Computer-aided segmentation and border detection in dermoscopic images is one of the core components of diagnostic procedures and therapeutic interventions for skin cancer. Automated assessment tools for dermoscopy images have become an important research field mainly because of inter- and intra-observer variations in human interpretation. In this study, we compare two approaches for automatic border detection in dermoscopy images: density based clustering (DBSCAN) and Fuzzy C-Means (FCM) clustering algorithms. In the first approach, if there exists enough density--greater than certain number of points--around a point, then either a new cluster is formed around the point or an existing cluster grows by including the point and its neighbors. In the second approach FCM clustering is used. This approach has the ability to assign one data point into more than one cluster.