Multiresolutional decomposition methods can have application in many areas such as in telecommunications, remote sensing, multimedia, signal and image processing. In this work, the two-dimensional (2D) nonseparable complementary filter (CF) banks and perfect reconstruction (PR) structures are presented. Developed for the processing of images, the 2D CF banks and PR structures were designed based on 2D multirate signal processing theory and complementary filters properties. The complementary filters were designed for an alias free decimation and interpolation. The perfect reconstruction conditions were studied for all types of sampling and filters, and although perfect reconstruction is achieved for quincunx sampling and filter, the analysis is aliasing free in all cases. The CF banks performance with images showed that the signal-to-noise ratio keeps high even for the cases where the reconstruction is not perfect. For PR structures, the reconstructed image is done perfectly, but at the cost of lower data compression. Examples of CF banks and PR structures analysis and synthesis with images are given.