The art of transparency

Artists throughout the ages have discovered a number of techniques to depict transparency. With only a few exceptions, these techniques follow closely the properties of physical transparency. The two best known properties are X-junctions and the luminance relations described by Metelli. X-junctions are seen where the contours of a transparent material cross contours of the surface behind; Metelli's constraints on the luminance relations between the direct and filtered portions of the surface specify a range of luminance values that are consistent with transparency. These principles have been used by artists since the time of ancient Egypt. However, artists also discovered that stimuli can be seen as transparent even when these physical constraints are not met. Ancient Greek artists, for example, were able to depict transparent materials in simple black-and-white line drawings. Artists also learned how to represent transparency in cases where neither X-junctions nor Metelli's constraints could apply: for example, where no portions of the objects behind the transparent material extend beyond it. Many painters convincingly portrayed transparency in these cases by depicting the effects the transparent medium would have on material or object properties. Here, we show how artists employed these and other techniques revealing their anticipation of current formalizations of perceived transparency, and we suggest new, as-yet-untested principles.