In our visual world, objects usually occlude parts of themselves and parts of other objects. Yet we do not have the idea of being surrounded with just object fragments. Somehow, the visual system is able to give us the impression of complete objects. In such cases, perceptual interpretations clearly exceed the information that is present in the retinal image.

In Fig. 1A, a typical textbook example of visual occlusion is shown. In principle, this pattern could be interpreted in many different ways. Usually, observers prefer a partly occluded square, which is preferred to other possible interpretations such as the ‘mosaic’ or a rather arbitrary completion. This phenomenon of occlusion was first studied by Chapanis and McCleary (1953); Dinnerstein and Wertheimer (1957) and Michotte, Thinès, and Crabbé (1964). The latter scientists specifically studied the apparent ability of the visual system to fill in the missing or occluded parts and referred to it with the – still frequently used – term ‘amodal completion’. Nowadays, the study of amodal completion receives considerable attention and is recognized more and more as a fundamental issue in visual perception.

One way to investigate preferred completions is to just ask observers to draw their interpretation of occlusion patterns. This procedure has the advantage of obtaining many different spontaneous interpretations but has the disadvantage of potential sensitivity to irrelevant task influences (e.g., drawing capacities). In other studies the perceptual relevance of amodal completion has been tested by more refined experimental paradigms. For example, Gerbino and Salmaso (1987) showed the functional equivalence of partly occluded shapes and complete shapes by means of a simultaneous matching task. On the basis of their experimental results, Gerbino and Salmaso (1987) argued that partly occluded shapes were perceived as complete by means of a possible ‘automatic transformation of the visual code’. Additionally, Sekuler and Palmer (1992) studied the time course of completion by means of the primed matching paradigm. Their main result was that within a short period of time (as short as 200 ms) a partly occluded figure is perceptually represented as complete.

We take the above as support for the perceptual relevance of amodal completion (further on in this paper we will briefly return to this issue) and focus on the figural properties that determine completion. Our starting point here is the observation that when looking at a pattern such as in Fig. 1, most observers have a clear preference for one specific occlusion interpretation. Generally, there is broad consensus and consistency with respect to the preferred completions. To explain and predict perceived completions, a distinction between ‘local’ and ‘global’ accounts has often been made in the literature. In the following, I will first briefly discuss the impact of local and global figural properties and after that examine their impact on two potential extensions of the (hitherto) rather limited stimulus domain in amodal completion research.

Local accounts strongly rely on the impact of local cues such as specific discontinuities of contours at points of occlusion. As a proponent of a local account, Kanizsa, 1975; Kanizsa, 1979 and Kanizsa, 1985 emphasized the role of Good Continuation in amodal completion, generally taking place at so-called T-junctions. Rock (1983) implicitly accounted for the effect of T-junctions by stating that the visual system avoids a coincidental meshing of borders: Generally, a continuation of the occluding contour at a T-junction avoids such a coincidental meshing. In recent years, Kellman and Shipley (1991) greatly influenced completion research by means of the so-called relatability criterion. This criterion predicts completion by a smooth curve whenever virtual linear extensions of contours meet behind the occluding surface at angles equal or larger than 90°.

In a critical review, however, Boselie and Wouterlood (1992) pointed out several drawbacks of the relatability criterion, and additionally demonstrated that the relatability criterion does not always predict the perceived shape correctly. Their counterexamples fall into classes such as ‘relatable edges, but no completion perceived’ and ‘non-relatable edges, but completion perceived’. Moreover, the status of linear extensions, coterminating in one common angle, as in the ‘square’ interpretation of Fig. 1, is not clear in Kellman and Shipley’s model. In addition, Wouterlood and Boselie (1992) developed their own local completion model, exclusively based on the principle of Good Continuation. Depending on the type of junctions between two surfaces, their model predicts either a mosaic of surfaces or a completion of one of the surfaces. In the latter case the completion always proceeds by means of a linear extension of the contours. In spite of their local account, Wouterlood and Boselie (1992) acknowledged the influence of pattern regularities on the perceptual outcome. To avoid regularity-based influences they therefore restricted the predictive domain of their model to completely irregular patterns. So, in fact, the example of Fig. 1 lies outside the stimulus domain for which Wouterlood and Boselie’s (1992) model has been designed.

In contrast to local approaches, global approaches take into account shape regularities such as symmetries. Within Structural Information Theory (SIT), initiated by Leeuwenberg, 1969 and Leeuwenberg, 1971 and further developed since then, this tendency has been operationalized by means of a regularity-based coding system. Within SIT, visual patterns are encoded by means of three different coding rules; Iteration, Symmetry and Alternation, and proceeds as follows. First, the encoding of a visual shape requires a mapping of the shape to a symbol series. Heuristically, this can be done by tracing the contour of the shape after having labelled all edges and angles such that equal edges and equal angles obtain equal symbols. Second, the symbol series is reduced by extracting the maximum amount of regularity from such a series (e.g., the symbol series aaaa can be encoded into 4*(a) by means of the Iteration rule; the series abba into S[(a)(b)] by the Symmetry rule; and the series akal into left angle bracket(a)right-pointing angle bracket/left angle bracket(k)(l)right-pointing angle bracket by the Alternation rule). Third, the interpretation with the simplest code, or the smallest amount of descriptive parameters, is predicted to be preferred. It should be noted here that the SIT account is not to be taken as an actual process account, but rather as an operational tool to determine regularity-based rankings of alternative pattern interpretations.