In this paper, we have presented a new and effective edge detection scheme based on least squares support vector machine (LS-SVM) classification in a contourlet Hidden Markov Tree Model (contourlet HMT). First, the input noisy image is decomposed into coarser and finer coefficients using a contourlet HMT transform to derive an efficient multiscale and multidirectional image representation. Second, the feature vector is performed through spatial regularity in a contourlet HMT domain, and the coarser coefficients classified using LS-SVM classifier into two classes: noise coefficients and edge coefficients. Next, all noisy contourlet HMT coefficients are well denoised by the BayesShrink method. Finally, the denoised coefficients and edge coefficients are fused using the weighted average rule, and the inverse contourlet HMT is applied to obtain the edge image. Experimental results demonstrate that our scheme can attain improved performance over state-of-the-art edge detection approaches, both qualitatively and quantitatively. Tests were performed on several images from the Berkeley dataset corrupted with Gaussian noise and on other images such as a cameraman, pepper and medical images. The results illustrate that the performance of the proposed scheme is stable. 
An edge detection scheme based on least squares support vector machine in a contourlet HMT domain