This will be the ninth in a series of summer school organized together with the Image Analysis and Computer Graphics section at DTU. The concept is to invite 2-4 internationally renowned experts to teach a week-long course together with local teachers from KU and DTU. The participants are a good mix of students from KU and DTU and international participants. The summer schools are held in remote locations to encourage interaction between students and teachers. In addition to bringing international expertise in to the groups, the summer schools also provide an important networking opportunity for the students.

• Subject area: Graphical Models:

Graphical models are a cornerstone in medical image analysis, computer vision, and machine learning. They offer a structured way of describing conditional dependencies in a model, and provide a strong theoretical framework both for reducing model complexity and for formulating efficient methodologies for parameter estimation.

A classic example of a graphical model is the Markov random field, a well known approach to classification in image analysis. Other examples include Bayesian networks, which have found applications in the modelling of complex geometrical structures such as proteins, and many other pattern recognition tasks. Finally, graphical models are natural tools in the design of probabilistic variants of neural networks, such as Deep Belief Networks, and restricted Boltzmann machines, both of which have been used for feature detection and image analysis in general.

The basic idea behind graphical models is to represent conditional dependencies between stochastic variables as a graph. A fully connected graph is the most general model, making no assumptions on the dependencies between variables. However, such models typically have an excessive number of variables, and are computationally intractable to estimate. By using prior information about the problem domain to remove edges in the graph, one implicitly introduces assumptions about conditional independence between variables, thereby reducing the complexity of the model and making the estimation procedure computationally tractable.

In addition to its role as a graphical tool to reduce model complexity, the graph itself is used as the basis for algorithms for model training and inference. In particular, message passing algorithms such as Belief Propagation use the structure of the graph to infer marginal distributions of all unobserved nodes.

• Scientific content:

The summer school will consist of 5 days of lectures and exercises. The students will be expected to read a predefined set of scientific articles on graphical models prior to the course. Additionally, the students should bring a poster presenting their research field (preferably with an angle towards machine learning in image analysis).

The course will consist of the following parts:

• A crash course on the basics of graphical models.
• A theoretical insight in the challenges of graphical models.
• A practical session with hands-on exercises.
• Applications of graphical models in image analysis.