In image processing and pattern recognition, the accuracy of most algorithms is dependent on a good parameterization, generally a computation scale or an estimation of the amount of noise, which may be global or variable within the input image. Recently, a simple and linear time algorithm for arc detection in images was proposed \cite{NKDL-Unsupervised_Nguyen10a}. Its accuracy is dependent on the correct evaluation of the amount of noise, which was set by the user in this former version. In the present work we integrate a promising unsupervised noise detection method \cite{NKDL-Unsupervised_KerautretL09} in this arc recognition method, in order to process images with or without noise, uniformly distributed or variable within the picture. We evaluate the performance of this algorithm and we compare it with standard arc and circle detection methods based on extensions of the Hough transform.