This paper presents an experimental study for assessing the applicability of general-purpose 3D segmentation algorithms for analyzing dental periapical lesions in cone-beam computed tomography (CBCT) scans. In the field of Endodontics, clinical studies have been unable to determine if a periapical granuloma can heal with non-surgical methods. Addressing this issue, Simon et al. recently proposed a diagnostic technique which non-invasively classifies target lesions using CBCT. Manual segmentation exploited in their study, however, is too time consuming and unreliable for real world adoption. On the other hand, many technically advanced algorithms have been proposed to address segmentation problems in various biomedical and non-biomedical contexts, but they have not yet been applied to the field of dentistry. Presented in this paper is a novel application of such segmentation algorithms to the clinically-significant dental problem. This study evaluates three state-of-the-art graph-based algorithms: a normalized cut algorithm based on a generalized eigen-value problem, a graph cut algorithm implementing energy minimization techniques, and a random walks algorithm derived from discrete electrical potential theory. In this paper, we extend the original 2D formulation of the above algorithms to segment 3D images directly and apply the resulting algorithms to the dental CBCT images. We experimentally evaluate quality of the segmentation results for 3D CBCT images, as well as their 2D cross sections. The benefits and pitfalls of each algorithm are highlighted.