There has been considerable debate about the perspectival / optical bases of the naturalism pioneered by Robert Campin and Jan van Eyck. Their paintings feature brilliantly rendered convex mirrors, which have been the subject of much comment, especially iconographical. David Hockney has recently argued that the Netherlandish painters exploited the image-forming capacities of concave mirrors. However, the secrets of the images within the painted mirrors have yet to be revealed. Using novel, rigorous techniques to analyse the geometric accuracy of the mirrors, unexpected findings emerge, which radically affect how we see the paintings as being generated. We focus on Jan van Eyck’s Arnolfini Portrait, and the Heinrich von Werl Triptych, here re-attributed to Robert Campin. The accuracy of the convex mirrors depicted in these paintings is assessed by applying mathematical techniques drawn from computer vision. The proposed algorithms allow us also to “rectify” the image in the mirror so that it becomes a normalised projection, thus providing us with a second view from the back of the painted room. The plausibility of the painters’ renderings of space in the convex mirrors can be assessed. The rectified images can be used for purposes of three-dimensional reconstruction as well as measuring accurate dimensions of objects and people. The surprising results presented in this paper cast a new light on the understanding of the artists’ techniques and their optical imitation of seen things, and potentially require a re-thinking of the foundations of Netherlandish naturalism. They also suggest that the von Werl panels should be re-instated as autograph works by R. Campin. Additionally, this research represents a further attempt to build a constructive dialogue between two very different disciplines: computer science and history of art. Despite their fundamental differences, the procedures followed by science and art history can learn and be enriched by each other.