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

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. 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. Pflaum, 5 ECTS
The course teaches how to develop and implement a graphical user interface for computational optics. The main application will be rate equations for laser simulation. Software will be written in C++ using the library Qt.