The objective of this paper is to study the robustness of computation of correlations under spatial constraints. The motivation of our paper is the specific case of functional magnetic resonance (fMRI) brain imaging data, where voxels are aggregated to compute correlations. In this paper we show that the way the spatial components are aggregating to com- pute correlation may have a strong influence on the resulting estimations. We then propose various estimators which take into account this spatial structure.