The contourlet transform: an efficient directional multiresolution image representation

The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information. The main challenge in exploring geometry in images comes from the discrete nature of the data. Thus, unlike other approaches, such as curvelets, that first develop a transform in the continuous domain and then discretize for sampled data, our approach starts with a discrete-domain construction and then studies its convergence to an expansion in the continuous domain. Specifically,…

• NS
  National Science Foundation

  Awards: 0237633, CAREER
• SN
  Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

  Award: 63664