In functional MRI (fMRI), the changes in cerebral haemodynamics related to stimulated neural brain activity are measured using standard clinical MR equipment. Small intensity variations in fMRI data have to be detected and distinguished from non-neural effects by careful image analysis. Based on multivariate statistics we describe an algorithm involving oblique rotation of the most significant principal components for an estimation of the temporal and spatial distribution of the stimulated neural activity over the whole image matrix. This algorithm takes advantage of strong local signal variations. A mathematical phantom was designed to generate simulated data for the evaluation of the method. In simulation experiments, the potential of the method to quantify small intensity changes, especially when processing data sets containing multiple sources of signal variations, was demonstrated. In vivo fMRI data collected in both visual and motor stimulation experiments were analysed, showing a proper location of the activated cortical regions within well known neural centres and an accurate extraction of the activation time profile. The suggested method yields accurate absolute quantification of in vivo brain activity without the need of extensive prior knowledge and user interaction.