Transparency Interpretation of X Junctions

Eric Saund, Ph.D.

An X-Junction occurs in an image when a semi-transparent object lies in front of an object boundary.

The chair is occluded by a semi-transparent panel. The panel gets blurry near the bottom. Here, we are concerned with the X-junction found at the clear, tinted part of the glass near the top. What about this scene makes it appear that that the tinted panel is placed in front of the chair?

This javascript app explores the interpretation of surface lightnesses at X-junctions. The app implements a theory for how people will interpret configurations of lighter and darker regions as semitransparent occluding surfaces.

Psychophysicists have proposed an "atmospheric" model for surface lightness perception. The lightness of a surface patch is interpreted as a combination of the lightness of some underlying surface, and a contribution from an occluding, semitransparent surface. Metelli's law states:


Sometimes an additive term is appended to the model.

This model can be applied to X-junctions under the assumption that some underlying contrast edge (p q) is partially occluded by a semitransparent surface resulting in lightnesses (r s).

While the model applies to color surfaces and occluders as well, this illustration uses color for illustrative purposes only. The demo applet deals only with grayscale lightness.

Adelson and Anandan noted that depending on the behavior of contrast signs as a lightness boundary is traversed through an X-junction, one of three conditions holds: a semitransparent overlap interpretation is possible in one, both, or neither direction. In other words, under some combinations of lightnesses, the pair (q s), or others, could be interpreted as being seen through an occluding semitransparent surface.

The applet demonstrates this atmospheric model for the interpretation of transparency at an X-junction. Depending on the relative lightnesses, a valid occluder could be a circle, a hole, or a rectangular strip.

Notes and Observations

This kind of analysis will be required to extend computational models of the perceptual organization of occluding surfaces to images containing X-junctions, which provide cues for surface transparency.