The two-dimensional S-transform (ST-2D) is a time-frequency representation that is widely used in medical image processing but prohibitive in both storage and computation time. The high computation time required for generating local spectrum discourages the use of ST-2D for analyzing textures in medical images. A two-dimensional fast time-frequency transform (FTFT-2D) for computing the local spectrum instantaneously and accurately is proposed. It can also be used to compute the complete redundant discrete ST-2D output, if needed. It reduces the storage requirement by generating a compressed form of the ST-2D. In addition, the memory efficient and adaptive nature of the FTFT-2D make it suitable for user-specific requirements.