shape Matching

We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for highly non-rigid shapes. To this end, we introduce a projected Laplace-Beltrami operator (PLBO) which combines intrinsic and extrinsic geometric information to measure the deformation quality induced by predicted correspondences. We integrate the PLBO, together with an orientation-aware regulariser, into a novel MIP formulation that can be solved to global optimality for many practical problems. In contrast to previous methods, our approach is provably invariant to rigid transformations and global scaling, initialisation-free, has optimality guarantees, and scales to high resolution meshes with (empirically observed) linear time. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets, including data with inconsistent meshing, as well as applications in mesh-to-point-cloud matching.

An Evaluation of Zero-Cost Proxies -- from Neural Architecture Performance to Model Robustness

Zero-cost proxies are nowadays frequently studied and used to search for neural architectures. They show an impressive ability to predict the performance of architectures by making use of their untrained weights. These techniques allow for immense search speed-ups. So far the joint search for well-performing and robust architectures has received much less attention in the field of NAS. Therefore, the main focus of zero-cost proxies is the clean accuracy of architectures, whereas the model robustness should play an evenly important part. In this paper, we analyze the ability of common zero-cost proxies to serve as performance predictors for robustness in the popular NAS-Bench-201 search space. We are interested in the single prediction task for robustness and the joint multi-objective of clean and robust accuracy. We further analyze the feature importance of the proxies and show that predicting the robustness makes the prediction task from existing zero-cost proxies more challenging. As a result, the joint consideration of several proxies becomes necessary to predict a model's robustness while the clean accuracy can be regressed from a single such feature.

Differentiable Sensor Layouts for End-to-End Learning of Task-Specific Camera Parameters

The success of deep learning is frequently described as the ability to train all parameters of a network on a specific application in an end-to-end fashion. Yet, several design choices on the camera level, including the pixel layout of the sensor, are considered as pre-defined and fixed, and high resolution, regular pixel layouts are considered to be the most generic ones in computer vision and graphics, treating all regions of an image as equally important. While several works have considered non-uniform, \eg, hexagonal or foveated, pixel layouts in hardware and image processing, the layout has not been integrated into the end-to-end learning paradigm so far. In this work, we present the first truly end-to-end trained imaging pipeline that optimizes the size and distribution of pixels on the imaging sensor jointly with the parameters of a given neural network on a specific task. We derive an analytic, differentiable approach for the sensor layout parameterization that allows for task-specific, local varying pixel resolutions. We present two pixel layout parameterization functions: rectangular and curvilinear grid shapes that retain a regular topology. We provide a drop-in module that approximates sensor simulation given existing high-resolution images to directly connect our method with existing deep learning models. We show that network predictions benefit from learnable pixel layouts for two different downstream tasks, classification and semantic segmentation.

WEAR: A Multimodal Dataset for Wearable and Egocentric Video Activity Recognition

Though research has shown the complementarity of camera- and inertial-based data, datasets which offer both modalities remain scarce. In this paper we introduce WEAR, a multimodal benchmark dataset for both vision- and wearable-based Human Activity Recognition (HAR). The dataset comprises data from 18 participants performing a total of 18 different workout activities with untrimmed inertial (acceleration) and camera (egocentric video) data recorded at 10 different outside locations. WEAR features a diverse set of activities which are low in inter-class similarity and, unlike previous egocentric datasets, not defined by human-object-interactions nor originate from inherently distinct activity categories. Provided benchmark results reveal that single-modality architectures have different strengths and weaknesses in their prediction performance. Further, in light of the recent success of transformer-based video action detection models, we demonstrate their versatility by applying them in a plain fashion using vision, inertial and combined (vision + inertial) features as input. Results show that vision transformers are not only able to produce competitive results using only inertial data, but also can function as an architecture to fuse both modalities by means of simple concatenation, with the multimodal approach being able to produce the highest average mAP, precision and close-to-best F1-scores. Up until now, vision-based transformers have neither been explored in inertial nor in multimodal human activity recognition, making our approach the first to do so. The dataset and code to reproduce experiments is publicly available via: mariusbock.github.io/wear

CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes

Jointly matching multiple, non-rigidly deformed 3D shapes is a challenging, $\mathcal{NP}$-hard problem. A perfect matching is necessarily cycle-consistent: Following the pairwise point correspondences along several shapes must end up at the starting vertex of the original shape. Unfortunately, existing quantum shape-matching methods do not support multiple shapes and even less cycle consistency. This paper addresses the open challenges and introduces the first quantum-hybrid approach for 3D shape multi-matching; in addition, it is also cycle-consistent. Its iterative formulation is admissible to modern adiabatic quantum hardware and scales linearly with the total number of input shapes. Both these characteristics are achieved by reducing the $N$-shape case to a sequence of three-shape matchings, the derivation of which is our main technical contribution. Thanks to quantum annealing, high-quality solutions with low energy are retrieved for the intermediate $\mathcal{NP}$-hard objectives. On benchmark datasets, the proposed approach significantly outperforms extensions to multi-shape matching of a previous quantum-hybrid two-shape matching method and is on-par with classical multi-matching methods.

Convergent Data-driven Regularizations for CT Reconstruction

The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (na\"{\i}ve) solution does not depend on the measured data continuously, regularization is needed to re-establish a continuous dependence. In this work, we investigate simple, but yet still provably convergent approaches to learning linear regularization methods from data. More specifically, we analyze two approaches: One generic linear regularization that learns how to manipulate the singular values of the linear operator in an extension of [1], and one tailored approach in the Fourier domain that is specific to CT-reconstruction. We prove that such approaches become convergent regularization methods as well as the fact that the reconstructions they provide are typically much smoother than the training data they were trained on. Finally, we compare the spectral as well as the Fourier-based approaches for CT-reconstruction numerically, discuss their advantages and disadvantages and investigate the effect of discretization errors at different resolutions.

QuAnt: Quantum Annealing with Learnt Couplings

Modern quantum annealers can find high-quality solutions to combinatorial optimisation objectives given as quadratic unconstrained binary optimisation (QUBO) problems. Unfortunately, obtaining suitable QUBO forms in computer vision remains challenging and currently requires problem-specific analytical derivations. Moreover, such explicit formulations impose tangible constraints on solution encodings. In stark contrast to prior work, this paper proposes to learn QUBO forms from data through gradient backpropagation instead of deriving them. As a result, the solution encodings can be chosen flexibly and compactly. Furthermore, our methodology is general and virtually independent of the specifics of the target problem type. We demonstrate the advantages of learnt QUBOs on the diverse problem types of graph matching, 2D point cloud alignment and 3D rotation estimation. Our results are competitive with the previous quantum state of the art while requiring much fewer logical and physical qubits, enabling our method to scale to larger problems. The code and the new dataset will be open-sourced.