Nowadays, point clouds (PCs) are a promising representation format for immersive content and target several emerging applications, notably in virtual and augmented reality. However, efficient coding solutions are critically needed due to the large amount of PC data required for high quality user experiences. To address these needs, several PC coding standards were developed and thus, objective PC quality metrics able to accurately account for the subjective impact of coding artifacts are needed. In this paper, a scale-invariant PC geometry quality assessment metric is proposed based on a new type of correspondence, namely between a point and a distribution of points. This metric is able to reliably measure the geometry quality for PCs with different intrinsic characteristics and degraded by several coding solutions. Experimental results show the superiority of the proposed quality metric over relevant state-of-the-art.