Filling-in models of completion: rejoinder to Kellman, Garrigan, Shipley, and Keane (2007) and Albert (2007)

There has been a growing interest in understanding the computations involved in the processes underlying visual segmentation and interpolation in conditions of occlusion. P. J. Kellman, P. Garrigan, T. F. Shipley, and B. P. Keane and M. K. Albert defended the view that identical contour interpolation mechanisms underlie modal and amodal completion. In the current rejoinder, the author provides further psychophysical evidence against this view and argues that no physiological data support the claim that modal and amodal contours are represented identically at any stage of processing. The author also shows that the illusory glass surfaces that Kellman et al. and Albert upheld as evidence against his arguments about luminance constraints in completion are explained by theoretical principles that he has previously articulated, and variants of these illusions receive no explanation within either of the models Kellman et al. and Albert propose. The author shows that the principles needed to explain these percepts embody fundamental asymmetries in the way that relative depth shapes segmentation and interpolation processes and that models of completion that lack these constraints--such as P. J. Kellman, P. Garrigan, and T. F. Shipley's and M. K. Albert's --cannot account for a host of documented completion phenomena.     

The interpolation of object and surface structure

One of the main theoretical challenges of vision science is to explain how the visual system interpolates missing structure. Two forms of visual completion have been distinguished on the basis of the phenomenological states that they induce. Modal completion refers to the formation of visible surfaces and/or contours in image regions where these properties are not specified locally. Amodal completion refers to the perceived unity of objects that are partially obscured by occluding surfaces. Although these two forms of completion elicit very different phenomenological states, it has been argued that a common mechanism underlies modal and amodal boundary and surface interpolation (the "identity hypothesis"; Kellman & Shipley, 1991; Kellman, 2001). Here, we provide new data, demonstrations, and theoretical principles that challenge this view. We show that modal boundary and surface completion processes exhibit a strong dependence on the prevailing luminance relationships of a scene, whereas amodal completion processes do not. We also demonstrate that the shape of interpolated contours can change when a figure undergoes a transition from a modal to an amodal appearance, in direct contrast to the identity hypothesis. We argue that these and previous results demonstrate that modal and amodal completion do not result from a common interpolation mechanism.     

Mechanisms of modal and amodal interpolation

P. J. Kellman and T. F. Shipley (1992) and P. J. Kellman, P. Garrigan, and T. F. Shipley (2005) suggested that completion of partly occluded objects and illusory objects involve the same or similar mechanisms at critical stages of contour interpolation. B. L. Anderson, M. Singh, and R. W. Fleming and B. L. Anderson (2007) presented a number of arguments against this view. The author analyzes 3 of these arguments, as well as B. L. Anderson's ecological justification for believing that these mechanisms must be very different, and suggests that their conclusions are unwarranted. The author also outlines a model consistent with the identity hypothesis and with recent physiological evidence, including a quantitative proposal for contour interpolation strength. The model suggests that V1 and V2 receive from higher visual areas feedback that modulates their responses to stimuli eliciting modal completion, amodal completion, and collinear contour facilitation. The model qualitatively explains the unstable percepts evoked by various recently devised stimuli.     

Interpolation processes in object perception: reply to Anderson (2007)

P. J. Kellman, P. Garrigan, & T. F. Shipley presented a theory of 3-D interpolation in object perception. Along with results from many researchers, this work supports an emerging picture of how the visual system connects separate visible fragments to form objects. In his commentary, B. L. Anderson challenges parts of that view, especially the idea of a common underlying interpolation component in modal and amodal completion (the identity hypothesis). Here the authors analyze Anderson's evidence and argue that he neither provides any reason to abandon the identity hypothesis nor offers a viable alternative theory. The authors offer demonstrations and analyses indicating that interpolated contours can appear modally despite absence of the luminance relations, occlusion geometry, and surface attachment that Anderson claims to be necessary. The authors elaborate crossing interpolations as key cases in which modal and amodal appearance must be consequences of interpolation. Finally, the authors dispute Anderson's assertion that vision researchers are misguided in using objective performance methods, and they argue that his challenges to relatability fail because contour and surface processes, as well as local and global influences, have been distinguished experimentally.     

Boundary completion, contrast polarity, and the perception of illusory tilt

What we perceive as a unitary object can be the result of integrative processes that generate a whole from parts. Although this issue of visual perception has been widely explored, recent experimental findings demonstrate that our knowledge is still incomplete. In particular, the question whether contour binding is affected by the sign of contrast (contrast polarity) across edges requires more in-depth examination. Here we show the effects of edge bindings that originate from the merging of laterally displaced edges with the same contrast polarity. We have studied a particular context in which such effects may emerge: a checkerboard with a series of alternated dark and light shapes superimposed on the corners of the squares. The phenomenal observations and experimental findings support the theories according to which boundary completions are originated by phenomena of edge propagation within a 'field of completion' (eg Shipley and Kellman, 2003 Perception 32 985-999) adjacent to an edge ending. Our findings conform to the Shipley and Kellman theory that boundary completion results from the interaction of edges as well as from edges and shapes lacking in oriented contours, the latter serving as 'receiving units', anchoring the paths of activations generated by oriented edges. We propose to integrate this theory with the hypothesis that interactions sensitive to the contrast sign generate conjunction paths of edges that alter their perceived orientation. Based on this perspective we propose an alternative account for the Café Wall illusion that can be extended to other phenomena of orientation misperception and to a Café Wall inversion effect that has not been observed previously.     

Complete mergeability and amodal completion.

When image fragments are taken to correspond to the visible portions of a single occluded object, the object is said to 'amodally complete' behind the occluder. Kellman and Shipley (Kellman, P. J., & Shipley, T. F. (1991). A theory of visual interpolation in objective perception. Cognitive Psychology, 23, 144-221) argued that when the virtual contour extensions of such image fragments subtend an obtuse or right angle, the contours are 'relatable' and therefore complete. However, edge and surface relatability are neither necessary nor sufficient for completion to be perceived (Tse, P. U. (1999) Volume completion. Cognitive Psychology). Evidence is offered that completion is not driven directly by image cues such as contour relatability, but is driven, rather, by intermediate representations, such as volumes that are inferred from global image cue relationships. Evidence suggests that several factors, none of which is necessary for amodal completion to occur, contribute to the perceived strength of amodal completion, including similarity of pattern or substance, proximity, and good volume continuation or complete mergeability. Two partially occluded volumes are completely mergeable when they can be extended into occluded space along the trajectory defined by their visible surfaces such that they merge entirely with each other. Mergeability is not measurable in the image because it describes an inferred relationship among volumes that must themselves be inferred from the image.     

The role of discontinuities in the perception of subjective figures

Recently we proposed a theory of visual interpolation (Kellman & Shipley, in press) that addresses a variety of unit formation phenomena, including the perception of partly occluded objects and subjective figures. A basic notion of the theory is that discontinuities in the first derivative of projected edges are the initiating conditions for interpolation of boundaries that are not physically specified. In this paper, we report four experiments in which this claim was tested in the domain of subjective figures. Experiments 1 and 2 demonstrate that discontinuities in the first derivative of the edges of inducing elements have a clear effect on the frequency of report and the perceived clarity of simple subjective figures. Similar effects are found when unfamiliar subjective figures and inducing elements are used (Experiment 3). Experiment 4 rules out the possibility that the discontinuities in the first derivative merely add to the clarity of subjective figures. These experiments suggest that first-order discontinuities play a central role in unit formation.     

Modal and amodal completion generate different shapes

Mechanisms of contour completion are critical for computing visual surface structure in the face of occlusion. Theories of visual completion posit that mechanisms of contour interpolation operate independently of whether the completion is modal or amodal--thereby generating identical shapes in the two cases. This identity hypothesis was tested in two experiments using a configuration of two overlapping objects and a modified Kanizsa configuration. Participants adjusted the shape of a comparison display in order to match the shape of perceived interpolated contours in a standard completion display. Results revealed large and systematic shape differences between modal and amodal contours in both configurations. Participants perceived amodal (i.e., partly occluded) contours to be systematically more angular--that is, closer to a corner--than corresponding modal (i.e., illusory) contours. The results falsify the identity hypothesis in its current form: Corresponding modal and amodal contours can have different shapes, and, therefore, mechanisms of contour interpolation cannot be independent of completion type.     

Ethnic group identification and group evaluation among minority and majority groups: testing the multiculturalism hypothesis

Following social identity theory, the author hypothesized that members of minority groups are more likely than majority group members to endorse multiculturalism more strongly and assimilationist thinking less strongly. In addition, the multiculturalism hypothesis proposes that the more minority groups endorse the ideology of multiculturalism (or assimilationism), the more (or less) likely they will be to identify with their ethnic in-group and to show positive in-group evaluation. In contrast, the more majority group members endorse multiculturalism (or assimilationism), the less (or more) likely they are to identify with their ethnic group and to show negative out-group evaluation. Results from 4 studies (correlational and experimental) provide support for this hypothesis among Dutch and Turkish participants living in the Netherlands.     

Object interpolation in three dimensions

Perception of objects in ordinary scenes requires interpolation processes connecting visible areas across spatial gaps. Most research has focused on 2-D displays, and models have been based on 2-D, orientation-sensitive units. The authors present a view of interpolation processes as intrinsically 3-D and producing representations of contours and surfaces spanning all 3 spatial dimensions. The authors propose a theory of 3-D relatability that indicates for a given edge which orientations and positions of other edges in 3 dimensions may be connected to it, and they summarize the empirical evidence for 3-D relatability. The theory unifies and illuminates a number of fundamental issues in object formation, including the identity hypothesis in visual completion, the relations of contour and surface processes, and the separation of local and global processing. The authors suggest that 3-D interpolation and 3-D relatability have major implications for computational and neural models of object perception.     

A critical discussion of Kellman and Shipley's (1991) theory of occlusion phenomena

Summary Kellman and Shipley (1991) recently advanced a new theory to explain the perception of partly occluded objects and illusory figures. The theory is a formalization of the Gestalt law of good continuation. In this paper we describe their account of occlusion when the contour of the occluded is completely specified by a display. Next, we outline some critical objections and present a number of counterexamples. Finally, we compare their theory with Wouterlood and Boselie's (in this issue) model of occlusion phenomena, which might also be considered as a formalization of the law of good continuation.     

Women,Men, and Persons: A Response to "Feminist Perspectives on Erikson's Theory: Their Relevance for Contemporary Identity Development Research"

The search for the structure of identity formation is a necessary undertaking for the comprehension of identity, identity changes, and identity development. This article attempts to show that the identification of structure and structural stages of identity implies a movement away from the identity status model.We support and clarify our claim by discussing how Kroger's (this issue) definition of the concepts of structure and structural stages in relation to the identity status model leads to serious restrictions in these concepts. The concept of structural integration is introduced as an alternative interpretation and definition of the structure of identity formation. The definition and theoretical implications of the concept of structural integration are clarified and related to other recent conceptual and empirical analyses of identity theory and research.We then go on to show how the concept of structural integration can be studied in empirical research.     

流动儿童歧视知觉与社会文化适应：社会支持和社会认同的作用

采用整群取样方法对选自北京市的1164名流动儿童进行问卷调查, 考察社会支持、社会认同在歧视知觉与社会文化适应关系中的作用。结果表明, 流动儿童的歧视知觉整体上并不明显, 其社会文化适应状况整体良好; 歧视知觉对社会文化适应有显著负向预测性(β=-0.39, p<0.001); 在歧视知觉与社会文化适应的负向预测关系中, 社会支持起部分中介作用, 城市认同有增强作用, 老家认同有缓冲作用; 社会支持的中介作用受到城市认同、老家认同的调节。     

Amodal completion, depth stratification, and illusory figures: a test of Kanizsa's explanation.

Subjective contours have been explained by Kanizsa as being a consequence of amodal completion of incomplete figures. According to the theory of amodal completion, figural incompleteness triggers the emergence of an illusory object superimposed on the gaps in the inducers, which in turn hide parts of the pattern, thus suggesting that the plane of the illusory object must always be seen to be above the plane of the inducers. A figure was created in which subjective contours are seen despite the fact that the perceived depth relationships run counter to that required by the theory of amodal completion. In four experiments, this depth relationship is confirmed by using direct and indirect measures which assess both registered and apprehended depth. By emphasizing a logical inconsistency in the explanation based on amodal completion, the results show that amodal completion, at least in Kanizsa-like patterns, cannot be considered as a causal factor for subjective contour figures.     

A theory of dynamic occluded and illusory object perception

Humans see whole objects from input fragmented in space and time, yet spatiotemporal object perception is poorly understood. The authors propose the theory of spatiotemporal relatability (STR), which describes the visual information and processes that allow visible fragments revealed at different times and places, due to motion and occlusion, to be assembled into unitary perceived objects. They present a formalization of STR that specifies spatial and temporal relations for object formation. Predictions from the theory regarding conditions that lead to unit formation were tested and confirmed in experiments with dynamic and static, occluded and illusory objects. Moreover, the results support the identity hypothesis of a common process for amodal and modal contour interpolation and provide new evidence regarding the relative efficiency of static and dynamic object formation. STR postulates a mental representation, the dynamic visual icon, that briefly maintains shapes and updates positions of occluded fragments to connect them with visible regions. The theory offers a unified account of interpolation processes for static, dynamic, occluded, and illusory objects.     

Volume completion.

The visual system completes image fragments into larger regions when those fragments are taken to be the visible portions of an occluded object. Kellman and Shipley (1991) argued that this "amodal" completion is based on the way that the contours of image fragments "relate." Contours relate when their imaginary extensions intersect at an obtuse or right angle. However, it is shown here that contour relatability is neither necessary nor sufficient for completion to take place. Demonstrations that go beyond traditional examples of overlapping flat surfaces reveal that "mergeable" volumes, rather than relatable contours, are the critical elements in completion phenomena. A volume is defined as a 3-D enclosure. Typically, this refers to a surface plus the inside that it encloses. Two volumes are mergeable when their unbounded visible surfaces are relatable or the insides enclosed by those surfaces can completely merge. Two surfaces are relatable when their visible portions can be extended into occluded space along the trajectories defined by their respective curvatures so that they merge into a common surface. A volume-based account of amodal completion subsumes surface completion as a special case and explains examples that neither a contour- nor a surface-based account can explain.     

Ingroup bias,self-enhancement and group identification

These two studies integrate self-enhancement and ingroup bias and analyse the phenomena from the social identity theory and self-categorization theory. In Study 1, the subjects (N=181) evaluated supporters of two presidential candidates on a rating scale. In Study 2, the subjects (N=302) evaluated either Finnish women's and men's positive characteristics (success condition) or negative characteristics (failure condition) which might play a role in achieving equality between the sexes in Finland. Self-evaluations were conducted on the same scale as those of ingroup and outgroup evaluations. The results showed that ingroup was evaluated more positively than outgroup (hypothesis 1) and that self was evaluated more positively than ingroup (in Study 2, however, this main effect was qualified by gender). As expected, group identification did not dilute self-enhancement (hypothesis 2) in either of the studies but strengthened self-enhancement in Study 1. Hypothesis 3 stated that self-enhancement is inversely related to ingroup favouritism but the hypothesis was only partially confirmed in that the correlation was predictably negative in Study 1 but near zero in both conditions of Study 2. Finally, contrary to hypothesis 4, it turned out that high identified group members evaluated self and ingroup more independently than lows which contradicts the idea of depersonalization. Together the results would be plausible if we rejected the unidimensional conception of interpersonal–intergroup behaviour and assumed instead that interpersonal and intergroup behaviour constitute two bipolar continua. © 1997 by John Wiley & Sons, Ltd.     

When does goal discrepancy induce compensatory effort? An application of self‐completion theory to social issues

The authors review research that applies self‐completion theory to goals targeting other people (as in the case of stereotyping and prejudice), goals that aim at the achievement of a certain social identity and goals based on the social identity. It is demonstrated that goal discrepancies lead to compensation for social as well as for non‐social goals. Based on self‐completion theory it is proposed that the identity‐relevance of the respective goal as well as the goal relevance of the subsequent task are of major importance considering the individuals’ compensation. The authors argue that the consideration of these factors advance our understanding of social phenomena.     

SPREADING OF VISUAL ATTENTION TO MODALLY VERSUS AMODALLY COMPLETED REGIONS

Abstract— Regions of objects that are partially obscured at the current retinal image are often perceptually filled in by the visual system (Kanizsa, 1979). In some cases (modal completion), this causes the filled-in region to appear tinged with the color and brightness of unobscured parts of that object, but m other cases (amodal completion), it does not (Michotte & Burke, 1951). It has recently been argued that modal and amodal completion both arise in preattentive vision, and may operate equivalently at that level (Davis & Driver, 1994, He & Nakayama, 1992, Shipley & Kellman, 1992). In this article, we show that they have different effects on attentive vision, with attention tending to spread to (and from) modally completed regions and their visible inducers, but not to (or from) comparable amodally completed regions and their inducers. This finding is consistent with visual attention operating on surfaces (e g, He & Nakayama, 1995) in a viewer-centered representation of the scene, after the operation of filling-in processes.     

On the Possibility of Inference to the Best Explanation

Various proposals have suggested that an adequate explanatory theory should reduce the number or the cardinality of the set of logically independent claims that need be accepted in order to entail a body of data. A (and perhaps the only) well-formed proposal of this kind is William Kneale’s: an explanatory theory should be finitely axiomatizable but it’s set of logical consequences in the data language should not be finitely axiomatizable. Craig and Vaught showed that Kneale theories (almost) always exist for any recursively enumerable but not finitely axiomatizable set of data sentences in a first order language with identity. Kneale’s criterion underdetermines explanation even given all possible data in the data language; gratuitous axioms may be “tacked on.” Define a Kneale theory, T, to be logically minimal if it is deducible from every Kneale theory (in the vocabulary of T) that entails the same statements in the data language as does T. If they exist, minimal Kneale theories are candidates for best explanations: they are “bold” in a sense close to Popper’s; some minimal Kneale theory is true if any Kneale theory is true; the minimal Kneale theory that is data equivalent to any given Kneale theory is unique; and no Kneale theory is more probable than some minimal Kneale theory. I show that under the Craig-Vaught conditions, no minimal Kneale theories exist.