It has become evident that the commonly used two-dimensional tensor product wavelet bases are not optimal for representing signals that resemble images. This motivated a variety of schemes beyond wavelets

such as ridgelets

curvelets

contourlets

and wedgelets. Contourlet transform provides an efficient representation for two-dimensional piecewise smooth images

and constructed in discrete domain. In this paper

contourlets and hidden Markov model using contourlet transform are discussed

and the deep insights on the keys to understanding the contourlet transform are stated in details. The applications of contourlets

comparing with wavelets

are also introduced

and comment on the potential of contourlets for these applications in the future is given.