Stable skeletons are promising as a compact, concise, and efficient descriptor since they can reflect much critical information about the original object, such as topology, connectivity, etc. However, extracting stable skeletons from images is very challenging since most existing skeleton extraction methods, also named skeletonization methods in some literature, are sensitive to noise, which limits the application of the skeletons in the recognition field. Many denoising methods have been proposed to extract stable skeletons to overcome this problem. However, up to now, there are few review papers to conclude these denoising methods and present their pros and cons. Therefore, In this paper, we survey existing denoising techniques for extracting stable skeletons from images. We first categorize these denoising methods, analyze their core idea, and then present their pros and cons for comparison. In addition, we also offer the potential research direction and possibly challenge.