Identifying phase discontinuity locations is a necessary and complex step in the phase unwrapping process, and it becomes more challenging when dealing with noisy wrapped phase maps that are produced through shearography or other speckle-based interferometry methods. Recently, the task of identifying phase discontinuities has been formulated into a two-class classification problem, where the phase discontinuities are identified by a complex neural network trained on plenty of image patches taken from wrapped phase maps. A simple but efficient classification framework is proposed for the phase discontinuities identification task. Six features are first designed to describe the characteristics of discontinuous and continuous pixels. Then, the naive Bayes classifier, working on these features, is employed as the classifier of our framework. Finally, a thinning procedure is performed on the classification results to get the one-pixel-width discontinuity location map which can be used for further phase unwrapping. The experiments on simulated wrapped phase maps are performed to validate the performance of the proposed approach. The experimental results show that the proposed approach can identify phase discontinuities in the wrapped phase maps well and has more robust performances when the signal-to-noise ratios of the phase maps are low.