Computational Optics

Prof. Dr. Pflaum, 5 ECTS

• Simulation of optical waves
• Solving Maxwell’s Equations with the Finite difference method
• Ray propagation methods
• Rate equations for photons
• Applications for simulations of laser and thin film solar cells

Prof. Dr. Maier, 5 ECTS

(also offered in winter term)

• Medical imaging helps physicians to take a view inside the human body and therefore allows better treatment and earlier diagnosis of serious diseases. However, as straightforward as the idea itself is, so diversified are the technical difficulties to overcome when implementing a clinically useful imaging device. We begin this module by discussing all available modalities and the actual imaging goals which highly affect the imaging result.
• Some modalities produce very noisy results, but there are multiple other artifacts that show up in raw acquisition data and have to be dealt with. We address these issues in the chapter preprocessing and show how to compensate for image distortions, how to interpolate defect pixels, and finally correct bias fields in magnetic resonance images.
• The largest portion of this course covers the theory of medical image reconstruction. Here, from a set of projections from different viewing angles a 3-D image is merged that allows a definite localization of anatomical and pathological features. Following roughly the historical development of CT devices, we study the process from parallel beam to fan beam geometry and include a discussion of phantoms as a tool for calibration and image quality assessment. We then move forward and learn about reconstruction in 3-D. Since the system matrix often grows in dimensions such that many direct solvers become infeasible, we also discuss pros and cons of iterative methods.
• In the final chapter, image registration is introduced as the concept of computing the mapping that maps the content of one image to another. Two different acquisitions usually result in images that are at least rotated and translated against each other. Image registration forms the set of tools that we need to match certain image features in order to align both images for further processing, image improvement or image overlays.

Prof. Dr. Maier, 5 ECTS

(also offered in winter term)

This module focuses on recent developments in image processing driven by medical applications. All algorithms are motivated by practical problems. The mathematical tools required to solve the considered image processing tasks will be introduced. In addition to the lectures, we also offer exercise classes. The exercises consist of theoretical parts where you immerse in lecture topics. But we also set emphasis on the practical implementation of the methods.

Dr. Riess, 5 ECTS

This module introduces the design of pattern analysis systems as well as the corresponding fundamental mathematical methods. The topics comprise:

• clustering methods: soft and hard clustering
• classification and regression trees and forests
• parametric and non-parametric density estimation: maximum-likelihood (ML) estimation, maximum-a-posteriori (MAP) estimation, histograms, Parzen estimation, relationship between folded histograms and Parzen estimation, adaptive binning with regression trees
• mean shift algorithm: local maximization using gradient ascent for non-parametric probability density functions, application of the mean shift algorithm for clustering, color quantization, object tracking
• linear and non-linear manifold learning: curse of dimensionality, various dimensionality reduction methods: principal component analysis (PCA), multidimensional scaling (MDS), isomaps, Laplacian eigenmaps
• Gaussian mixture models (GMM) and hidden Markov models (HMM): expectation maximization algorithm, parameter estimation, computation of the optimal sequence of states/Viterbi algorithm, forward-backward algorithm, scaling
• Markov random fields (MRF): definition, probabilities on undirected graphs, clique potentials, Hammersley-Clifford theorem, inference via Gibbs sampling and graph cuts

Prof. Dr. Tim Weyrich, 5 ECTS

Never in human history have we been able to record so much of our environment in so little time with such high quality. Since the rise of smartphones, nearly everyone carries a powerful camera with them in their daily lives. This module introduces the theoretical and practical aspects of modern photography and capture algorithms: universal models of colour, computer-controlled cameras, lighting and shape capture.
The lecture covers the following topics:

• Cameras, sensors and colour
• Image processing (e.g., blending, warping)
• Radiometry
• Appearance acquisition
• Structured-light 3D acquisition
• Image-based and video-based rendering

Prof. Dr. Egger, Prof. Dr. Maier, 5 ECTS

This module discusses important algorithms from the field of computer vision. The emphasis lies on 3-D vision algorithms, covering the geometric foundations of computer vision, and central algorithms such as stereo vision, structure from motion, optical flow, and 3-D multiview reconstruction. Participants of this advanced course are expected to bring experience from prior lectures either from the field of pattern recognition or from the field of computer graphics.

The module introduces computer vision algorithms that are central to the field. In the exercises, participants autonomously implement and evaluate these algorithms. The participants work throughout the time on popular computer vision algorithms, like for example stereo vision, optical flow, and 3-D multiview reconstruction. For these problems, the participants

• describe perspective projection, rotations, and related geometric foundations,
• explain the presented methods,
• discuss the advantages and disadvantages of different modalities for acquiring 3-D information,
• implement individually and in small groups code,
• discover best practices in data acquisition,
• explore and rank different choices for evaluation,
• discuss and present in groups the advantages and disadvantages of their implementations,
• discuss and reflect the social impact of applications of computer vision algorithms.

Prof. Dr. Harald Köstler, 5 ECTS

The module includes two interlinked topics. First, an introduction to the techniques of optical imaging (e.g. for biological specimen) with a special focus on recently evolving super-resolution techniques beyond the diffraction barrier. Second, the students will be given an overview of existing numerical techniques in imaging processing especially for image deblurring. The focus lies on algorithms based on sparse coding and deep learning methods. Additionally one makes use of information about the imaging system. The algorithms are applied to optical imaging and implemented in Matlab or Python.

Prof. Dr. Maier, 5 ECTS

Mathematical foundations of machine learning based on the following classification methods:

• Bayesian classifier
• Logistic Regression
• Naive Bayes classifier
• Discriminant Analysis
• norms and norm dependent linear regression
• Rosenblatt’s Perceptron
• unconstraint and constraint optimization
• Support Vector Machines (SVM)
• kernel methods
• Expectation Maximization (EM) Algorithm and Gaussian Mixture Models (GMMs)
• Independent Component Analysis (ICA)
• Model Assessment
• AdaBoost

Prof. Dr. Breininger, 5 ECTS

Deep Learning-based algorithms showed great performance in many fields of image processing and pattern recognition and compete with technologies such as compressive sensing and iterative optimization. The basis for the success of these algorithms is the availability of large amounts of data (big data) for training and of high computing power (typically GPUs).
In this seminar we try to explore advanced deep learning methods. In particular, we will aim to develop a deeper understanding of certain topics, for example: graph neural networks, unsupervised learning, differentiable learning, invertible learning, neural ordinary differential equations, transfer learning, multi-task learning, uncertainty DL, etc