Statistical Shape Modelling: Useful Learning Resources
Gaussian ProcessesWe used Gaussian Processes as our fundamental modelling technique but could only show you a small part of what Gaussian Processes can offer. You can find a wealth of literature about Gaussian Processes in the field of statistics. In this course, we have used Gaussian Processes to represent spatial data. This type of Gaussian Processes is usually referred to as Gaussian random field in the statistics literature. An introduction to Gaussian random fields, with additional pointers, is given in this review article:Abrahamsen, Petter. A review of Gaussian random fields and correlation functions, 1997.Another area where Gaussian Processes proved to be very useful is machine learning. An excellent introduction to Gaussian Processes and their use in machine learning is given in this free online book:Rasmussen, Carl Edward and Williams, Christopher K. I. Gaussian processes for machine learning, 2006.If you would like to acquire an understanding of the mathematical structures associated with Gaussian Processes and their connection to kernel methods and differential equations, we strongly recommend the following article:Steinke, Florian and Schölkopf, Bernhard. Kernels, regularization and differential equations, 2008.
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Statistical Shape Modelling: Computing the Human Anatomy
Model-based image analysis and pattern theoryIn this course, we have shown you how you can perform model fitting using a simple iterative algorithm. The problem of fitting would deserve much more attention and although these simple algorithms can get you started, more sophisticated methods are needed to successfully apply model fitting to image analysis. We refer again to the paper by Heimann and Meinzer for a overview of different methods used in model-based image segmentation:Heimann, Tobias, and Meinzer, Hans-Peter. Statistical shape models for 3D medical image segmentation: a review, 2009.The problem of model-based image analysis can be seen as a special case of the pattern analysis problem. Pattern theory provides a very general framework for the description of patterns based on probabilistic models that are then fitted to the data using an analysis-by-synthesis approach. We recommend the following book by D. Mumford and A. Desolneux, but remark that the mathematical prerequisites are much higher than what has been required in this course:Mumford, David and Desolneux, Agnès. Pattern theory: the stochastic analysis of real-world signals, 2010.In our research group we are following this general analysis-by-synthesis approach. Specifically, we have implemented a fully probabilistic fitting framework using Markov Chain Monte Carlo methods. We have recently produced an interactive tutorial on our probabilistic fitting approach. The tutorial is designed to be a continuation of this course. Although the approach is illustrated on the problem of fitting 2D face photographs using a 3D statistical face model, the concepts are general and can be directly applied for analysing medical images.
ScalaIf you continue working with Scalismo, it is essential that you learn more about the programming language Scala, as you would eventually like to use Scalismo as a library that can be used in your own applications. There are many good books on Scala available. We particularly like the book:Welsh, Noel and Gurnell, Dave. Essential scala, 2011.Another good introduction to Scala:Cay, Horstmann. Scala for the impatient, 2012.whose first chapters covering the basics of the language are available here.
Software packagesShape modelling is very much an applied discipline and software plays an extremely important role. I hope we could convince you that a system like Scalismo, which can directly visualise what is going on, is of great help.Note that the Scalismo version used for this course (v0.10) is not the latest version. This is due to the fact that version release speed of software is rather high, which would require shooting new tutorial videos frequently. On the Scalismo webpage you will find the tutorial articles that you worked on during this course translated to the latest version of Scalismo. The tutorials will also help you to switch to Scalismo as a library, which we recommend when you are working on real projects.We have recently also released the software library scalismo-faces, which specifically targets the application of face image analysis. It contains a complete computer graphics pipeline and complements scalismo with functionality for handling color mehes and 2D color images.If you prefer to use R instead of Scala, you can use the package Morpho together with RvtkStatismo. These packages together offer all the functionality that we covered in this course as well as great visualisation capabilities.If you liked modelling with Gaussian Processes, but prefer working in C++, you can use Statismo. It supports all the concepts we have taught in the course and is designed to work together with the popular open sources image analysis libraries VTK and ITK.
Statistical Shape Modelling: Computing the Human Anatomy
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