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Hanno Gottschalk

Publications and source records attributed to Hanno Gottschalk.

At least 91 records · Page 5Linked to original sources
arXiv2020

YOdar: Uncertainty-based Sensor Fusion for Vehicle Detection with Camera and Radar Sensors

In this work, we present an uncertainty-based method for sensor fusion with camera and radar data. The outputs of two neural networks, one processing camera and the other one radar data, are combined in an uncertainty aware manner. To this end, we gather the outputs and corresponding meta information for both networks. For each predicted object, the gathered information is post-processed by a gradient boosting method to produce a joint prediction of both networks. In our experiments we combine the YOLOv3 object detection network with a customized $1D$ radar segmentation network and evaluate our method on the nuScenes dataset. In particular we focus on night scenes, where the capability of object detection networks based on camera data is potentially handicapped. Our experiments show, that this approach of uncertainty aware fusion, which is also of very modular nature, significantly gains performance compared to single sensor baselines and is in range of specifically tailored deep learning based fusion approaches.

cs.CV↗
arXiv2020

An analytical study in multi physics and multi criteria shape optimization

A simple multi-physical system for the potential flow of a fluid through a shroud in which a mechanical component, like a turbine vane, is placed, is modeled mathematically. We then consider a multi criteria shape optimization problem, when the shape of the component is allowed to vary under a certain set of 2nd order Hölder continuous differentiable transformations of a baseline shape with boundary of the same continuity class. As objective functions, we consider a simple loss model for the fluid dynamical efficiency and the probability of failure of the component due to repeated application of loads that stem from the fluid's static pressure. For this multi-physical system, it is shown that under certain conditions the Pareto front is maximal in the sense that the Pareto front of the feasible set coincides with Pareto front of its closure. We also show that the set of all optimal forms with respect to scalarization techniques deforms continuously (in the Hausdorff metric) with respect to preference parameters.

math.OC↗
arXiv2020

MetaBox+: A new Region Based Active Learning Method for Semantic Segmentation using Priority Maps

We present a novel region based active learning method for semantic image segmentation, called MetaBox+. For acquisition, we train a meta regression model to estimate the segment-wise Intersection over Union (IoU) of each predicted segment of unlabeled images. This can be understood as an estimation of segment-wise prediction quality. Queried regions are supposed to minimize to competing targets, i.e., low predicted IoU values / segmentation quality and low estimated annotation costs. For estimating the latter we propose a simple but practical method for annotation cost estimation. We compare our method to entropy based methods, where we consider the entropy as uncertainty of the prediction. The comparison and analysis of the results provide insights into annotation costs as well as robustness and variance of the methods. Numerical experiments conducted with two different networks on the Cityscapes dataset clearly demonstrate a reduction of annotation effort compared to random acquisition. Noteworthily, we achieve 95%of the mean Intersection over Union (mIoU), using MetaBox+ compared to when training with the full dataset, with only 10.47% / 32.01% annotation effort for the two networks, respectively.

cs.CV↗
arXiv2020

Time-Dynamic Estimates of the Reliability of Deep Semantic Segmentation Networks

In the semantic segmentation of street scenes with neural networks, the reliability of predictions is of highest interest. The assessment of neural networks by means of uncertainties is a common ansatz to prevent safety issues. As in applications like automated driving, video streams of images are available, we present a time-dynamic approach to investigating uncertainties and assessing the prediction quality of neural networks. We track segments over time and gather aggregated metrics per segment, thus obtaining time series of metrics from which we assess prediction quality. This is done by either classifying between intersection over union equal to 0 and greater than 0 or predicting the intersection over union directly. We study different models for these two tasks and analyze the influence of the time series length on the predictive power of our metrics.

cs.CV↗
arXiv2020

Coarsening in Algebraic Multigrid using Gaussian Processes

Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic multigrid approaches have shown that multigrid efficiency can be obtained without having to resort to properties of the PDE. Yet the required setup of these methods poses a not negligible overhead cost. Methods from machine learning have attracted attention to streamline processes based on statistical models being trained on the available data. Interpreting algebraically smooth error as an instance of a Gaussian process, we develop a new, data driven approach to construct adaptive algebraic multigrid methods. Based on Gaussian a priori distributions, Kriging interpolation minimizes the mean squared error of the a posteriori distribution, given the data on the coarse grid. Going one step further, we exploit the quantification of uncertainty in the Gaussian process model in order to construct efficient variable splittings. Using a semivariogram fit of a suitable covariance model we demonstrate that our approach yields efficient methods using a single algebraically smooth vector.

math.NA↗
arXiv2020

Tracing locally Pareto optimal points by numerical integration

We suggest a novel approach for the efficient and reliable approximation of the Pareto front of sufficiently smooth unconstrained bi-criteria optimization problems. Optimality conditions formulated for weighted sum scalarizations of the problem yield a description of (parts of) the Pareto front as a parametric curve, parameterized by the scalarization parameter (i.e., the weight in the weighted sum scalarization). Its sensitivity w.r.t. parameter variations can be described by an ordinary differential equation (ODE). Starting from an arbitrary initial Pareto optimal solution, the Pareto front can then be traced by numerical integration. We provide an error analysis based on Lipschitz properties and suggest an explicit Runge-Kutta method for the numerical solution of the ODE. The method is validated on bi-criteria convex quadratic programming problems for which the exact solution is explicitly known, and numerically tested on complex bi-criteria shape optimization problems involving finite element discretizations of the state equation.

math.OC↗
arXiv2020

GivEn -- Shape Optimization for Gas Turbines in Volatile Energy Networks

This paper describes the project GivEn that develops a novel multicriteria optimization process for gas turbine blades and vanes using modern "adjoint" shape optimization algorithms. Given the many start and shut-down processes of gas power plants in volatile energy grids, besides optimizing gas turbine geometries for efficiency, the durability understood as minimization of the probability of failure is a design objective of increasing importance. We also describe the underlying coupling structure of the multiphysical simulations and use modern, gradient based multicriteria optimization procedures to enhance the exploration of Pareto-optimal solutions.

math.OC↗
arXiv2019

MetaFusion: Controlled False-Negative Reduction of Minority Classes in Semantic Segmentation

In semantic segmentation datasets, classes of high importance are oftentimes underrepresented, e.g., humans in street scenes. Neural networks are usually trained to reduce the overall number of errors, attaching identical loss to errors of all kinds. However, this is not necessarily aligned with human intuition. For instance, an overlooked pedestrian seems more severe than an incorrectly detected one. One possible remedy is to deploy different decision rules by introducing class priors which assigns larger weight to underrepresented classes. While reducing the false-negatives of the underrepresented class, at the same time this leads to a considerable increase of false-positive indications. In this work, we combine decision rules with methods for false-positive detection. We therefore fuse false-negative detection with uncertainty based false-positive meta classification. We present proof-of-concept results for CIFAR-10, and prove the efficiency of our method for the semantic segmentation of street scenes on the Cityscapes dataset based on predicted instances of the 'human' class. In the latter we employ an advanced false-positive detection method using uncertainty measures aggregated over instances. We thereby achieve improved trade-offs between false-negative and false-positive samples of the underrepresented classes.

cs.CV↗
arXiv2019

Detection of False Positive and False Negative Samples in Semantic Segmentation

In recent years, deep learning methods have outperformed other methods in image recognition. This has fostered imagination of potential application of deep learning technology including safety relevant applications like the interpretation of medical images or autonomous driving. The passage from assistance of a human decision maker to ever more automated systems however increases the need to properly handle the failure modes of deep learning modules. In this contribution, we review a set of techniques for the self-monitoring of machine-learning algorithms based on uncertainty quantification. In particular, we apply this to the task of semantic segmentation, where the machine learning algorithm decomposes an image according to semantic categories. We discuss false positive and false negative error modes at instance-level and review techniques for the detection of such errors that have been recently proposed by the authors. We also give an outlook on future research directions.

cs.CV↗
arXiv2019

Prediction Error Meta Classification in Semantic Segmentation: Detection via Aggregated Dispersion Measures of Softmax Probabilities

We present a method that "meta" classifies whether seg-ments predicted by a semantic segmentation neural networkintersect with the ground truth. For this purpose, we employ measures of dispersion for predicted pixel-wise class probability distributions, like classification entropy, that yield heat maps of the input scene's size. We aggregate these dispersion measures segment-wise and derive metrics that are well-correlated with the segment-wise IoU of prediction and ground truth. This procedure yields an almost plug and play post-processing tool to rate the prediction quality of semantic segmentation networks on segment level. This is especially relevant for monitoring neural networks in online applications like automated driving or medical imaging where reliability is of utmost importance. In our tests, we use publicly available state-of-the-art networks trained on the Cityscapes dataset and the BraTS2017 dataset and analyze the predictive power of different metrics as well as different sets of metrics. To this end, we compute logistic LASSO regression fits for the task of classifying IoU=0 vs. IoU>0 per segment and obtain AUROC values of up to 91.55%. We complement these tests with linear regression fits to predict the segment-wise IoU and obtain prediction standard deviations of down to 0.130 as well as $R^2$ values of up to 84.15%. We show that these results clearly outperform standard approaches.

cs.CV↗
arXiv2019

Gradient Based Biobjective Shape Optimization to Improve Reliability and Cost of Ceramic Components

We consider the simultaneous optimization of the reliability and the cost of a ceramic component in a biobjective PDE constrained shape optimization problem. A probabilistic Weibull-type model is used to assess the probability of failure of the component under tensile load, while the cost is assumed to be proportional to the volume of the component. Two different gradient-based optimization methods are suggested and compared at 2D test cases. The numerical implementation is based on a first discretize then optimize strategy and benefits from efficient gradient computations using adjoint equations. The resulting approximations of the Pareto front nicely exhibit the trade-off between reliability and cost and give rise to innovative shapes that compromise between these conflicting objectives.

math.OC↗
arXiv2019

The Ethical Dilemma when (not) Setting up Cost-based Decision Rules in Semantic Segmentation

Neural networks for semantic segmentation can be seen as statistical models that provide for each pixel of one image a probability distribution on predefined classes. The predicted class is then usually obtained by the maximum a-posteriori probability (MAP) which is known as Bayes rule in decision theory. From decision theory we also know that the Bayes rule is optimal regarding the simple symmetric cost function. Therefore, it weights each type of confusion between two different classes equally, e.g., given images of urban street scenes there is no distinction in the cost function if the network confuses a person with a street or a building with a tree. Intuitively, there might be confusions of classes that are more important to avoid than others. In this work, we want to raise awareness of the possibility of explicitly defining confusion costs and the associated ethical difficulties if it comes down to providing numbers. We define two cost functions from different extreme perspectives, an egoistic and an altruistic one, and show how safety relevant quantities like precision / recall and (segment-wise) false positive / negative rate change when interpolating between MAP, egoistic and altruistic decision rules.

cs.CV↗
arXiv2019

Application of Decision Rules for Handling Class Imbalance in Semantic Segmentation

As part of autonomous car driving systems, semantic segmentation is an essential component to obtain a full understanding of the car's environment. One difficulty, that occurs while training neural networks for this purpose, is class imbalance of training data. Consequently, a neural network trained on unbalanced data in combination with maximum a-posteriori classification may easily ignore classes that are rare in terms of their frequency in the dataset. However, these classes are often of highest interest. We approach such potential misclassifications by weighting the posterior class probabilities with the prior class probabilities which in our case are the inverse frequencies of the corresponding classes in the training dataset. More precisely, we adopt a localized method by computing the priors pixel-wise such that the impact can be analyzed at pixel level as well. In our experiments, we train one network from scratch using a proprietary dataset containing 20,000 annotated frames of video sequences recorded from street scenes. The evaluation on our test set shows an increase of average recall with regard to instances of pedestrians and info signs by $25\%$ and $23.4\%$, respectively. In addition, we significantly reduce the non-detection rate for instances of the same classes by $61\%$ and $38\%$.

cs.CV↗
arXiv2018

Classification Uncertainty of Deep Neural Networks Based on Gradient Information

We study the quantification of uncertainty of Convolutional Neural Networks (CNNs) based on gradient metrics. Unlike the classical softmax entropy, such metrics gather information from all layers of the CNN. We show for the EMNIST digits data set that for several such metrics we achieve the same meta classification accuracy -- i.e. the task of classifying predictions as correct or incorrect without knowing the actual label -- as for entropy thresholding. We apply meta classification to unknown concepts (out-of-distribution samples) -- EMNIST/Omniglot letters, CIFAR10 and noise -- and demonstrate that meta classification rates for unknown concepts can be increased when using entropy together with several gradient based metrics as input quantities for a meta classifier. Meta classifiers only trained on the uncertainty metrics of known concepts, i.e. EMNIST digits, usually do not perform equally well for all unknown concepts. If we however allow the meta classifier to be trained on uncertainty metrics for some out-of-distribution samples, meta classification for concepts remote from EMNIST digits (then termed known unknowns) can be improved considerably.

cs.LG↗
arXiv2018

Shape gradients for the failure probability of a mechanical component under cyclical loading

This work provides a numerical calculation of shape gradients of failure probabilities for mechanical components using a first discretize, then adjoint approach. While deterministic life prediction models for failure mechanisms are not (shape) differentiable, this changes in the case of probabilistic life prediction. The probabilistic, or reliability based, approach thus opens the way for efficient adjoint methods in the design for mechanical integrity. In this work we propose, implement and validate a method for the numerical calculation of the shape gradients of failure probabilities for the failure mechanism low cycle fatigue (LCF), which applies to polycrystalline metal. Numerical examples range from a bended rod to a complex geometry from a turbo charger in 3D.

math.NA↗
arXiv2018

Effect of local anisotropy on fatigue crack initiation in a coarse grained nickel-base superalloy

In the present work, theoretical approaches, based on grain orientation dependent Young's modulus and Schmid factor are used to describe the influence of local grain orientation on crack initiation behaviour of the coarse grained nickel base superalloy René80. Especially for strongly anisotropic crystal structures with large grain size, such as the investigated material, the local elastic properties must be taken into account for assessment of fatigue crack initiation. With an extension of Schmid's law, the resulting shear stress amplitude, which triggers local cyclic plastic deformation, can be calculated depending on local Young's modulus and Schmid factor. A Monte Carlo simulation with 100,000 samples shows how random grain orientation affects these parameters. Furthermore, the product of Young's modulus and Schmid factor (called $E\cdot m$) is used as a parameter to determine how grain orientation influences resulting shear stress amplitude for given total strain amplitude. In addition to the theoretical work using that approach, this model is also validated using isothermal LCF experiments by determining local grain orientation influence on the crack initiation site using SEM-EBSD analyses.

cond-mat.mtrl-sci↗
arXiv2018

Deep Bayesian Active Semi-Supervised Learning

In many applications the process of generating label information is expensive and time consuming. We present a new method that combines active and semi-supervised deep learning to achieve high generalization performance from a deep convolutional neural network with as few known labels as possible. In a setting where a small amount of labeled data as well as a large amount of unlabeled data is available, our method first learns the labeled data set. This initialization is followed by an expectation maximization algorithm, where further training reduces classification entropy on the unlabeled data by targeting a low entropy fit which is consistent with the labeled data. In addition the algorithm asks at a specified frequency an oracle for labels of data with entropy above a certain entropy quantile. Using this active learning component we obtain an agile labeling process that achieves high accuracy, but requires only a small amount of known labels. For the MNIST dataset we report an error rate of 2.06% using only 300 labels and 1.06% for 1000 labels. These results are obtained without employing any special network architecture or data augmentation.

cs.LG↗