An algorithm for automatic curve detection

In this article we consider the problem of automatic detection of curves, as opposed to straight lines, over a noisy image. We develop a two step model selection procedure based on a contourlet expansion of the image and prove the method is consistent in probability. The first step is based on usual threshold methods for frames. The second step selects pixels that spread energy over several simultaneous directions which is a known property of curve-like figures. We apply the proposed method to synthetic images and show its capability to separate curves from a noisy background and from a random collection of small straight lines. A practical application to seismic grids is also considered.