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We propose a method to extract salient contour groups from cluttered regions using Markov Random Fields. Our technique delineates smooth, long, and elliptical curves out of clutter. To extract salient curves, we use the following perceptual rules: smoothness, proximity, co-circularity, co-elliptic, and length. Our method consists of the following steps: obtaining individual smooth contours along their saliency measures; starting from the most salient contour search for possible grouping options for each contour; continuing the grouping until an optimum solution is reached. We introduce circularity and saliency measures for open curves. We applied our method to discern coronal loops from cluttered solar images, and were able to successfully obtain the entire set of desired coronal loops while eliminating any cluttered background.