This paper details the recently introduced Ray Histogram Fusion (RHF) filter for accelerating Monte Carlo renderers [M. Delbracio et al., Boosting Monte Carlo Rendering by Ray Histogram Fusion, ACM Transactions on Graphics, 33 (2014)]. In this filter, each pixel in the image is characterized by the colors of the rays that reach its surface. Pixels are compared using a statistical distance on the associated ray color distributions. Based on this distance, it decides whether two pixels can share their rays or not. The RHF filter is consistent: as the number of samples increases, more evidence is required to average two pixels. The algorithm provides a significant gain in PSNR, or equivalently accelerates the rendering process by using many fewer Monte Carlo samples without observable bias. Since the RHF filter depends only on the Monte Carlo samples color values, it can be naturally combined with all rendering effects.