Contourlet Transforms For Feature Detection

Contourlet Transforms For Feature Detection Literature Review Wei-shi Tsai March 6th, 2008 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 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. What features are needed?

Multiresolution Localization Critical sampling Directionality Anisotropy 2-D separable transforms satisfy the first

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

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

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

2-D Discrete Wavelet Transform Contourlet Transform