The art of transparency

Abstract

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.

Keywords: highlights; material perception; perception; transparency; visual art.

Figure 1.

(a) Photograph of a paintbrush in a transparent glass half filled with water. Refraction by the water produces a discontinuity in the brush. (b) The photograph is altered to remove the effect of refraction, but transparency is still perceived.

Figure 2.

(a) Single-reversing junction where the lower square is normally seen as transparent and in front of the darker square on the farther surface. The red cross indicates an X-junction. (b) Non-reversing junction where either square may be seen as transparent and in front of the other. (c) Double-reversing junction where no transparency is seen. (d) The disc with X-junctions appears transparent. (e) Shifting the halves of the disc removes the X-junctions and eliminates the perception of transparency. Inequality signs in panels (a) through (d) indicate the luminance relations between adjacent surfaces, oriented in accordance with the corresponding boundary.

Figure 3.

Ancient Egyptian art. Tomb of Jesekaresneb, 18th Dynasty (c. 1550–1292 BC). Logical operators indicate the luminance relations between adjacent surfaces (inequality signs are oriented in accordance with the corresponding boundary).

Figure 4.

Portrait of a Lady (c. 1460) by Rogier van der Weyden. Inequality signs indicate the luminance relations between adjacent surfaces (oriented in accordance with the corresponding boundary).

Figure 5.

Some of the depicted forms appear transparent. Wassily Kandinsky's On White II (1923). Inequality signs indicate the luminance relations between adjacent surfaces (oriented in accordance with the corresponding boundary).

Figure 6.

An example of failed transparency, Mosaic of Nereis Riding Hippokampus, Imperial Roman period.

Figure 7.

Transparency perception achieved without following luminance constraints. Greek red-figure pottery (c. 530–560).

Figure 8.

It is perceptually unclear whether the front window contains glass or not. Nighthawk (1942) by Edward Hopper.

Figure 9.

Highlights are the main indicator for the presence of a transparent material covering the fruit. Roman Fresco, Pompeii.

Figure 10.

The visibility of the edge is the main indicator for the presence of a transparent sphere. Although physically incorrect, the reflections still support the perception of transparency. From The Gardens of Aedena (1988) by Moebius.

Figure 11.

Characteristic reflection patterns are often found in sheer materials, such as sheer curtains, where folds modulate how much light passes through or is reflected from the material. (a) An underskirt can be seen through the sheer red robe. Hua Qing in Her Bath by Kang Tao (1723–1795). (b) The material the woman holds in her hand appears transparent, although there are no X-junctions. Fresco, Pompeii.

Figure 12.

Left panel: Central figure of Ghent Altar (1425) by Jan van Eyck. Right panel: Detail of the transparent scepter.

Figure 13.

Object-based inference: It looks like a person diving in a swimming pool. He must be seen through transparent water. Portrait of an Artist (Pool with Two Figures) (1972) by David Hockney.

Figure 14.

Object-based inferences are key for perceiving the bowl as transparent. Fresco in the Villa di Poppea in Oplontis (c. 70 AD).

Figure 15.

Object knowledge can be overruled by other cues. Here, color, texture, and the object-based inference that the red object at the position of the man must be a seat like all the others overrules knowledge of the opaqueness of human bodies. Teatro alla Scala (2010) by Liu Bolin.