Superpixels group perceptually similar pixels to create visually meaningful entities while heavily reducing the number of primitives for subsequent processing steps. As of these properties, superpixel algorithms have received much attention since their naming in 2003 [1]. By today, publicly available superpixel algorithms have turned into standard tools in low-level vision. As such, and due to their quick adoption in a wide range of applications, appropriate benchmarks are crucial for algorithm selection and comparison. Until now, the rapidly growing number of algorithms as well as varying experimental setups hindered the development of a unifying benchmark. We present a comprehensive evaluation of 28 state-of-the-art superpixel algorithms utilizing a benchmark focussing on fair comparison and designed to provide new insights relevant for applications. To this end, we explicitly discuss parameter optimization and the importance of strictly enforcing connectivity. Furthermore, by extending well-known metrics, we are able to summarize algorithm performance independent of the number of generated superpixels, thereby overcoming a major limitation of available benchmarks. Furthermore, we discuss runtime, robustness against noise, blur and affine transformations, implementation details as well as aspects of visual quality. Finally, we present an overall ranking of superpixel algorithms which redefines the stateof-the-art and enables researchers to easily select appropriate algorithms and the corresponding implementations which themselves are made publicly available as part of our benchmark at davidstutz.de/projects/superpixel-benchmark/.

Obtaining deep networks that are robust against adversarial examples and generalize well is an open problem. A recent hypothesis [102,95] even states that both robust and accurate models are impossible, i.e., adversarial robustness and generalization are conflicting goals. In an effort to clarify the relationship between robustness and generalization, we assume an underlying, low-dimensional data manifold and show that: 1. regular adversarial examples leave the manifold; 2. adversarial examples constrained to the manifold, i.e., on-manifold adversarial examples, exist; 3. onmanifold adversarial examples are generalization errors, and on-manifold adversarial training boosts generalization; 4. regular robustness and generalization are not necessarily contradicting goals. These assumptions imply that both robust and accurate models are possible. However, different models (architectures, training strategies etc.) can exhibit different robustness and generalization characteristics. To confirm our claims, we present extensive experiments on synthetic data (with known manifold) as well as on EMNIST [19], Fashion-MNIST [106] and CelebA [59].

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We address the problem of 3D shape completion from sparse and noisy point clouds, a fundamental problem in computer vision and robotics. Recent approaches are either data-driven or learning-based: Datadriven approaches rely on a shape model whose parameters are optimized to fit the observations; Learningbased approaches, in contrast, avoid the expensive optimization step by learning to directly predict complete shapes from incomplete observations in a fullysupervised setting. However, full supervision is often not available in practice. In this work, we propose a weakly-supervised learning-based approach to 3D shape completion which neither requires slow optimization nor direct supervision. While we also learn a shape prior on synthetic data, we amortize, i.e., learn, maximum likelihood fitting using deep neural networks resulting in efficient shape completion without sacrificing accuracy. On synthetic benchmarks based on ShapeNet (Chang et al, 2015) and ModelNet (Wu et al, 2015) as well as on real robotics data from KITTI (Geiger et al, 2012) and Kinect (Yang et al, 2018), we demonstrate that the proposed amortized maximum likelihood approach is able to compete with the fully supervised baseline of Dai et al (2017) and outperforms the data-driven approach of Engelmann et al (2016), while requiring less supervision and being significantly faster.

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