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It has been recently shown that spatial patterns of activation within regions of interest (ROIs) in functional magnetic resonance imaging (fMRI) data can be used as sensitive markers of brain activation differences. In this paper, we propose novel invariant features for characterizing such spatial activation patterns based on spherical harmonic (SPHARM) data representations. The proposed three dimensional (3-D) spatial features are novel in that; first, they provide a unique representation of any ROI's functional data; second, they simultaneously account for inherent inter-subject anatomical variability that may influence any spatial characterization; third, they are invariant to similarity transformations and hence allow for direct comparisons between ROIs without any requirement for normalization to an atlas. We present quantitative validation demonstrating our method's improved sensitivity in performing group analysis when compared to traditional spatial normalization using synthetic data at the ROI level. We also use the proposed technique along with traditional normalization approach on real fMRI data collected from PD patients and normal subjects. The proposed features provide a powerful means to sensitively detect group-wise changes in ROI-based fMRI activation patterns even in the presence of anatomical variability.