T-junctions: Cues for segmentation rather than for occlusion

In everyday situations, we experience a world of whole objects, even though many of these objects are partly occluded by each other. For instance, the stimulus at the left in the figure below could, in theory, have been caused by a red rectangle and a blue cross (which are the visible shapes), or by a red rectangle partly occluding a different blue object, or by a blue cross partly occluding a different red obkect. To predict whether humans perceive an interpretation involving a partly occluded object, and if so, how the visible part of this object is completed amodally (i.e., beyond the visual input) into a whole object, both local and global approaches have been proposed.




Local approaches, on the one hand, focus on the junctions where the visible edges of different objects meet -- at the top of the figure above, two so-called T-junctions are highlighted. According to local approaches, T-junctions are cues for occlusion, which implies, for the stimulus above, that the rectangle is predicted to be an occluder. Local approaches then predict further that the visible edges of the cross are continued smoothly behind the occluder until they meet, yielding a non-cross as whole object.

Global approaches, on the other hand, focus on the shapes of all combinations of candidate whole objects -- at the bottom of the figure above, the shapes of the visible cross and rectangle are highlighted. For each candidate whole object (be it a totally visible object or a partly occluded object), global approaches quantify the goodness-of-shape and then select the best-of-shape combination. In the stimulus above, the already visible cross and rectangle have a higher total goodness-of-shape than any other combination, so that global approaches predict no occlusion.

Does this mean that, according to global approaches, T-junctions are not relevant to amodal completion? No, but the amodal completion model within the global approach of SIT model leads to a nuanced answer along the following line of reasoning.

To explain amodal completion, this model considers all combinations of candidate whole objects. For each combination, it first quantifies the goodness-of-shape of the objects separately, namely, by the structural complexity of the simplest SIT code for each object. The sum of these complexities yields the total shape complexity I_shape. Then, for each combination, it quantifies the complexity of the relative position which the candidate objects would have in the stimulus, yielding the positional complexity I_position. Finally, the combination with the smallest sum I_shape + I_position is predicted to be the perceived stimulus interpretaton.

SIT's amodal completion model has been shown to have considerable predictive power. Without going into quantification details, the next figure shows its predictions for some stimuli. These stimuli consist of edges which, at their point of contact, form one of four different junction types (as highlighted by the circles). For each stimulus, the "two objects" hypothesis and the "one object" hypothesis are considered, and the boxes indicate the predicted interpretations.




Thus, for instance, the third stimulus (with an L-junction) is predicted to be perceived as one object (a hook), whereas the second stimulus (with a T-junction) is predicted to be perceived as two objects (two separate edges). These predictions have been confirmed empirically by Feldman (2007) and illustrate that a T-junction is a cue for segmentation, even if occlusion is not at hand.

Hence, if occlusion is at hand then, according to SIT's global approach, T-junctions are primarily cues for segmentation and not direct cues for occlusion. By consequence, to predict whether or not one the resulting segments is perceived as belonging to a partly occluded object, one must take into account the shapes of all candidate whole objects.


For further demos on these issues, see Object versus viewer and Occam, von Helmholtz, and Bayes

For a further discussion on this specific issue, see Acta Psychologica 2011
For a full account of SIT's amodal completion model, see Perception 1994
For a multidisciplinary and historical embedding of this occlusion model, see Psychological Bulletin 2000