Inspired by the characteristics of the human visual system, a novel method is proposed for detecting the visually salient regions on 3D point clouds. First, the local distinctness of each point is evaluated based on the difference with its local surroundings. Then, the point cloud is decomposed into small clusters, and the initial global rarity value of each cluster is calculated; a random walk ranking method is then used to introduce cluster-level global rarity refinement to each point in all the clusters. Finally, an optimization framework is proposed to integrate both the local distinctness and the global rarity values to obtain the final saliency detection result of the point cloud. We compare the proposed method with several relevant algorithms and apply it to some computer graphics applications, such as interest point detection, viewpoint selection, and mesh simplification. The experimental results demonstrate the superior performance of the proposed method.