Fast curve estimation using preconditioned generalized Radon transform

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Abstract
A new algorithm for fast curve parameter estimation based on the generalized Radon transform is proposed. The algorithm works on binary images, obtained, e.g., by edge filtering or deconvolution. The fundamental idea of the suggested algorithm is the use of a precondition map to reduce the computational cost of the generalized Radon transform. The precondition map is composed of irregular regions in the parameter domain, which contain peaks that represent curves in the image. To generate the precondition map, a fast mapping procedure named image point mapping is developed. As the image point mapping scheme maps image points into the corresponding parameter values in the parameter domain, it is possible to improve computational efficiency by recognizing image points with value zero. Initially, the suggested algorithm estimates the precondition map and subsequently applies the generalized Radon transform within the regions specified by the precondition map. The required parameter domain sampling and the resulting blurring are also investigated. The suggested algorithm is successfully applied to the identification of hyperbolas in seismic images, and two numerical examples are given.

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