Connecting mathematical models for image processing and neural networks

This thesis deals with the connections between mathematical models for image processing and deep learning. While data-driven deep learning models such as neural networks are flexible and well performing, they are often used as a black box. This makes it hard to provide theoretical model guarantees and scientific insights. On the other hand, more traditional, model-driven approaches such as diffusion, wavelet shrinkage, and variational models offer a rich set of mathematical foundations. Our goal is to transfer these foundations to neural networks. To this end, we pursue three strategies. First, we design trainable variants of traditional models and reduce their parameter set after training to obtain transparent and adaptive models. Moreover, we investigate the architectural design of numerical solvers for partial differential equations and translate them into building blocks of popular neural network architectures. This yields criteria for stable networks and inspires novel design concepts. Lastly, we present novel hybrid models for inpainting that rely on our theoretical findings. These strategies provide three ways for combining the best of the two worlds of model- and data-driven approaches. Our work contributes to the overarching goal of closing the gap between these worlds that still exists in performance and understanding.Gegenstand dieser Arbeit sind die Zusammenhänge zwischen mathematischen Modellen zur Bildverarbeitung und Deep Learning. Während datengetriebene Modelle des Deep Learning wie z.B. neuronale Netze flexibel sind und gute Ergebnisse liefern, werden sie oft als Black Box eingesetzt. Das macht es schwierig, theoretische Modellgarantien zu liefern und wissenschaftliche Erkenntnisse zu gewinnen. Im Gegensatz dazu bieten traditionellere, modellgetriebene Ansätze wie Diffusion, Wavelet Shrinkage und Variationsansätze eine Fülle von mathematischen Grundlagen. Unser Ziel ist es, diese auf neuronale Netze zu übertragen. Zu diesem Zweck verfolgen wir drei Strategien. Zunächst entwerfen wir trainierbare Varianten von traditionellen Modellen und reduzieren ihren Parametersatz, um transparente und adaptive Modelle zu erhalten. Außerdem untersuchen wir die Architekturen von numerischen Lösern für partielle Differentialgleichungen und übersetzen sie in Bausteine von populären neuronalen Netzwerken. Daraus ergeben sich Kriterien für stabile Netzwerke und neue Designkonzepte. Schließlich präsentieren wir neuartige hybride Modelle für Inpainting, die auf unseren theoretischen Erkenntnissen beruhen. Diese Strategien bieten drei Möglichkeiten, das Beste aus den beiden Welten der modell- und datengetriebenen Ansätzen zu vereinen. Diese Arbeit liefert einen Beitrag zum übergeordneten Ziel, die Lücke zwischen den zwei Welten zu schließen, die noch in Bezug auf Leistung und Modellverständnis besteht.ERC Advanced Grant INCOVI

EyePACT: eye-based parallax correction on touch-enabled interactive displays

The parallax effect describes the displacement between the perceived and detected touch locations on a touch-enabled surface. Parallax is a key usability challenge for interactive displays, particularly for those that require thick layers of glass between the screen and the touch surface to protect them from vandalism. To address this challenge, we present EyePACT, a method that compensates for input error caused by parallax on public displays. Our method uses a display-mounted depth camera to detect the user's 3D eye position in front of the display and the detected touch location to predict the perceived touch location on the surface. We evaluate our method in two user studies in terms of parallax correction performance as well as multi-user support. Our evaluations demonstrate that EyePACT (1) significantly improves accuracy even with varying gap distances between the touch surface and the display, (2) adapts to different levels of parallax by resulting in significantly larger corrections with larger gap distances, and (3) maintains a significantly large distance between two users' fingers when interacting with the same object. These findings are promising for the development of future parallax-free interactive displays

The ANHEQ evaluation criteria: introducing reliable rating scales for assessing Nordic Hamstring Exercise quality

Background: The Nordic Hamstring Exercise (NHE) is very popular for selective eccentric hamstring strengthening. However, NHE-related research is hindered by insufficient details about implementation and reporting. Available tools to assess study quality (e.g., PEDro or TESTEX scale) are too unspecific to account for the specific demands of NHE. Therefore, this study aimed to introduce two rating scales for Assessing Nordic Hamstring Exercise Quality (ANHEQ) of assessment and intervention studies. Methods: Eighteen graduated sports scientists, sports physiotherapists and elite coaches with scientific experience independently evaluated the quality of published NHE studies via ANHEQ scales, each comprising eight items and a maximal 13-point score. Inter-rater agreement was analyzed by using criterion-based reference values, while Krippendorff´s alpha determined inter-rater reliability. Systematic differences of the summated ANHEQ scores were determined using Friedman tests. Results: Inter-rater agreement was 87 ± 5% for NHE assessments and 88 ± 6% for interventions with single items ranging from 71 to 100%. Alpha values for inter-rater reliability ranged from fair (.250) to perfect (1.00) depending on the item. Total ANHEQ scores revealed coefficients of .829 (almost perfect) and .772 (substantial) without significant inter-rater differences (p = .292). Conclusions: The ANHEQ scales are suitable tools to rate NHE execution quality and data presentation. They facilitate a comprehensive review of NHE-related evidence and potentially improve the design and reporting of future NHE studies

Optical control of the refractive index of a single atom

We experimentally demonstrate the elementary case of electromagnetically induced transparency (EIT) with a single atom inside an optical cavity probed by a weak field. We observe the modification of the dispersive and absorptive properties of the atom by changing the frequency of a control light field. Moreover, a strong cooling effect has been observed at two-photon resonance, increasing the storage time of our atoms twenty-fold to about 16 seconds. Our result points towards all-optical switching with single photons