Teaching

• 1.1 Scope of the Lecture | Introduction
• 1.2 Linear filters | Convolution
• 1.3 Interactive Semantic Segmentation with ilastik
• 2.1 Human Vision | Imaging
• 2.2 Downsampling an Image
• 2.3 Upsampling | Image Interpolation
• 3.1 Shallow vs Deep Learning
• 3.2 Training of a Neural Network (Introduction)
• 4.1 Convolutional Neural Networks | Image Classification
• 4.2 Training of a Neural Network | Optimization
• 4.3 U-net architecture | Semantic Segmentation
• 5.1 Fundamentals of Instance Segmentation
• 5.2 Proposal-based Instance Segmentation
• 5.3 Hough-transform
• 5.4 Instance Segmentation by Similarity Learning
• 6.1 Efficiently Solvable Graph Problems (Introduction)
• 6.2 Shortest Paths | Dijkstra Algorithm
• 6.3 Shortest Paths | 1D Labeling Problems
• 6.4 Shortest Paths | Segmented Least Squares
• 7.1 Dynamic Programming on Trees (Introduction)
• 7.2 Dynamic Programming on Trees | Message Passing
• 7.3 Dynamic Programming on Trees | Applications in Computer Vision
• 8.1 Watershed Algorithm | Clinical Application
• 8.2 Shortest Path vs. Widest Path | Seeded Segmentation
• 8.3 Minimax Paths | Prim's Algorithm
• 8.4 All-pairs Minimax Paths | Minimum Spanning Tree
• 8.5 Seeded Watershed Segmentation | ilastik Demo
• 8.6 Watershed Segmentation | Connection to Deep Learning
• 9.1 Recap of Shortest Path Algorithm
• 9.2 All-pairs Shortest Paths | Distance Product
• 9.3 The Algebraic Path Problem
• 9.4 Infimal Convolution | Euclidean Distance Transform
• 10.1 Tracking: Introduction and Overview
• 10.2 Tracking by Assignment | Min-Cost Flow
• 10.3 (Integer) Linear Programming | Polyhedral Geometry
• 10.4 Total Unimodularity
• 11.1 Optimal Transport: Introduction and Motivation
• 11.2 Discrete Optimal Transport
• 11.3 Discrete Optimal Transport (cont.) | Sinkhorn Iterations
• 11.4 Wasserstein Generative Adversarial Networks

• 1. Introduction and PCA
• 2. SVD and KDE
• 3. Mean-Shift and k-Means
• 4. Classification, k-NN, Cross-Validation, and Decision Trees
• 5. Decision Trees and Random Forests
• 6. Bayes Theorem, Statistical Decision Theory, and Quadratic Discriminant Analysis
• 7. Linear Regression
• 8. Regularized Linear Regression (Ridge, Lasso, ...)
• 9. Gaussian Process Regression
• 10. Logistic Regression and Generalized Linear Models
• 11. Perceptron and Multi-Layer Perceptron
• 12. Projection Trick and Function Counting Theorem
• 13. Backpropagation and Neural Network Training
• 14. CNNs and Deep Learning Tricks
• 15. Bayesian Networks/Probabilistic Graphical Models
• 16. Hidden Markov Models
• 17. Kalman Filter
• 18. Guest Lecture (not recorded)
• 19. Multicut and Correlation Clustering
• 20. Cluster Analysis
• 21. Dimension Reduction

• 1. Introduction
• 2. Undirected Probabilistic Graphical Models
• 2.1 MAP & Priors
• 2.2 Markov Random Fields
• 2.3 Gibbs Sampling
• 2.4 MRF as Integer Linear Program (I)
• 2.5 MRF as Integer Linear Program (II)
• 2.6 Tree-Shaped MRF
• 2.7 Belief Propagation
• 2.8 Gaussian MRF (I)
• 2.9 Gaussian MRF (II)
• 3. Neural Networks
• 3.1 Perceptrons
• 3.2 Back Propagation
• 3.3 Introduction to Deep Learning
• 3.4 Deep Learning Architectures
• 3.5 Natural Gradient Optimization (I)
• 3.6 Natural Gradient Optimization (II)
• 3.7 Combining Graphical Models & Neural Networks (I)
• 3.8 Combining Graphical Models & Neural Networks (II)
• 4. Directed Probabilistic Graphical Models
• 4.1 Reinforcement Learning
• 4.2 Policy Gradient
• 6.3 Robotics

1 Introduction

• 1.1 Applications of Pattern Recognition
• 1.2 k-Nearest Neighbors Classification
• 1.3 Probability Theory
• 1.4 Statistical Decision Theory

2 Correlation measures, Gaussian Models

• 2.1 Pearson Correlation
• 2.2 Alternative Correl. Measures
• 2.3 Gaussian Graphical Models
• 2.4 Discriminant Analysis

3 Dimensionality Reduction

• 3.1 Regularized LDA/QDA
• 3.2 Principal Component Analysis (PCA)
• 3.3 Bilinear Decompositions

4 Neural Networks

• 4.1 History of Neural Networks
• 4.2 Perceptrons
• 4.3 Multilayer Perceptrons
• 4.4 The Projection Trick
• 4.5 Radial Basis Function Networks

5 Support Vector Machines

• 5.1 Loss Functions
• 5.2 Linear Soft-Margin SVM
• 5.3 Nonlinear SVM

6 Kernels, Random Forest

• 6.1 Kernels
• 6.2 One Class SVM
• 6.3 Random Forest
• 6.4 Random Forest Feature Importance

7 Regression

• 7.1 Least-Squares Regression
• 7.2 Optimum Experimental Design
• 7.3 Case Study: Functional MRI
• 7.4 Case Study: CT
• 7.5 Regularized Regression

8 Gaussian Processes

• 8.1 Gaussian Process Regression
• 8.2 GP Regression: Interpretation
• 8.3 Gaussian Stochastic Processes
• 8.4 Covariance Function

9 Unsupervised Learning

• 9.1 Kernel Density Estimation
• 9.2 Cluster Analysis
• 9.3 Expectation Maximization
• 9.4 Gaussian Mixture Models

10 Directed Graphical Models

• 10.1 Bayesian Networks
• 10.2 Variable Elimination
• 10.3 Message Passing
• 10.4 State Space Models

11 Optimization

• 11.1 The Lagrangian Method
• 11.2 Constraint Qualifications
• 11.3 Linear Programming
• 11.4 The Simplex Algorithm

12 Structured Learning

• 12.1 StructSVM
• 12.2 Cutting Planes

1 Introduction

• Introduction
• Human early vision
• Image representations

2 Patches in Image Analysis

• Block Matching
• Texture Synthesis
• Non-Local Means for Image Denoising
• BM3D for image denoising

3 Fourier Transformation

• Unitary transformations
• The Fourier Transform
• The Discrete Fourier Transform (DFT)
• 2D-DFT: Application to Images

4 Wavelets

• Fourier Transform
• Time Frequency Decompositions
• The Wavelet Transform

5 Images as Topographic Maps

• Watershed
• Maximally Stable Extremal Regions (MSER)
• Mathematical Morphology
• Minkowski functionals

6 Gaussian Random Fields

• Markov Random Fields (MRFs)
• Gaussian Markov Random Fields (GMRF)
• Intrinsic GMRFs (IGMRF)

7 Fields of Experts, Discrete MRFs

• Factor Graphs
• Fields of Experts
• Discrete-Valued MRFs
• MAP inference via Integer Linear Programming (ILP)

8 Binary pairwise MRFs and Graph Cut

• Integer Linear Programs (continued)
• Pseudo Boolean Functions (PBFs)
• Quadratic PBFs with submodular terms
• Max-Flow / Min-Cut
• Graph Cuts

9 Structured learning

• Introduction
• Example model: Tracking by assignment
• Structured Support Vector Machine (structSVM)
• Structured Learning: Applications

10 Light Fields and Compressive Sensing

• Light Fields
• Coded Aperture Imaging
• Compressive Sensing