Shuang Zhao

The painting Salvator Mundi is attributed to Leonardo da Vinci and depicts Jesus holding a transparent orb. The authors study the optical accuracy of the fine illumination effects in this painting using inverse rendering. Their experimental results provide plausible explanations for the strange glow inside the orb, the anomalies on the orb and the mysterious three white spots, supporting the optical accuracy of the orb's rendering down to its fine-grain details.

When judging optical properties of a translucent object, humans often look at sharp geometric features such as edges and thin parts. Analysis of the physics of light transport shows that these sharp geometries are necessary for scientific imaging systems to be able to accurately measure the underlying material optical properties. In this paper, we examine whether human perception of translucency is likewise affected by the presence of sharp geometry, by confounding our perceptual inferences about an object's optical properties. We employ physically accurate simulations to create visual stimuli of translucent materials with varying shapes and optical properties under different illuminations. We then use these stimuli in psychophysical experiments, where human observers are asked to match an image of a target object by adjusting the material parameters of a match object with different geometric sharpness, lighting, and 3D geometry. We find that the level of geometric sharpness significantly affects perceived translucency by observers. These findings generalize across a few illumination conditions and object shapes. Our results suggest that the perceived translucency of an object depends on both the underlying material's optical parameters and 3D shape of the object. We also find that models based on image contrast cannot fully predict the perceptual results.

A debate in the scientific literature has arisen regarding whether the orb depicted in Salvator Mundi, which has been attributed by some experts to Leonardo da Vinci, was rendered in a optically faithful manner or not. Some hypothesize that it was solid crystal while others hypothesize that it was hollow, with competing explanations for its apparent lack of background distortion and its three white spots. In this paper, we study the optical accuracy of the Salvator Mundi using physically based rendering, a sophisticated computer graphics tool that produces optically accurate images by simulating light transport in virtual scenes. We created a virtual model of the composition centered on the translucent orb in the subject's hand. By synthesizing images under configurations that vary illuminations and orb material properties, we tested whether it is optically possible to produce an image that renders the orb similarly to how it appears in the painting. Our experiments show that an optically accurate rendering qualitatively matching that of the painting is indeed possible using materials, light sources, and scientific knowledge available to Leonardo da Vinci circa 1500. We additionally tested alternative theories regarding the composition of the orb, such as that it was a solid calcite ball, which provide empirical evidence that such alternatives are unlikely to produce images similar to the painting, and that the orb is instead hollow.

When judging material properties of a translucent object, we often look at sharp geometric features such as edges. Image analysis shows edges of translucent objects exhibit distinctive light scattering profiles. Around the edges of translucent objects, there is often a rapid change of material thickness, which provides valuable information for recovering material properties. It was found that perception of 3D shape is different between opaque and translucent objects. Here, we examine whether geometry affects the perception of translucent material perception.

The images used in the experiment are computer-generated using Mitsuba physically based renderer. The shape of an object is described as 2D height fields (in which each pixel contains the amount of extrusion from the object surface to the base plane). We varied both material properties and 3D shapes of the stimuli: for the former, we used materials with varying optical densities (used by the radiative transfer model) so that the object would have different levels of ground-truth translucency; for the latter, we applied different amounts of Gaussian blur to the underlying height fields. Seven observers finished a paired-comparison experiment where they viewed a pair of images that had different ground-truth translucency and blur levels. They were asked to judge which object appeared to be more translucent. We also included control conditions where the objects in both images have the same blur levels.

We found that when there was no difference in the level of blurring between the images, observers could discriminate material properties of the two objects well (mean accuracy = 81%). However, when the two objects differ in the blur level, all observers started to make more mistakes (mean accuracy = 71%). We conclude that observers’ sensitivity to translucent appearance is affected by the sharpness of the 3D geometry of the object, thus suggesting 3D shape affects material perception for translucency.