The univariate approach without a smoothing filter for detecting activation patterns in functional magnetic resonance imaging (fMRI) data suffers from a low sensitivity due to presence of high noise. The poor performance of univariate methods such as ordinary correlation is due to lack of their ability to take advantage of spatial correlation that exists in fMR images among group of neighboring voxels. To rectify this problem multivariate approaches such as canonical correlation analysis (CCA), adaptive canonical correlation analysis (ACCA) and spatial Gaussian smoothing accompanied with univariate correlation has already been applied to fMR images to improve both sensitivity and specificity. In this work idea of smoothing fMR images with ACCA has been extended to adaptive two-dimensional canonical correlation analysis (A2DCCA) to obtain improvements in detection performance in terms of specificity. It is shown on synthetic and real fMRI data that A2DCCA produces better specificity than ACCA and Gaussian smoothing.