This paper presents an enhanced version and an incremental learning version of the visual-attentionimitation convex hull algorithm reported in our latest paper in Liu et al. (2012) [3]. The enhanced algorithm merges the virtue of point comparison of the Graham scan algorithm into the visual-attentionimitation convex hull algorithm. In comparison with its previous edition, the proposed algorithm achieved a significant time saving. In view of machine learning, there are interesting situations where training data acquisition must take place over time. An incremental learning version is also proposed in this paper in order to compute convex hulls of point sets whose points are acquired over time. The incremental learning version reuses the prior results and computes the new convex hull without processing of previous points. Experimental results show that the incremental learning version is more flexible and more efficient for incremental learning tasks.