An increased interest in immersive applications has drawn attention to emerging 3D imaging representation formats, notably light fields and point clouds (PCs). Nowadays, PCs are one of the most popular 3D media formats, due to recent developments in PC acquisition, namely depth sensors and signal processing algorithms. To obtain high fidelity 3D representations of visual scenes a huge amount of PC data is typically acquired, which demands efficient compression solutions. As in classical 2D media formats, the final perceived PC quality plays an importance role in the overall user experience and, thus, objective metrics capable to measure the PC quality in a reliable way are essential. In this context, this paper proposes and evaluates a set of objective quality metrics for the geometry component of PC data, which plays a very important role on the final perceived quality. Based on the popular PSNR PC geometry quality metric, novel improved PSNR-based metrics are proposed by exploiting the intrinsic PC characteristics and the rendering process that must occur before visualization. The experimental results show the superiority of the best proposed metrics over state-of-the-art, obtaining an improvement up to 0.32% in the Pearson correlation coefficient.