Applications of nonlinear diffusion in image processing and computer vision

Nonlinear diffusion processes can be found in many recent methods for image processing and computer vision. In this article, four applications are surveyed: nonlinear diffusion filtering, variational image regularization, optic flow estimation, and geodesic active contours. For each of these techniques we explain the main ideas, discuss theoretical properties and present an appropriate numerical scheme. The numerical schemes are based on additive operator splittings (AOS). In contrast to traditional multiplicative splittings such as ADI, LOD or D'yakonov splittings, all axes are treated in the same manner, and additional possibilities for efficient realizations on parallel and distributed architectures appear. Geodesic active contours lead to equations that resemble mean curvature motion. For this application, a novel AOS scheme is presented that uses harmonie averaging and does not require reinitializations of the distance function in each iteration step

Quantum back-action evasion and filtering in optomechanical systems

The measurement precision of optomechanical sensors reached sensitivity levels such that they have to be described by quantum theory. In quantum mechanics, every measurement will introduce a back-action on the measured system itself. For optomechanical force sensors, a trade-off between back-action and measurement precision exists through the interplay of quantum shot noise and quantum radiation pressure noise. Finding the optimal power to balance these effects leads to the standard quantum limit (SQL), which bounds the sensitivity of force sensing. To overcome the SQL and reach the fundamental bound of parameter estimation, the quantum Cramér-Rao bound, techniques called quantum smoothing and quantum back-action evasion are required. The first part of this thesis explores quantum smoothing in the context of optomechanical force sensing. Quantum smoothing combines the concepts of prediction and retrodiction to estimate the parameters of a system in the past. To illustrate the intricacies of these estimations in the quantum setting, two filters, the Kalman and Wiener filters, are introduced. Their prediction and retrodiction estimates are given for a simple optomechanical setup, and resulting differences are analyzed concerning the available quantum smoothing theories in the literature. In the second part of this thesis, a back-action evasion technique called coherent quantum-noise cancellation (CQNC) is explored. In CQNC, an effective negative-mass oscillator is coupled to an optomechanical sensor to create destructive interference of quantum radiation pressure noise. An all-optical realization of such an effective negative-mass oscillator is introduced, and a comprehensive study of its performance in a cascaded CQNC scheme is given. We determine ideal CQNC conditions, analyze non-ideal noise cancellation and provide a case study. Under feasible parameters, the case study shows a possible reduction of radiation pressure noise of 20% and that the effective negative-mass oscillator as the first subsystem in the cascade is the preferable order.Die Messgenauigkeit optomechanischer Sensoren hat eine Sensitvität erreicht, sodass sie im Rahmen der Quantentheorie beschrieben werden müssen. Quantenmechanik besagt, dass jede Messung eine Rückkopplung auf das vermessene System induziert. Bei optomechanischen Kraftsensoren is ein Kompromiss zwischen Rückkopplung und Messgenauigkeit durch die Verzahnung von Schrotrauschen und Strahlungsdruckrauschen begründet. Die Verwendung der optimalen Leistung, derart dass diese beiden Prozesse in Waage liegen, führt zum Standardquantenlimit (SQL). Hierdurch wird die Messgenauigkeit begrenzt. Um das SQL zu überwinden und die fundamentale Grenze der Parameterschätzung zu erreichen, welche durch Quanten-Cramér-Rao-Ungleichung bestimmt ist, werden die Methoden der Quantenglättung und Rückkopplungsumgehung benötigt. Im ersten Teil dieser Arbeit wird das Gebiet der Quantenglättung im Kontext von optomechanischer Kraftmessung untersucht. Die Quantenglättung kombiniert die Methoden der Vorhersage und Retrodiktion, um Abschätzungen an die Parameter eines Quantensystems zu tätigen, welche in der Vergangenheit liegen. Um die Feinheiten dieser Abschätzungen für Quantensysteme zu demonstrieren, werden zwei Filter, der Kalman- und der Wiener-Filter eingeführt. An einem einfachen optomechanischen System, werden deren Ergebnisse für die Vorhersage und Retrodiktion berechnet. Mögliche Diskrepanzen werden im Kontext der verfügbaren Theorien der Quantenglättung beleuchtet. Im zweiten Teil dieser Dissertation wird eine Rückkopplungsumgehungsmethode, die kohärente Quantenrauschunterdrückung (coherent quantum-noise cancellation, CQNC) untersucht. Bei CQNC wird ein Oszillator mit effektiver negativer Masse an einen optomechanischen Sensor gekoppelt, um destruktiv mit dem Strahlungsdruckrauschen zu interferieren. Eine mögliche optische Realisierung eines solchen negativen Masse Oszillators wird vorgestellt und mit einem optomechanischem Kraftsensor kaskadiert. Dieser Aufbau wird hinsichtlich seiner Rauschünterdrückungfähigkeit untersucht. Diesbezüglich ermitteln wir die Bedingungen für eine vollständige Abwendung von Strahlungsdruckrauschen und analysieren den Einfluss von möglichen Abweichungen von diesen Bedingungen auf die Rauschünterdrückung. Zuletzt präsentieren wir eine Fallstudie eines möglichen experimentellen Aufbaus. Die Fallstudie zeigt eine mögliche Strahlungsdrückreduzierung von 20% und dass der Oszillator mit effektiver negativer Masse als erstes System in der Kaskade zu bervorzugen ist

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

Anisotropic Diffusion Partial Differential Equations in Multi-Channel Image Processing : Framework and Applications

We review recent methods based on diffusion PDE's (Partial Differential Equations) for the purpose of multi-channel image regularization. Such methods have the ability to smooth multi-channel images anisotropically and can preserve then image contours while removing noise or other undesired local artifacts. We point out the pros and cons of the existing equations, providing at each time a local geometric interpretation of the corresponding processes. We focus then on an alternate and generic tensor-driven formulation, able to regularize images while specifically taking the curvatures of local image structures into account. This particular diffusion PDE variant is actually well suited for the preservation of thin structures and gives regularization results where important image features can be particularly well preserved compared to its competitors. A direct link between this curvature-preserving equation and a continuous formulation of the Line Integral Convolution technique (Cabral and Leedom, 1993) is demonstrated. It allows the design of a very fast and stable numerical scheme which implements the multi-valued regularization method by successive integrations of the pixel values along curved integral lines. Besides, the proposed implementation, based on a fourth-order Runge Kutta numerical integration, can be applied with a subpixel accuracy and preserves then thin image structures much better than classical finite-differences discretizations, usually chosen to implement PDE-based diffusions. We finally illustrate the efficiency of this diffusion PDE's for multi-channel image regularization - in terms of speed and visual quality - with various applications and results on color images, including image denoising, inpainting and edge-preserving interpolation

PDE Based Enhancement of Color Images in RGB Space

International audienceA novel method for color image enhancement is proposed as an extension of scalar diffusion-shock filter coupling model, where noisy and blurred images are denoised and sharpened. The proposed model is based on using single vectors of the gradient magnitude and the second derivatives as a technique to relate different color components of the image. This model can be viewed as a generalization of Bettahar-Stambouli filter to multi-valued images. The proposed algorithm is more efficient than the mentioned filter and some previous works on color image denoising and deblurring without creating false colors

Truck-based mobile wireless sensor networks for the experimental observation of vehicle–bridge interaction

Heavy vehicles driving over a bridge create a complex dynamic phenomenon known as vehicle–bridge interaction. In recent years, interest in vehicle–bridge interaction has grown because a deeper understanding of the phenomena can lead to improvements in bridge design methods while enhancing the accuracy of structural health monitoring techniques. The mobility of wireless sensors can be leveraged to directly monitor the dynamic coupling between the moving vehicle and the bridge. In this study, a mobile wireless sensor network is proposed for installation on a heavy truck to capture the vertical acceleration, horizontal acceleration and gyroscopic pitching of the truck as it crosses a bridge. The vehicle-based wireless monitoring system is designed to interact with a static, permanent wireless monitoring system installed on the bridge. Specifically, the mobile wireless sensors time-synchronize with the bridge's wireless sensors before transferring the vehicle response data. Vertical acceleration and gyroscopic pitching measurements of the vehicle are combined with bridge accelerations to create a time-synchronized vehicle–bridge response dataset. In addition to observing the vehicle vibrations, Kalman filtering is adopted to accurately track the vehicle position using the measured horizontal acceleration of the vehicle and positioning information derived from piezoelectric strip sensors installed on the bridge deck as part of the bridge monitoring system. Using the Geumdang Bridge (Korea), extensive field testing of the proposed vehicle–bridge wireless monitoring system is conducted. Experimental results verify the reliability of the wireless system and the accuracy of the vehicle positioning algorithm.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90810/1/0964-1726_20_6_065009.pd