Investigation of the carotid artery plays an important role in the diagnosis of cerebrovascular events. Segmentation of the lumen and vessel wall in Magnetic Resonance (MR) images is the first step towards evaluating any possible cardiovascular diseases like atherosclerosis. However, the automatic segmentation of the lumen is still a challenge due to the low quality of the images and the presence of other elements such as stenosis and malformations that compromise the accuracy of the results. In this article, a method to identify the location of the lumen without user interaction is presented. The proposed method uses the modified mean roundness to calculate the circularity index of the regions identified by the K-means algorithm and return the one with the maximum value, i.e. the potential lumen region. Then, an active contour is employed to refine the boundary of this region. The method achieved an average Dice coefficient of 0.78 +/- 0.14 and 0.61 +/- 0.21 in 181 3D-T1-weighted and 181 proton density-weighted MR images, respectively. The results show that this method is promising for the correct identification and location of the lumen even in images corrupted by noise