The convex hull is a fundamental geometrical structure for many applications where groups of points must be enclosed or represented by a convex polygon. Although efficient sequential convex hull algorithms exist, and are constantly being used in applications, their computation time is often considered an issue for time-sensitive tasks such as real-time collision detection, clustering or image processing for virtual reality, among others, where fast response times are required. In this work we propose a parallel GPU-based adaptation of heaphull, which is a state of the art CPU algorithm that computes the convex hull by first doing a efficient filtering stage followed by the actual convex hull computation. More specifically, this work parallelizes the filtering stage, adapting it to the GPU programming model as a series of parallel reductions. Experimental evaluation shows that the proposed implementation significantly improves the performance of the convex hull computation, reaching up to $4\times$ of speedup over the sequential CPU-based heaphull and between $3\times \sim 4\times$ over existing GPU based approaches.