  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.
