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Volterra and Wiener series
(2011)

Volterra and Wiener series are two classes of polynomial representations of nonlinear systems. They are perhaps the best understood and most widely used nonlinear system representations in signal processing and system identification. A Volterra or Wiener representation can be thought of as a natural extension of the classical linear system representation. In addition to the convolution of the input signal with the system's impulse response, the system representation includes a series of nonlinear terms that contain products of increasing order of the input signal with itself. It can be shown that these polynomial extension terms allow for representing a large class of nonlinear systems which basically encompasses all systems with scalar outputs that are time-invariant and have noninfinite memory.

Visualization-Assisted Development of Deep Learning Models in Offline Handwriting Recognition
(2018)

Deep learning is a field of machine learning that has been the focus of active research and successful applications in recent years. Offline handwriting recognition is one of the research fields and applications were deep neural networks have shown high accuracy. Deep learning models and their training pipeline show a large amount of hyper-parameters in their data selection, transformation, network topology and training process that are sometimes interdependent. This increases the overall difficulty and time necessary for building and training a model for a specific data set and task at hand. This work proposes a novel visualization-assisted workflow that guides the model developer through the hyper-parameter search in order to identify relevant parameters and modify them in a meaningful way. This decreases the overall time necessary for building and training a model. The contributions of this work are a workflow for hyper-parameter search in offline handwriting recognition and a heat map based visualization technique for deep neural networks in multi-line offline handwriting recognition. This work applies to offline handwriting recognition, but the general workflow can possibly be adapted to other tasks as well.

Vortrag

Classification of point clouds by different types of geometric primitives is an essential part in the reconstruction process of CAD geometry. We use support vector machines (SVM) to label patches in point clouds with the class labels tori, ellipsoids, spheres, cones, cylinders or planes. For the classification features based on different geometric properties like point normals, angles, and principal curvatures are used. These geometric features are estimated in the local neighborhood of a point of the point cloud. Computing these geometric features for a random subset of the point cloud yields a feature distribution. Different features are combined for achieving best classification results. To minimize the time consuming training phase of SVMs, the geometric features are first evaluated using linear discriminant analysis (LDA).
LDA and SVM are machine learning approaches that require an initial training phase to allow for a subsequent automatic classification of a new data set. For the training phase point clouds are generated using a simulation of a laser scanning device. Additional noise based on an laser scanner error model is added to the point clouds. The resulting LDA and SVM classifiers are then used to classify geometric primitives in simulated and real laser scanned point clouds.
Compared to other approaches, where all known features are used for classification, we explicitly compare novel against known geometric features to prove their effectiveness.

Digital cameras are used in a large variety of scientific and industrial applications. For most applications the acquired data should represent the real light intensity per pixel as accurately as possible. However, digital cameras are subject to different sources of noise which distort the resulting image. Noise includes photon noise, fixed pattern noise and read noise. The aim of the radiometric calibration is to improve the quality of the resulting images by reducing the influence of the different types of noise on the measured data. In this paper, a new approach for the radiometric calibration of digital cameras using sparse Gaussian process regression is presented. Gaussian process regression is a kernel based supervised machine learning technique. It is used to learn the response of a camera system from a set of training images to allow for the calibration of new images. Compared to the standard Gaussian process method or flat field correction our sparse approach allows for faster calibration and higher reconstruction quality.

Digital cameras are subject to physical, electronic and optic effects that result in errors and noise in the image. These effects include for example a temperature dependent dark current, read noise, optical vignetting or different sensitivities of individual pixels. The task of a radiometric calibration is to reduce these errors in the image and thus improve the quality of the overall application. In this work we present an algorithm for radiometric calibration based on Gaussian processes. Gaussian processes are a regression method widely used in machine learning that is particularly useful in our context. Then Gaussian process regression is used to learn a temperature and exposure time dependent mapping from observed gray-scale values to true light intensities for each pixel. Regression models based on the characteristics of single pixels suffer from excessively high runtime and thus are unsuitable for many practical applications. In contrast, a single regression model for an entire image with high spatial resolution leads to a low quality radiometric calibration, which also limits its practical use. The proposed algorithm is predicated on a partitioning of the pixels such that each pixel partition can be represented by one single regression model without quality loss. Partitioning is done by extracting features from the characteristic of each pixel and using them for lexicographic sorting. Splitting the sorted data into partitions with equal size yields the final partitions, each of which is represented by the partition centers. An individual Gaussian process regression and model selection is done for each partition. Calibration is performed by interpolating the gray-scale value of each pixel with the regression model of the respective partition. The experimental comparison of the proposed approach to classical flat field calibration shows a consistently higher reconstruction quality for the same overall number of calibration frames.