Computational Anatomy in Theano

To model deformation of anatomical shapes, non-linear statistics are required to take into account the non-linear structure of the data space. Computer implementations of non-linear statistics and differential geometry algorithms often lead to long and complex code sequences. The aim of the paper is to show how the Theano framework can be used for simple and concise implementation of complex differential geometry algorithms while being able to handle complex and high-dimensional data structures. We show how the Theano framework meets both of these requirements. The framework provides a symbolic language that allows mathematical equations to be directly translated into Theano code, and it is able to perform both fast CPU and GPU computations on high-dimensional data. We show how different concepts from non-linear statistics and differential geometry can be implemented in Theano, and give examples of the implemented theory visualized on landmark representations of Corpus Callosum shapes.