The line-fitting problem has been transposed to the signal-processing framework: Array-processing methods can be applied to virtual signals generated from the image, to estimate straight-line orientations. This paper deals with the estimation of straight and distorted lines in images by fast array-processing methods. Hough transform and snake methods retrieve straight lines and distorted contours, but present limitations. We adapt a fast high-resolution method, the propagator method, to the estimation of multiple distorted contours. For the first time, a method is proposed to cope with the intrinsically limited size of images, which reduces the accuracy of the high-resolution methods due to the low number of signal realizations. Moreover, an extension to images impaired by correlated noise is proposed. For this, an extension of the subspace-based methods to a method based on higher-order statistics is proposed. Distorted contours are assimilated to distorted wavefronts and retrieved with a novel optimization method. The performance of the proposed method is validated on several images.