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  1. Contourlet Transforms For Feature Detection Literature Review Wei-shi Tsai March 6th, 2008

  2. Feature Detection • Focus will be on edge detection • Gradient operators (Sobel, Roberts) • Laplacian operators • LoG (Laplacian of Gaussian) • DoG (Difference of Gaussians) • Canny method • Anisotropic diffusion

  3. 2-D Wavelet Transform • Separable extension of the 1-D wavelet transform • Can be used for edge detection depending on the scale level and the noise in the image • Can only detect edges in the horizontal, vertical, and 45° orientations.

  4. What features are needed? • Multiresolution • Localization • Critical sampling • Directionality • Anisotropy 2-D separable transforms satisfy the first three requirements.

  5. Curvelets (Candes and Donoho, 1999) First fixed transform to capture contours. However, it is defined in the continuous domain.

  6. Contourlets (Do and Vetterli, 2005) • Captures smooth contours and edges at any orientation • Filters noise • Derived directly from discrete domain instead of extending from continuous domain • Can be implemented using filter banks

  7. Contourlet filter bank The transform decouples the multiscale and the directional decompositions.

  8. Decomposition • The multiscale decomposition is handled by a Laplacian pyramid. • The directional decomposition is handled by a directional filter bank.

  9. 2-D Discrete Wavelet Transform

  10. Contourlet Transform