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2017


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The Numerics of GANs

Mescheder, L., Nowozin, S., Geiger, A.

In Proceedings from the conference "Neural Information Processing Systems 2017., (Editors: Guyon I. and Luxburg U.v. and Bengio S. and Wallach H. and Fergus R. and Vishwanathan S. and Garnett R.), Curran Associates, Inc., Advances in Neural Information Processing Systems 30 (NIPS), December 2017 (inproceedings)

Abstract
In this paper, we analyze the numerics of common algorithms for training Generative Adversarial Networks (GANs). Using the formalism of smooth two-player games we analyze the associated gradient vector field of GAN training objectives. Our findings suggest that the convergence of current algorithms suffers due to two factors: i) presence of eigenvalues of the Jacobian of the gradient vector field with zero real-part, and ii) eigenvalues with big imaginary part. Using these findings, we design a new algorithm that overcomes some of these limitations and has better convergence properties. Experimentally, we demonstrate its superiority on training common GAN architectures and show convergence on GAN architectures that are known to be notoriously hard to train.

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pdf Project Page [BibTex]

2017


pdf Project Page [BibTex]


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On the Design of LQR Kernels for Efficient Controller Learning

Marco, A., Hennig, P., Schaal, S., Trimpe, S.

Proceedings of the 56th IEEE Annual Conference on Decision and Control (CDC), pages: 5193-5200, IEEE, IEEE Conference on Decision and Control, December 2017 (conference)

Abstract
Finding optimal feedback controllers for nonlinear dynamic systems from data is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful framework for direct controller tuning from experimental trials. For selecting the next query point and finding the global optimum, BO relies on a probabilistic description of the latent objective function, typically a Gaussian process (GP). As is shown herein, GPs with a common kernel choice can, however, lead to poor learning outcomes on standard quadratic control problems. For a first-order system, we construct two kernels that specifically leverage the structure of the well-known Linear Quadratic Regulator (LQR), yet retain the flexibility of Bayesian nonparametric learning. Simulations of uncertain linear and nonlinear systems demonstrate that the LQR kernels yield superior learning performance.

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arXiv PDF On the Design of LQR Kernels for Efficient Controller Learning - CDC presentation DOI Project Page [BibTex]

arXiv PDF On the Design of LQR Kernels for Efficient Controller Learning - CDC presentation DOI Project Page [BibTex]


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Probabilistic Line Searches for Stochastic Optimization

Mahsereci, M., Hennig, P.

Journal of Machine Learning Research, 18(119):1-59, November 2017 (article)

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link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Bounding Boxes, Segmentations and Object Coordinates: How Important is Recognition for 3D Scene Flow Estimation in Autonomous Driving Scenarios?

Behl, A., Jafari, O. H., Mustikovela, S. K., Alhaija, H. A., Rother, C., Geiger, A.

In Proceedings IEEE International Conference on Computer Vision (ICCV), IEEE, Piscataway, NJ, USA, IEEE International Conference on Computer Vision (ICCV), October 2017 (inproceedings)

Abstract
Existing methods for 3D scene flow estimation often fail in the presence of large displacement or local ambiguities, e.g., at texture-less or reflective surfaces. However, these challenges are omnipresent in dynamic road scenes, which is the focus of this work. Our main contribution is to overcome these 3D motion estimation problems by exploiting recognition. In particular, we investigate the importance of recognition granularity, from coarse 2D bounding box estimates over 2D instance segmentations to fine-grained 3D object part predictions. We compute these cues using CNNs trained on a newly annotated dataset of stereo images and integrate them into a CRF-based model for robust 3D scene flow estimation - an approach we term Instance Scene Flow. We analyze the importance of each recognition cue in an ablation study and observe that the instance segmentation cue is by far strongest, in our setting. We demonstrate the effectiveness of our method on the challenging KITTI 2015 scene flow benchmark where we achieve state-of-the-art performance at the time of submission.

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pdf suppmat Poster Project Page [BibTex]

pdf suppmat Poster Project Page [BibTex]


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Sparsity Invariant CNNs

Uhrig, J., Schneider, N., Schneider, L., Franke, U., Brox, T., Geiger, A.

International Conference on 3D Vision (3DV) 2017, International Conference on 3D Vision (3DV), October 2017 (conference)

Abstract
In this paper, we consider convolutional neural networks operating on sparse inputs with an application to depth upsampling from sparse laser scan data. First, we show that traditional convolutional networks perform poorly when applied to sparse data even when the location of missing data is provided to the network. To overcome this problem, we propose a simple yet effective sparse convolution layer which explicitly considers the location of missing data during the convolution operation. We demonstrate the benefits of the proposed network architecture in synthetic and real experiments \wrt various baseline approaches. Compared to dense baselines, the proposed sparse convolution network generalizes well to novel datasets and is invariant to the level of sparsity in the data. For our evaluation, we derive a novel dataset from the KITTI benchmark, comprising 93k depth annotated RGB images. Our dataset allows for training and evaluating depth upsampling and depth prediction techniques in challenging real-world settings.

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pdf suppmat Project Page Project Page [BibTex]

pdf suppmat Project Page Project Page [BibTex]


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OctNetFusion: Learning Depth Fusion from Data

Riegler, G., Ulusoy, A. O., Bischof, H., Geiger, A.

International Conference on 3D Vision (3DV) 2017, International Conference on 3D Vision (3DV), October 2017 (conference)

Abstract
In this paper, we present a learning based approach to depth fusion, i.e., dense 3D reconstruction from multiple depth images. The most common approach to depth fusion is based on averaging truncated signed distance functions, which was originally proposed by Curless and Levoy in 1996. While this method is simple and provides great results, it is not able to reconstruct (partially) occluded surfaces and requires a large number frames to filter out sensor noise and outliers. Motivated by the availability of large 3D model repositories and recent advances in deep learning, we present a novel 3D CNN architecture that learns to predict an implicit surface representation from the input depth maps. Our learning based method significantly outperforms the traditional volumetric fusion approach in terms of noise reduction and outlier suppression. By learning the structure of real world 3D objects and scenes, our approach is further able to reconstruct occluded regions and to fill in gaps in the reconstruction. We demonstrate that our learning based approach outperforms both vanilla TSDF fusion as well as TV-L1 fusion on the task of volumetric fusion. Further, we demonstrate state-of-the-art 3D shape completion results.

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pdf Video 1 Video 2 Project Page Project Page [BibTex]

pdf Video 1 Video 2 Project Page Project Page [BibTex]


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Direct Visual Odometry for a Fisheye-Stereo Camera

Liu, P., Heng, L., Sattler, T., Geiger, A., Pollefeys, M.

In Proceedings IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, Piscataway, NJ, USA, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), September 2017 (inproceedings)

Abstract
We present a direct visual odometry algorithm for a fisheye-stereo camera. Our algorithm performs simultaneous camera motion estimation and semi-dense reconstruction. The pipeline consists of two threads: a tracking thread and a mapping thread. In the tracking thread, we estimate the camera pose via semi-dense direct image alignment. To have a wider field of view (FoV) which is important for robotic perception, we use fisheye images directly without converting them to conventional pinhole images which come with a limited FoV. To address the epipolar curve problem, plane-sweeping stereo is used for stereo matching and depth initialization. Multiple depth hypotheses are tracked for selected pixels to better capture the uncertainty characteristics of stereo matching. Temporal motion stereo is then used to refine the depth and remove false positive depth hypotheses. Our implementation runs at an average of 20 Hz on a low-end PC. We run experiments in outdoor environments to validate our algorithm, and discuss the experimental results. We experimentally show that we are able to estimate 6D poses with low drift, and at the same time, do semi-dense 3D reconstruction with high accuracy.

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pdf Project Page [BibTex]

pdf Project Page [BibTex]


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Augmented Reality Meets Deep Learning for Car Instance Segmentation in Urban Scenes

Alhaija, H. A., Mustikovela, S. K., Mescheder, L., Geiger, A., Rother, C.

In Proceedings of the British Machine Vision Conference 2017, Proceedings of the British Machine Vision Conference, September 2017 (inproceedings)

Abstract
The success of deep learning in computer vision is based on the availability of large annotated datasets. To lower the need for hand labeled images, virtually rendered 3D worlds have recently gained popularity. Unfortunately, creating realistic 3D content is challenging on its own and requires significant human effort. In this work, we propose an alternative paradigm which combines real and synthetic data for learning semantic instance segmentation models. Exploiting the fact that not all aspects of the scene are equally important for this task, we propose to augment real-world imagery with virtual objects of the target category. Capturing real-world images at large scale is easy and cheap, and directly provides real background appearances without the need for creating complex 3D models of the environment. We present an efficient procedure to augment these images with virtual objects. This allows us to create realistic composite images which exhibit both realistic background appearance as well as a large number of complex object arrangements. In contrast to modeling complete 3D environments, our data augmentation approach requires only a few user interactions in combination with 3D shapes of the target object category. We demonstrate the utility of the proposed approach for training a state-of-the-art high-capacity deep model for semantic instance segmentation. In particular, we consider the task of segmenting car instances on the KITTI dataset which we have annotated with pixel-accurate ground truth. Our experiments demonstrate that models trained on augmented imagery generalize better than those trained on synthetic data or models trained on limited amounts of annotated real data.

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pdf Project Page [BibTex]

pdf Project Page [BibTex]


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Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks

Mescheder, L., Nowozin, S., Geiger, A.

In Proceedings of the 34th International Conference on Machine Learning, 70, Proceedings of Machine Learning Research, (Editors: Doina Precup, Yee Whye Teh), PMLR, International Conference on Machine Learning (ICML), August 2017 (inproceedings)

Abstract
Variational Autoencoders (VAEs) are expressive latent variable models that can be used to learn complex probability distributions from training data. However, the quality of the resulting model crucially relies on the expressiveness of the inference model. We introduce Adversarial Variational Bayes (AVB), a technique for training Variational Autoencoders with arbitrarily expressive inference models. We achieve this by introducing an auxiliary discriminative network that allows to rephrase the maximum-likelihood-problem as a two-player game, hence establishing a principled connection between VAEs and Generative Adversarial Networks (GANs). We show that in the nonparametric limit our method yields an exact maximum-likelihood assignment for the parameters of the generative model, as well as the exact posterior distribution over the latent variables given an observation. Contrary to competing approaches which combine VAEs with GANs, our approach has a clear theoretical justification, retains most advantages of standard Variational Autoencoders and is easy to implement.

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pdf suppmat Project Page arxiv-version Project Page [BibTex]

pdf suppmat Project Page arxiv-version Project Page [BibTex]


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Coupling Adaptive Batch Sizes with Learning Rates

Balles, L., Romero, J., Hennig, P.

In Proceedings Conference on Uncertainty in Artificial Intelligence (UAI) 2017, pages: 410-419, (Editors: Gal Elidan and Kristian Kersting), Association for Uncertainty in Artificial Intelligence (AUAI), Conference on Uncertainty in Artificial Intelligence (UAI), August 2017 (inproceedings)

Abstract
Mini-batch stochastic gradient descent and variants thereof have become standard for large-scale empirical risk minimization like the training of neural networks. These methods are usually used with a constant batch size chosen by simple empirical inspection. The batch size significantly influences the behavior of the stochastic optimization algorithm, though, since it determines the variance of the gradient estimates. This variance also changes over the optimization process; when using a constant batch size, stability and convergence is thus often enforced by means of a (manually tuned) decreasing learning rate schedule. We propose a practical method for dynamic batch size adaptation. It estimates the variance of the stochastic gradients and adapts the batch size to decrease the variance proportionally to the value of the objective function, removing the need for the aforementioned learning rate decrease. In contrast to recent related work, our algorithm couples the batch size to the learning rate, directly reflecting the known relationship between the two. On three image classification benchmarks, our batch size adaptation yields faster optimization convergence, while simultaneously simplifying learning rate tuning. A TensorFlow implementation is available.

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Code link (url) Project Page [BibTex]

Code link (url) Project Page [BibTex]


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Slow Flow: Exploiting High-Speed Cameras for Accurate and Diverse Optical Flow Reference Data

Janai, J., Güney, F., Wulff, J., Black, M., Geiger, A.

In Proceedings IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2017, pages: 1406-1416, IEEE, Piscataway, NJ, USA, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017 (inproceedings)

Abstract
Existing optical flow datasets are limited in size and variability due to the difficulty of capturing dense ground truth. In this paper, we tackle this problem by tracking pixels through densely sampled space-time volumes recorded with a high-speed video camera. Our model exploits the linearity of small motions and reasons about occlusions from multiple frames. Using our technique, we are able to establish accurate reference flow fields outside the laboratory in natural environments. Besides, we show how our predictions can be used to augment the input images with realistic motion blur. We demonstrate the quality of the produced flow fields on synthetic and real-world datasets. Finally, we collect a novel challenging optical flow dataset by applying our technique on data from a high-speed camera and analyze the performance of the state-of-the-art in optical flow under various levels of motion blur.

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pdf suppmat Project page Video DOI Project Page [BibTex]

pdf suppmat Project page Video DOI Project Page [BibTex]


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OctNet: Learning Deep 3D Representations at High Resolutions

Riegler, G., Ulusoy, O., Geiger, A.

In Proceedings IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2017, IEEE, Piscataway, NJ, USA, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017 (inproceedings)

Abstract
We present OctNet, a representation for deep learning with sparse 3D data. In contrast to existing models, our representation enables 3D convolutional networks which are both deep and high resolution. Towards this goal, we exploit the sparsity in the input data to hierarchically partition the space using a set of unbalanced octrees where each leaf node stores a pooled feature representation. This allows to focus memory allocation and computation to the relevant dense regions and enables deeper networks without compromising resolution. We demonstrate the utility of our OctNet representation by analyzing the impact of resolution on several 3D tasks including 3D object classification, orientation estimation and point cloud labeling.

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pdf suppmat Project Page Video Project Page [BibTex]

pdf suppmat Project Page Video Project Page [BibTex]


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A Multi-View Stereo Benchmark with High-Resolution Images and Multi-Camera Videos

Schöps, T., Schönberger, J. L., Galliani, S., Sattler, T., Schindler, K., Pollefeys, M., Geiger, A.

In Proceedings IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2017, IEEE, Piscataway, NJ, USA, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017 (inproceedings)

Abstract
Motivated by the limitations of existing multi-view stereo benchmarks, we present a novel dataset for this task. Towards this goal, we recorded a variety of indoor and outdoor scenes using a high-precision laser scanner and captured both high-resolution DSLR imagery as well as synchronized low-resolution stereo videos with varying fields-of-view. To align the images with the laser scans, we propose a robust technique which minimizes photometric errors conditioned on the geometry. In contrast to previous datasets, our benchmark provides novel challenges and covers a diverse set of viewpoints and scene types, ranging from natural scenes to man-made indoor and outdoor environments. Furthermore, we provide data at significantly higher temporal and spatial resolution. Our benchmark is the first to cover the important use case of hand-held mobile devices while also providing high-resolution DSLR camera images. We make our datasets and an online evaluation server available at http://www.eth3d.net.

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pdf suppmat Project Page Project Page [BibTex]

pdf suppmat Project Page Project Page [BibTex]


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Toroidal Constraints for Two Point Localization Under High Outlier Ratios

Camposeco, F., Sattler, T., Cohen, A., Geiger, A., Pollefeys, M.

In Proceedings IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2017, IEEE, Piscataway, NJ, USA, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017 (inproceedings)

Abstract
Localizing a query image against a 3D model at large scale is a hard problem, since 2D-3D matches become more and more ambiguous as the model size increases. This creates a need for pose estimation strategies that can handle very low inlier ratios. In this paper, we draw new insights on the geometric information available from the 2D-3D matching process. As modern descriptors are not invariant against large variations in viewpoint, we are able to find the rays in space used to triangulate a given point that are closest to a query descriptor. It is well known that two correspondences constrain the camera to lie on the surface of a torus. Adding the knowledge of direction of triangulation, we are able to approximate the position of the camera from \emphtwo matches alone. We derive a geometric solver that can compute this position in under 1 microsecond. Using this solver, we propose a simple yet powerful outlier filter which scales quadratically in the number of matches. We validate the accuracy of our solver and demonstrate the usefulness of our method in real world settings.

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pdf suppmat Project Page Project Page [BibTex]

pdf suppmat Project Page pdf Project Page [BibTex]


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Dynamic Time-of-Flight

Schober, M., Adam, A., Yair, O., Mazor, S., Nowozin, S.

Proceedings IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2017, pages: 170-179, IEEE, Piscataway, NJ, USA, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017 (conference)

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DOI [BibTex]

DOI [BibTex]


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Semantic Multi-view Stereo: Jointly Estimating Objects and Voxels

Ulusoy, A. O., Black, M. J., Geiger, A.

In Proceedings IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2017, IEEE, Piscataway, NJ, USA, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017 (inproceedings)

Abstract
Dense 3D reconstruction from RGB images is a highly ill-posed problem due to occlusions, textureless or reflective surfaces, as well as other challenges. We propose object-level shape priors to address these ambiguities. Towards this goal, we formulate a probabilistic model that integrates multi-view image evidence with 3D shape information from multiple objects. Inference in this model yields a dense 3D reconstruction of the scene as well as the existence and precise 3D pose of the objects in it. Our approach is able to recover fine details not captured in the input shapes while defaulting to the input models in occluded regions where image evidence is weak. Due to its probabilistic nature, the approach is able to cope with the approximate geometry of the 3D models as well as input shapes that are not present in the scene. We evaluate the approach quantitatively on several challenging indoor and outdoor datasets.

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YouTube pdf suppmat Project Page [BibTex]

YouTube pdf suppmat Project Page [BibTex]


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Virtual vs. Real: Trading Off Simulations and Physical Experiments in Reinforcement Learning with Bayesian Optimization

Marco, A., Berkenkamp, F., Hennig, P., Schoellig, A. P., Krause, A., Schaal, S., Trimpe, S.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 1557-1563, IEEE, Piscataway, NJ, USA, IEEE International Conference on Robotics and Automation (ICRA), May 2017 (inproceedings)

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PDF arXiv ICRA 2017 Spotlight presentation Virtual vs. Real - Video explanation DOI Project Page [BibTex]

PDF arXiv ICRA 2017 Spotlight presentation Virtual vs. Real - Video explanation DOI Project Page [BibTex]


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Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets

Klein, A., Falkner, S., Bartels, S., Hennig, P., Hutter, F.

Proceedings of the 20th International Conference on Artificial Intelligence and Statistics (AISTATS 2017), 54, pages: 528-536, Proceedings of Machine Learning Research, (Editors: Sign, Aarti and Zhu, Jerry), PMLR, April 2017 (conference)

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pdf link (url) Project Page [BibTex]

pdf link (url) Project Page [BibTex]


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Early Stopping Without a Validation Set

Mahsereci, M., Balles, L., Lassner, C., Hennig, P.

arXiv preprint arXiv:1703.09580, 2017 (article)

Abstract
Early stopping is a widely used technique to prevent poor generalization performance when training an over-expressive model by means of gradient-based optimization. To find a good point to halt the optimizer, a common practice is to split the dataset into a training and a smaller validation set to obtain an ongoing estimate of the generalization performance. In this paper we propose a novel early stopping criterion which is based on fast-to-compute, local statistics of the computed gradients and entirely removes the need for a held-out validation set. Our experiments show that this is a viable approach in the setting of least-squares and logistic regression as well as neural networks.

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link (url) Project Page Project Page [BibTex]


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Krylov Subspace Recycling for Fast Iterative Least-Squares in Machine Learning

Roos, F. D., Hennig, P.

arXiv preprint arXiv:1706.00241, 2017 (article)

Abstract
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time approximations, such as spectral and inducing-point methods, have been suggested and are now in wide use. These are low-rank approximations that choose the low-rank space a priori and do not refine it over time. While this allows linear cost in the data-set size, it also causes a finite, uncorrected approximation error. Authors from numerical linear algebra have explored ways to iteratively refine such low-rank approximations, at a cost of a small number of matrix-vector multiplications. This idea is particularly interesting in the many situations in machine learning where one has to solve a sequence of related symmetric positive definite linear problems. From the machine learning perspective, such deflation methods can be interpreted as transfer learning of a low-rank approximation across a time-series of numerical tasks. We study the use of such methods for our field. Our empirical results show that, on regression and classification problems of intermediate size, this approach can interpolate between low computational cost and numerical precision.

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link (url) Project Page [BibTex]


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Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settings

Kanagawa, M., Sriperumbudur, B. K., Fukumizu, K.

Arxiv e-prints, arXiv:1709.00147v1 [math.NA], 2017 (article)

Abstract
This paper presents convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We provide convergence guarantees based on two different assumptions on a quadrature rule: one on quadrature weights, and the other on design points. More precisely, we show that convergence rates can be derived (i) if the sum of absolute weights remains constant (or does not increase quickly), or (ii) if the minimum distance between distance design points does not decrease very quickly. As a consequence of the latter result, we derive a rate of convergence for Bayesian quadrature in misspecified settings. We reveal a condition on design points to make Bayesian quadrature robust to misspecification, and show that, under this condition, it may adaptively achieve the optimal rate of convergence in the Sobolev space of a lesser order (i.e., of the unknown smoothness of a test integrand), under a slightly stronger regularity condition on the integrand.

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arXiv [BibTex]

arXiv [BibTex]


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New Directions for Learning with Kernels and Gaussian Processes (Dagstuhl Seminar 16481)

Gretton, A., Hennig, P., Rasmussen, C., Schölkopf, B.

Dagstuhl Reports, 6(11):142-167, 2017 (book)

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DOI [BibTex]

DOI [BibTex]


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Computer Vision for Autonomous Vehicles: Problems, Datasets and State-of-the-Art

Janai, J., Güney, F., Behl, A., Geiger, A.

Arxiv, 2017 (article)

Abstract
Recent years have witnessed amazing progress in AI related fields such as computer vision, machine learning and autonomous vehicles. As with any rapidly growing field, however, it becomes increasingly difficult to stay up-to-date or enter the field as a beginner. While several topic specific survey papers have been written, to date no general survey on problems, datasets and methods in computer vision for autonomous vehicles exists. This paper attempts to narrow this gap by providing a state-of-the-art survey on this topic. Our survey includes both the historically most relevant literature as well as the current state-of-the-art on several specific topics, including recognition, reconstruction, motion estimation, tracking, scene understanding and end-to-end learning. Towards this goal, we first provide a taxonomy to classify each approach and then analyze the performance of the state-of-the-art on several challenging benchmarking datasets including KITTI, ISPRS, MOT and Cityscapes. Besides, we discuss open problems and current research challenges. To ease accessibility and accommodate missing references, we will also provide an interactive platform which allows to navigate topics and methods, and provides additional information and project links for each paper.

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pdf Project Page Project Page [BibTex]


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Efficiency of analytical and sampling-based uncertainty propagation in intensity-modulated proton therapy

Wahl, N., Hennig, P., Wieser, H. P., Bangert, M.

Physics in Medicine & Biology, 62(14):5790-5807, 2017 (article)

Abstract
The sensitivity of intensity-modulated proton therapy (IMPT) treatment plans to uncertainties can be quantified and mitigated with robust/min-max and stochastic/probabilistic treatment analysis and optimization techniques. Those methods usually rely on sparse random, importance, or worst-case sampling. Inevitably, this imposes a trade-off between computational speed and accuracy of the uncertainty propagation. Here, we investigate analytical probabilistic modeling (APM) as an alternative for uncertainty propagation and minimization in IMPT that does not rely on scenario sampling. APM propagates probability distributions over range and setup uncertainties via a Gaussian pencil-beam approximation into moments of the probability distributions over the resulting dose in closed form. It supports arbitrary correlation models and allows for efficient incorporation of fractionation effects regarding random and systematic errors. We evaluate the trade-off between run-time and accuracy of APM uncertainty computations on three patient datasets. Results are compared against reference computations facilitating importance and random sampling. Two approximation techniques to accelerate uncertainty propagation and minimization based on probabilistic treatment plan optimization are presented. Runtimes are measured on CPU and GPU platforms, dosimetric accuracy is quantified in comparison to a sampling-based benchmark (5000 random samples). APM accurately propagates range and setup uncertainties into dose uncertainties at competitive run-times (GPU ##IMG## [http://ej.iop.org/images/0031-9155/62/14/5790/pmbaa6ec5ieqn001.gif] {$\leqslant {5}$} min). The resulting standard deviation (expectation value) of dose show average global ##IMG## [http://ej.iop.org/images/0031-9155/62/14/5790/pmbaa6ec5ieqn002.gif] {$\gamma_{{3}\% / {3}~{\rm mm}}$} pass rates between 94.2% and 99.9% (98.4% and 100.0%). All investigated importance sampling strategies provided less accuracy at higher run-times considering only a single fraction. Considering fractionation, APM uncertainty propagation and treatment plan optimization was proven to be possible at constant time complexity, while run-times of sampling-based computations are linear in the number of fractions. Using sum sampling within APM, uncertainty propagation can only be accelerated at the cost of reduced accuracy in variance calculations. For probabilistic plan optimization, we were able to approximate the necessary pre-computations within seconds, yielding treatment plans of similar quality as gained from exact uncertainty propagation. APM is suited to enhance the trade-off between speed and accuracy in uncertainty propagation and probabilistic treatment plan optimization, especially in the context of fractionation. This brings fully-fledged APM computations within reach of clinical application.

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link (url) [BibTex]

link (url) [BibTex]


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Analytical probabilistic modeling of RBE-weighted dose for ion therapy

Wieser, H., Hennig, P., Wahl, N., Bangert, M.

Physics in Medicine and Biology (PMB), 62(23):8959-8982, 2017 (article)

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link (url) [BibTex]

link (url) [BibTex]

2015


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Exploiting Object Similarity in 3D Reconstruction

Zhou, C., Güney, F., Wang, Y., Geiger, A.

In International Conference on Computer Vision (ICCV), December 2015 (inproceedings)

Abstract
Despite recent progress, reconstructing outdoor scenes in 3D from movable platforms remains a highly difficult endeavor. Challenges include low frame rates, occlusions, large distortions and difficult lighting conditions. In this paper, we leverage the fact that the larger the reconstructed area, the more likely objects of similar type and shape will occur in the scene. This is particularly true for outdoor scenes where buildings and vehicles often suffer from missing texture or reflections, but share similarity in 3D shape. We take advantage of this shape similarity by locating objects using detectors and jointly reconstructing them while learning a volumetric model of their shape. This allows us to reduce noise while completing missing surfaces as objects of similar shape benefit from all observations for the respective category. We evaluate our approach with respect to LIDAR ground truth on a novel challenging suburban dataset and show its advantages over the state-of-the-art.

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pdf suppmat [BibTex]

2015


pdf suppmat [BibTex]


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FollowMe: Efficient Online Min-Cost Flow Tracking with Bounded Memory and Computation

Lenz, P., Geiger, A., Urtasun, R.

In International Conference on Computer Vision (ICCV), International Conference on Computer Vision (ICCV), December 2015 (inproceedings)

Abstract
One of the most popular approaches to multi-target tracking is tracking-by-detection. Current min-cost flow algorithms which solve the data association problem optimally have three main drawbacks: they are computationally expensive, they assume that the whole video is given as a batch, and they scale badly in memory and computation with the length of the video sequence. In this paper, we address each of these issues, resulting in a computationally and memory-bounded solution. First, we introduce a dynamic version of the successive shortest-path algorithm which solves the data association problem optimally while reusing computation, resulting in faster inference than standard solvers. Second, we address the optimal solution to the data association problem when dealing with an incoming stream of data (i.e., online setting). Finally, we present our main contribution which is an approximate online solution with bounded memory and computation which is capable of handling videos of arbitrary length while performing tracking in real time. We demonstrate the effectiveness of our algorithms on the KITTI and PETS2009 benchmarks and show state-of-the-art performance, while being significantly faster than existing solvers.

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pdf suppmat video project [BibTex]

pdf suppmat video project [BibTex]


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Automatic LQR Tuning Based on Gaussian Process Optimization: Early Experimental Results

Marco, A., Hennig, P., Bohg, J., Schaal, S., Trimpe, S.

Machine Learning in Planning and Control of Robot Motion Workshop at the IEEE/RSJ International Conference on Intelligent Robots and Systems (iROS), pages: , , Machine Learning in Planning and Control of Robot Motion Workshop, October 2015 (conference)

Abstract
This paper proposes an automatic controller tuning framework based on linear optimal control combined with Bayesian optimization. With this framework, an initial set of controller gains is automatically improved according to a pre-defined performance objective evaluated from experimental data. The underlying Bayesian optimization algorithm is Entropy Search, which represents the latent objective as a Gaussian process and constructs an explicit belief over the location of the objective minimum. This is used to maximize the information gain from each experimental evaluation. Thus, this framework shall yield improved controllers with fewer evaluations compared to alternative approaches. A seven-degree-of-freedom robot arm balancing an inverted pole is used as the experimental demonstrator. Preliminary results of a low-dimensional tuning problem highlight the method’s potential for automatic controller tuning on robotic platforms.

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PDF DOI Project Page [BibTex]

PDF DOI Project Page [BibTex]


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Towards Probabilistic Volumetric Reconstruction using Ray Potentials

(Best Paper Award)

Ulusoy, A. O., Geiger, A., Black, M. J.

In 3D Vision (3DV), 2015 3rd International Conference on, pages: 10-18, Lyon, October 2015 (inproceedings)

Abstract
This paper presents a novel probabilistic foundation for volumetric 3-d reconstruction. We formulate the problem as inference in a Markov random field, which accurately captures the dependencies between the occupancy and appearance of each voxel, given all input images. Our main contribution is an approximate highly parallelized discrete-continuous inference algorithm to compute the marginal distributions of each voxel's occupancy and appearance. In contrast to the MAP solution, marginals encode the underlying uncertainty and ambiguity in the reconstruction. Moreover, the proposed algorithm allows for a Bayes optimal prediction with respect to a natural reconstruction loss. We compare our method to two state-of-the-art volumetric reconstruction algorithms on three challenging aerial datasets with LIDAR ground truth. Our experiments demonstrate that the proposed algorithm compares favorably in terms of reconstruction accuracy and the ability to expose reconstruction uncertainty.

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code YouTube pdf suppmat DOI Project Page [BibTex]

code YouTube pdf suppmat DOI Project Page [BibTex]


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Displets: Resolving Stereo Ambiguities using Object Knowledge

Güney, F., Geiger, A.

In IEEE Conf. on Computer Vision and Pattern Recognition (CVPR) 2015, pages: 4165-4175, IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), June 2015 (inproceedings)

Abstract
Stereo techniques have witnessed tremendous progress over the last decades, yet some aspects of the problem still remain challenging today. Striking examples are reflecting and textureless surfaces which cannot easily be recovered using traditional local regularizers. In this paper, we therefore propose to regularize over larger distances using object-category specific disparity proposals (displets) which we sample using inverse graphics techniques based on a sparse disparity estimate and a semantic segmentation of the image. The proposed displets encode the fact that objects of certain categories are not arbitrarily shaped but typically exhibit regular structures. We integrate them as non-local regularizer for the challenging object class 'car' into a superpixel based CRF framework and demonstrate its benefits on the KITTI stereo evaluation.

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pdf abstract suppmat [BibTex]

pdf abstract suppmat [BibTex]


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Object Scene Flow for Autonomous Vehicles

Menze, M., Geiger, A.

In IEEE Conf. on Computer Vision and Pattern Recognition (CVPR) 2015, pages: 3061-3070, IEEE, IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), June 2015 (inproceedings)

Abstract
This paper proposes a novel model and dataset for 3D scene flow estimation with an application to autonomous driving. Taking advantage of the fact that outdoor scenes often decompose into a small number of independently moving objects, we represent each element in the scene by its rigid motion parameters and each superpixel by a 3D plane as well as an index to the corresponding object. This minimal representation increases robustness and leads to a discrete-continuous CRF where the data term decomposes into pairwise potentials between superpixels and objects. Moreover, our model intrinsically segments the scene into its constituting dynamic components. We demonstrate the performance of our model on existing benchmarks as well as a novel realistic dataset with scene flow ground truth. We obtain this dataset by annotating 400 dynamic scenes from the KITTI raw data collection using detailed 3D CAD models for all vehicles in motion. Our experiments also reveal novel challenges which can't be handled by existing methods.

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pdf abstract suppmat DOI [BibTex]

pdf abstract suppmat DOI [BibTex]


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Inference of Cause and Effect with Unsupervised Inverse Regression

Sgouritsa, E., Janzing, D., Hennig, P., Schölkopf, B.

In Proceedings of the 18th International Conference on Artificial Intelligence and Statistics, 38, pages: 847-855, JMLR Workshop and Conference Proceedings, (Editors: Lebanon, G. and Vishwanathan, S.V.N.), JMLR.org, AISTATS, 2015 (inproceedings)

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Web PDF [BibTex]

Web PDF [BibTex]


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Probabilistic Interpretation of Linear Solvers

Hennig, P.

SIAM Journal on Optimization, 25(1):234-260, 2015 (article)

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Web PDF link (url) DOI [BibTex]

Web PDF link (url) DOI [BibTex]


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Joint 3D Object and Layout Inference from a single RGB-D Image

(Best Paper Award)

Geiger, A., Wang, C.

In German Conference on Pattern Recognition (GCPR), 9358, pages: 183-195, Lecture Notes in Computer Science, Springer International Publishing, 2015 (inproceedings)

Abstract
Inferring 3D objects and the layout of indoor scenes from a single RGB-D image captured with a Kinect camera is a challenging task. Towards this goal, we propose a high-order graphical model and jointly reason about the layout, objects and superpixels in the image. In contrast to existing holistic approaches, our model leverages detailed 3D geometry using inverse graphics and explicitly enforces occlusion and visibility constraints for respecting scene properties and projective geometry. We cast the task as MAP inference in a factor graph and solve it efficiently using message passing. We evaluate our method with respect to several baselines on the challenging NYUv2 indoor dataset using 21 object categories. Our experiments demonstrate that the proposed method is able to infer scenes with a large degree of clutter and occlusions.

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pdf suppmat video project DOI [BibTex]

pdf suppmat video project DOI [BibTex]


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Probabilistic Line Searches for Stochastic Optimization

Mahsereci, M., Hennig, P.

In Advances in Neural Information Processing Systems 28, pages: 181-189, (Editors: C. Cortes, N.D. Lawrence, D.D. Lee, M. Sugiyama and R. Garnett), Curran Associates, Inc., 29th Annual Conference on Neural Information Processing Systems (NIPS), 2015 (inproceedings)

Abstract
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a probabilistic line search by combining the structure of existing deterministic methods with notions from Bayesian optimization. Our method retains a Gaussian process surrogate of the univariate optimization objective, and uses a probabilistic belief over the Wolfe conditions to monitor the descent. The algorithm has very low computational cost, and no user-controlled parameters. Experiments show that it effectively removes the need to define a learning rate for stochastic gradient descent. [You can find the matlab research code under `attachments' below. The zip-file contains a minimal working example. The docstring in probLineSearch.m contains additional information. A more polished implementation in C++ will be published here at a later point. For comments and questions about the code please write to mmahsereci@tue.mpg.de.]

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Matlab research code link (url) [BibTex]

Matlab research code link (url) [BibTex]


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Discrete Optimization for Optical Flow

Menze, M., Heipke, C., Geiger, A.

In German Conference on Pattern Recognition (GCPR), 9358, pages: 16-28, Springer International Publishing, 2015 (inproceedings)

Abstract
We propose to look at large-displacement optical flow from a discrete point of view. Motivated by the observation that sub-pixel accuracy is easily obtained given pixel-accurate optical flow, we conjecture that computing the integral part is the hardest piece of the problem. Consequently, we formulate optical flow estimation as a discrete inference problem in a conditional random field, followed by sub-pixel refinement. Naive discretization of the 2D flow space, however, is intractable due to the resulting size of the label set. In this paper, we therefore investigate three different strategies, each able to reduce computation and memory demands by several orders of magnitude. Their combination allows us to estimate large-displacement optical flow both accurately and efficiently and demonstrates the potential of discrete optimization for optical flow. We obtain state-of-the-art performance on MPI Sintel and KITTI.

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pdf suppmat project DOI [BibTex]

pdf suppmat project DOI [BibTex]


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A Random Riemannian Metric for Probabilistic Shortest-Path Tractography

Hauberg, S., Schober, M., Liptrot, M., Hennig, P., Feragen, A.

In 18th International Conference on Medical Image Computing and Computer Assisted Intervention, 9349, pages: 597-604, Lecture Notes in Computer Science, MICCAI, 2015 (inproceedings)

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PDF DOI [BibTex]

PDF DOI [BibTex]


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Joint 3D Estimation of Vehicles and Scene Flow

Menze, M., Heipke, C., Geiger, A.

In Proc. of the ISPRS Workshop on Image Sequence Analysis (ISA), 2015 (inproceedings)

Abstract
Three-dimensional reconstruction of dynamic scenes is an important prerequisite for applications like mobile robotics or autonomous driving. While much progress has been made in recent years, imaging conditions in natural outdoor environments are still very challenging for current reconstruction and recognition methods. In this paper, we propose a novel unified approach which reasons jointly about 3D scene flow as well as the pose, shape and motion of vehicles in the scene. Towards this goal, we incorporate a deformable CAD model into a slanted-plane conditional random field for scene flow estimation and enforce shape consistency between the rendered 3D models and the parameters of all superpixels in the image. The association of superpixels to objects is established by an index variable which implicitly enables model selection. We evaluate our approach on the challenging KITTI scene flow dataset in terms of object and scene flow estimation. Our results provide a prove of concept and demonstrate the usefulness of our method.

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PDF [BibTex]

PDF [BibTex]


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Probabilistic numerics and uncertainty in computations

Hennig, P., Osborne, M. A., Girolami, M.

Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 471(2179), 2015 (article)

Abstract
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

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PDF DOI [BibTex]

PDF DOI [BibTex]