In this paper, a set of non-rigid image registration and neural activity modelling methods using functional MR Images (fMRI) are proposed based on transform-invariant feature representations. Our work made two contributions. First, we propose to use a transform-invariant feature to improve image registration performance of Iterative Closest Point (ICP) based methods. The proposed feature utilises Gaussian Mixture Models (GMM) to describe the local topological structure of fMRI data. Second, we propose to use a 3-dimensional Scale-Invariant Feature Transform (SIFT) based descriptor to represent neural activities related to drinking behaviour. As a result, neural activities patterns of different subjects drinking water or intaking glucose can be recognised, with strong robustness against various artefacts.