In 1912, Max Wertheimer published his paper on phi motion, widely recognized as the start of Gestalt psychology. Because of its continued relevance in modern psychology, this centennial anniversary is an excellent opportunity to take stock of what Gestalt psychology has offered and how it has changed since its inception. We first introduce the key findings and ideas in the Berlin school of Gestalt psychology, and then briefly sketch its development, rise, and fall. Next, we discuss its empirical and conceptual problems, and indicate how they are addressed in contemporary research on perceptual grouping and figure-ground organization. In particular, we review the principles of grouping, both classical (e.g., proximity, similarity, common fate, good continuation, closure, symmetry, parallelism) and new (e.g., synchrony, common region, element and uniform connectedness), and their role in contour integration and completion. We then review classic and new image-based principles of figure-ground organization, how it is influenced by past experience and attention, and how it relates to shape and depth perception. After an integrated review of the neural mechanisms involved in contour grouping, border ownership, and figure-ground perception, we conclude by evaluating what modern vision science has offered compared to traditional Gestalt psychology, whether we can speak of a Gestalt revival, and where the remaining limitations and challenges lie. A better integration of this research tradition with the rest of vision science requires further progress regarding the conceptual and theoretical foundations of the Gestalt approach, which is the focus of a second review article. Johan Wagemans was supported by the Methusalem program from the Flemish Government (METH/08/02) for a research program aimed at the integration of Gestalt psychology into modern vision science (see www .gestaltrevision.be) and by fellowships from the Research Fund (FWOFlanders) and from IEA-Paris during his sabbatical. James H. Elder was supported by NSERC, OCE, and GEOIDE. Michael Kubovy was supported by National Science Foundation (NSF) Grants BCS 1027120 and 1027259. Stephen E. Palmer was supported by NSF Grants BCS 1059088 and 0745820. Mary A. Peterson was supported by NSF Grant BCS0960529. Manish Singh was supported by National Institutes of Health (NIH) Grant EY021494 (joint with Jacob Feldman) and NSF Grant DGE 0549115 (Rutgers IGERT in Perceptual Science). Rüdiger von der Heydt was supported by NIH Grants EY02966 and EY16281 and by Office of Naval Research Grant N000141010278. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies. We would like to thank Stephanie Poot for administrative help with the reference list, the copyrights, and the layout, as well as M. Dorothee Augustin, Wouter Braet, Peter Claessens, Maarten Demeyer, Lee deWit, Sergei Gepshtein, Frouke Hermens, Ruth Kimchi, Ervin Poljac, Peter Van der Helm, and Cees van Leeuwen for comments on previous drafts. Correspondence concerning this article should be addressed to Johan Wagemans, University of Leuven (KU Leuven), Laboratory of Experimental Psychology, Tiensestraat 102, Box 3711, BE-3000 Leuven, Belgium. E-mail: johan.wagemans@psy.kuleuven.be Psychological Bulletin © 2012 American Psychological Association 2012, Vol. 138, No. 6, 1172-1217 0033-2909/12/$12.00 DOI: 10.1037 1172 Exactly 100 years ago, Wertheimer (1912) published his paper on phi motion-perception of pure motion, without object motion-which many consider to be the beginning of Gestalt psychology as an important school of thought. The present status of Gestalt psychology is ambiguous. On the one hand, many psychologists believe that the Gestalt school died with its founding fathers in the 1940s or after some devastating empirical findings regarding electrical field theory in the 1950s, or that it declined because of fundamental limitations that blocked further progress, while stronger theoretical and experimental frameworks arose in the 1960s and 1970s that have dominated the field ever since (e.g., cognitive science, neuroscience). On the other hand, almost all psychology textbooks still contain a Gestalt-like chapter on perceptual organization (although often poorly connected to the other chapters), and new empirical papers on Gestalt phenomena appear with increasing frequency. We are convinced that Gestalt psychology is still relevant to current psychology in several ways. First, questions regarding the emergence of structure in perceptual experience and the subjective nature of phenomenal awareness (e.g., visual illusions, perceptual switching, context effects) continue to inspire contemporary scientific research, using methods and tools that were not at the Gestaltists' disposal. Second, the revolutionary ideas of the Gestalt movement continue to challenge some of the fundamental assumptions of mainstream vision science and cognitive neuroscience (e.g., elementary building blocks, channels, modules, informationprocessing stages). Much progress has been made in the field of nonlinear dynamical systems, both theoretically and empirically (e.g., techniques to measure and analyze cortical dynamics), progress that allows modern vision scientists to surpass some of the limitations in old-school Gestalt psychology as well as those in mainstream vision research. The centennial anniversary of Gestalt psychology is therefore an excellent opportunity to take stock of what we have discovered about core Gestalt phenomena of perceptual organization and how our understanding of the underlying mechanisms has evolved since Wertheimer's seminal contribution. Due to this review's scope, we divide it in two parts: This article deals with perceptual grouping and figure-ground organization, whereas the second covers modern developments regarding the general conceptual and theoretical frameworks that underlie Gestalt ideas (e.g., holism, emergence, dynamics, simplicity). In Table 1 , we provide an overview of the topics covered in the first review article, together with the section headings, the questions or issues being raised, and some of the answers provided. One of the aims of our review is to remove the many misunderstandings surrounding Gestalt psychology, which are listed separately in Table 2 , along with a more balanced view on the actual state of affairs. To put these two reviews in perspective, we first introduce the key findings and ideas of the founders of Gestalt psychology, along with a brief sketch of its further development, rise, and fall (for an extensive treatment, see Ash, 1995) . The historical section ends with a discussion of Gestalt psychology's empirical and conceptual problems and an indication of how these limitations are being addressed in current research. We then review current research on perceptual grouping and figure-ground organization in more detail in the remaining sections. We focus on these two topics because they were the most important ones in the Gestalt tradition of perceptual organization and still are today, even for vision in general. This section addresses four questions regarding Gestalt psychology: (a) How did it start? (b) What does it stand for? (c) How did it evolve? (d) Where does it stand now? What Max Wertheimer discovered in 1912 was called phi motion, a special case of apparent motion. (For an excellent discussion of its historical importance, see R. Sekuler, 1996 ; for a demonstration of the phenomenon and for a review of its misrepresentation in later sources, see Steinman, Pizlo, & Pizlo, 2000.) According to the conventional view of apparent motion, we see an object at several successive positions and motion is then added subjectively. If this were correct, then an object would have to be seen as moving, and at least two positions-the starting and end points-would be required to produce seen motion. Neither of these conditions held in the case of phi motion. In the key experiment, a white strip was placed on a dark background in each of two slits in the wheel of a tachistoscope, and the rotation speed was adjusted to vary the time required for the light to pass from one slit to the next (i.e., the interval between the two). Above a certain threshold value (ϳ200 ms), observers saw the two lines in succession. With much shorter intervals (ϳ30 ms), the two lines appeared to flash simultaneously. At the optimal stage (ϳ60 ms), observers perceived a motion that could not be distinguished from real motion. When the interval was decreased slightly below 60 ms, after repeated exposures, observers perceived motion without a moving object-that is, pure phenomenal or phi motion. Although only three observers were tested, "the characteristic phenomena appeared in every case unequivocally, spontaneously, and compellingly" (Wertheimer, /1961 (Wertheimer, , p. 1042. In the same paper, Wertheimer proposed a physiological model described in terms of a short circuit and a flooding back of the current flow ("transverse functions of a special kind;" Wertheimer, /1961 Wertheimer, , p. 1085, which produced what he called "a unitary continuous whole-process" (Wertheimer, /1961 (Wertheimer, , p. 1087. He then extended this theory to the psychology of pure simultaneity (for the perception of form or shape) and of pure succession (for the perception of rhythm or melody). These extensions were decisive for the emergence of Gestalt theory. The phi phenomenon was the perception of a pure process, a transition that could not be composed from more primitive percepts of a single object at two locations. In other words, perceived motion was not added subjectively after the sensory registration of two spatiotemporal events but had its own phenomenological characteristics and ontological status. From this phenomenon, Wertheimer concluded that structured wholes or Gestalten, rather than sensations, are the primary units of mental life. This was the key idea of the new and revolutionary Gestalt theory, developed by Wertheimer and his colleagues in Berlin. An overview of how the 1173 100 YEARS OF VISUAL GESTALTS: I Berlin school of Gestalt psychology distinguished itself from the dominant view of structuralism and empiricism, as well as of related Gestalt schools, is given in Table 3 . The notion of Gestalt had already been introduced into psychology by Christian von Ehrenfels in his essay "On Gestalt Qualities" (1890/1988). Based on the observation that humans can recognize two melodies as identical even when no two corresponding notes in them have the same frequency, von Ehrenfels argued that these forms must possess a "Gestalt quality"-a characteristic that is immediately given, along with the elementary sensations that serve as its foundation, a characteristic that is dependent on its constituent objects but rises above them. For von Ehrenfels, Gestalt qualities rest unidirectionally on sense data: Wholes are more than the sums of their parts, but the parts are the foundation (Grundlage) of the whole. In contrast, Wertheimer claimed that functional relations determine what will appear as the whole and what will appear as parts (i.e., reciprocal dependency). Often the whole is grasped even before the individual parts enter consciousness. The contents of our awareness are by and large not additive but possess a characteristic coherence. They are structures that are segregated from the background, often with an inner center, to which the other parts are related hierarchically. Such structures or Gestalten are different from the sum of the parts. They arise from continuous global processes in the brain, rather than combinations of elementary excitations. With this step, Wertheimer separated himself from the Graz school of Gestalt psychology, represented by Alexius Meinong, Christian von Ehrenfels, and Vittorio Benussi. They maintained a distinction between sensation and perception, the latter produced on the basis of the former. The Berlin school, represented by Max Wertheimer, Kurt Koffka, and Wolfgang Köhler, considered a Gestalt as a whole in itself, not founded on any more elementary objects. In their view, perception was not the product of sensations but arose through dynamic physical processes in the brain. As a result, the Berlin school also rejected stage theories of perception proposed by the Leipzig school, represented by Felix Krüger and Friedrich Sander, in which the gradual emergence of Gestalten (Aktualgenese or microgenesis) played a central role. Although the Berlin theorists adhered to a nonmechanistic theory of causation and did not analyze the processes into stages, they did believe that the functional relations in the emergence of Gestalts could be specified by laws of perceptual organization. Two major developments are generally considered as highlights in the history of Gestalt psychology: Köhler's discussion of "physical Gestalten" (1920/1938) and Wertheimer's proposal of "Gestalt laws of perceptual organization" (1923/1938c). Köhler extended We discuss the classic configural principles of figure-ground organization: convexity, symmetry, small region, surroundedness. New Image-Based Principles of Figure- Ground Organization We discuss new image-based principles of figure-ground organization: lower region, top-bottom polarity, extremal edges and gradient cuts, edge-region grouping, articulating motion, advancing region motion, contour entropy as a ground cue (ϩ part salience, axiality). Nonimage-Based Influences on Figure- Ground Perception We discuss the evidence for nonimage-based influences on figure-ground organization: past experience, attention and perceptual set. 5.5 Figure-Ground Organization in Relation to Shape and Depth Perception We discuss how figure-ground organization relates to shape and depth perception. 5. the Gestalt concept from perception and behavior to the physical world, thus attempting to unify holism (i.e., the doctrine stressing the importance of the whole) and natural science. He proposed to treat the neurophysiological processes underlying Gestalt phenomena in terms of the physics of field continua rather than that of particles or point-masses. In such continuous field systems, which he called strong Gestalten, the mutual dependence among the parts is so great that no displacement or change of state can occur without influencing all the other parts of the system. Köhler showed that stationary electric currents, heat currents, and all phenomena of flow are strong Gestalten in this sense. These he distinguished from what he called weak Gestalten, which do not show this mutual interdependence. In addition, Köhler (1920) tried to construct a specific testable theory of brain processes that could account for perceived Gestalten in vision. He thought of visual Gestalten as the result of an integrated process in what he referred to as "the entire optical sector" (Köhler, 1920 (Köhler, /1938 , including retina, optical tract, and cortical areas, as well as transverse functional connections among conducting nerve fibers (i.e., a recurrent neural network in modern terms). He proposed an electrical field theory, in which "the lines of flow are free to follow different paths within the homogeneous conducting system, and the place where a given line of flow will end in the central field is determined in every case by the conditions in the system as a whole" (Köhler, 1920 (Köhler, /1938 . In modern terms, Köhler had described the visual system as a self-organizing physical system. These ideas led Köhler to postulate a psychophysical isomorphism between the psychological reality and the brain events underlying it: "Actual consciousness resembles in each case the real structural properties of the corresponding psychophysiological process" (Köhler, 1920 (Köhler, /1938 . By this he meant functional instead of geometrical similarity indicating that brain processes do not take the form of the perceived objects themselves. In addition, he insisted that such a view does not prescribe complete homogeneity of the cortex but is perfectly compatible with functional articulation. Experiments to establish the postulated connections between experienced and physical Gestalten in the brain were at the time nearly impossible to conduct, but decades later, Köhler attempted to do so (see below). Around the same time, Max Wertheimer (1922) further developed his Gestalt epistemology and outlined the research practice of experimental phenomenology that was based on it. He first stated the principles publically in a manifesto published in Volume 1 of Psychologische Forschung in 1922. Wertheimer called for descriptions of conscious experience in terms of the units people naturally perceive, rather than the artificial ones imposed by standard scientific methods. By assuming that conscious experience is composed of units analogous to physical point-masses or chemical elements, psychologists constrain themselves to a piecemeal inquiry into the contents of consciousness, building up higher entities from constituent elements, using associative connections. In fact, such and-summations (Und-Summe), as Wertheimer called them, appear "only rarely, only under certain characteristic conditions, only within very narrow limits, and perhaps never more than approximately" (Wertheimer, /1938a . Rather, what is given in experience "is itself in varying degrees 'structured' ('gestaltet'), it consists of more or less definitely structured wholes and whole-processes with their whole-properties and laws, characteristic whole-tendencies and whole-determinations of parts" (Wertheimer, /1938a . The perceptual field does not appear to us as a collection of disjointed sensations, but possesses a particular organization of spontaneously combined and segregated objects. In 1923, Wertheimer published a follow-up paper, which was an attempt to elucidate the fundamental principles of that organization. The most general principle was the so-called law of Präg-nanz, stating, in its most general sense, that the perceptual field and objects within it will take on the simplest and most encompassing (ausgezeichnet) structure permitted by the given conditions. For Köhler (1920) , this tendency towards the Prägnanz of the Gestalt was just another example that phenomenal Gestalten were like physical Gestalten: As shown by Maxwell and Planck, all processes in physical systems, left to themselves, show a tendency to achieve the maximal level of stability (homogeneity, simplicity, symmetry) with the minimum expenditure of energy allowed by the prevailing conditions. More specific principles that determine perceptual organization according to Wertheimer were proximity, similarity, uniform density, common fate, direction, good continuation and whole properties (or Ganzeigenschaften) such as closure, equilibrium, and symmetry. Empirical work on these principles existed before Wertheimer's landmark paper (for a recent review, see Vezzani, Marino, & Giora, 2012) , but now the general claim that perceptual experience is organized was turned into a complex open-ended research program aimed at the discovery of the laws or principles governing perceptual organization in both its static and dynamic aspects. It is this research program that Wertheimer, Koffka, and Köhler started to work on with their students, once they had acquired professorships at major universities in Germany in the 1920s and 1930s. We cannot cover this flourishing period of the Berlin school of Gestalt psychology extensively here, but a few highlights that deserve mentioning in passing are studies by Kurt Gottschaldt on embedded figures (1926), Joseph Ternus on phenomenal identity (1926), Karl Duncker on induced motion (1929), Wolfgang Metzger on a homogeneous Ganzfeld (1930) and motion in depth (1934). In the meantime, Gestalt thinking also affected research on other sense modalities (e.g., binaural hearing by Erich von Hornbostel), on learning and memory (e.g., Otto von Lauenstein and Hedwig von Restorff), and on thought (e.g., Karl Duncker). Later, Gestalt theory was also applied to action and emotion (by Kurt Lewin), to neuropathology and the organism as a whole (by Adhemar Gelb and Kurt Goldstein), and to film theory and aesthetics (by Rudolf Arnheim). This period marked the high point but not the end of Gestalt psychology's theoretical development, its research productivity, and its impact on German science and culture. Around this time, Gestalt theory also started to have some impact on research in the United States, mainly owing to Wolfgang Köhler and Kurt Koffka (see King & Wertheimer, 2005, Chapter 10). For instance, Koffka's (1935) notion of vector fields inspired some interesting empirical work published in the American Journal of Psychology (Brown & Voth, 1937; Orbison, 1939 ). Reviews Sensations are the primary units of mental life. Experimental phenomenology: Perceptual experience must be described in terms of the units people naturally perceive. Introspection: Perceptual experience must be analyzed as combinations of elementary sensations of physical stimuli as their building blocks. Percepts arise on the basis of continuous whole-processes in the brain; percepts organize themselves by mutual interactions in the brain. Percepts are associated combinations of elementary excitations. Perceptual organization is based on innate, intrinsic, autonomous laws. Perceptual organization is based on perceptual learning, past experience, intentions. Simplicity or minimum principle. Likelihood principle Graz school of Gestalt psychology (Meinong; von Ehrenfels, Benussi) Gestalten (structured experiences, wholes) are different from the sum of the parts. Gestalt qualities are more than the sum of the constituent primary sensations. Two-sided or reciprocal dependency between parts and wholes: One-sided dependency between parts and wholes (the wholes depend on the parts, but the parts do not depend on the whole). -There are specifiable functional relations that decide what will appear or function as a whole and what as parts. -Often the whole is grasped even before the individual parts enter consciousness. Perception "emerges" through self-organization; perception arises nonmechanistically through an autonomous process in the brain. Perception is "produced" on the basis of sensations. No analysis into stages, but functional relations in the emergence of Gestalts can be specified by Gestalt laws of perceptual organization. Stage theory: Aktualgenese, microgenesis. Holism integrated with natural science (physical Gestalten, isomorphism, minimum principle). Mystic holism, segregated from natural science. of Gestalt psychology appeared in Psychological Review on a regular basis (e.g., Helson, 1933; Hsiao, 1928) , a comprehensive book on state-of-the-art Gestalt psychology was published as early as 1935 (Hartmann, 1935) , and 3 years later Ellis's (1938) influential collection of translated excerpts of core Gestalt readings made some of the original sources accessible to a non-Germanspeaking audience. Already in 1922, at Robert Ogden's invitation, Koffka had published a full account of the Gestalt view on perception in Psychological Bulletin. At first sight, Gestalt theory seemed to develop rather consistently, from studying the fundamental laws of psychology first under the simplest conditions, in elementary problems of perception, before including complex sets of conditions, and turning to other domains such as memory, thinking, emotion, aesthetics, and so forth. At the same time, however, the findings obtained did not always fit the original theories, which posed serious challenges to the Gestalt framework. Even more devastating to the development of Gestalt psychology was the emergence of the Nazi regime in Germany from 1933 to World War II. In this period, many of the psychology professors at German universities lost their posts because of the discrimination against and prosecution of Jews, so they emigrated to the United States to take on new positions there. The works by German psychologists who stayed, for instance, Edwin Rausch's monograph on "summative" and "nonsummative" concepts (1937) and Wolfgang Metzger's (1941) psychology textbook, were largely ignored outside Germany. Metzger's synoptic account of research on the Gestalt theory of perception entitled Gesetze des Sehens (Laws of Seeing), first published in 1936 and later reissued and vastly expanded three times, was only translated into English in 2006. After emigrating to the United States, the founding fathers of Gestalt psychology did not perform many new experiments. Instead, they mainly wrote books in which they outlined their views (e.g., Koffka, 1935; Köhler, 1940; Wertheimer, 1945) . The major exception was Köhler who had taken up physiological psychology using electroencephalograph (EEG) recording and other methods in an attempt to directly verify his isomorphism postulate. Initially, his work with Hans Wallach on figural aftereffects appeared to support his interpretation in terms of satiation of cortical currents (Köhler & Wallach, 1944) . Afterwards, he was able to directly measure cortical currents-as EEG responses picked up from electrodes at the scalp-whose flow direction corresponded to the direction of movement of objects in the visual field (Köhler & Held, 1949) . Soon after that breakthrough, however, Lashley, Chow, and Semmes (1951) performed a more critical test of Köhler's electric field theory and its underlying postulate of isomorphism. If the flows of current picked up from the scalp in Köhler and Held's experiments indeed reflected the organized pattern of perception and not merely the applied stimulation, and if that pattern of perception would result from a global figure-field across the whole cortex, a marked alteration of the currents should distort the perception of these visual figures. By inserting metallic strips and metal pins in large regions of the visual cortex of rhesus monkeys, Lashley et al. could short-circuit the cortical currents. Surprisingly, the monkeys could still perform the learned shape discriminations, demonstrating that global cortical currents were not a necessary condition for pattern perception. In subsequent experiments, Sperry, Miner, and Myers (1955) performed extensive slicing and dense impregnation with metallic wires across the entire visual cortex of cats, and showed that these animals too could still perform rather difficult shape discriminations (e.g., between a prototypical triangle and distorted variants). Together, these two studies effectively ruled out electrical field theory as an explanation of cortical integration and undermined the empirical basis of any isomorphism between cortical flows of current and organized patterns of perception. Köhler (1965) naturally reacted to these developments but his counterarguments and suggestions for further experiments were largely ignored, and to most scientists at the time, the matter was closed. Electrical field theory, which had been one of the pillars of Gestalt psychology's scientific basis, was considered dead and buried. While Gestalt psychology declined in the English-speaking world after World War II, Italy remained a stronghold of Gestalt psychology. For instance, Metzger dedicated the third edition of his Gesetze des Sehens to his "Italian and Japanese friends." Among his friends were Musatti, Metelli, and Kanizsa-three major figures in Italian psychology. In spite of being Benussi's student and successor (from the Graz school), Cesare Musatti was responsible for introducing the Berlin school of Gestalt psychology in Italy and training important students in this tradition-most notably Metelli and Kanizsa, whose contributions continue to be felt today. Fabio Metelli is best known for his work on the perception of transparency (e.g., Metelli, 1974) . Gaetano Kanizsa's most famous studies were performed in the 1950s with papers on subjective contours (e.g., the so-called Kanizsa triangle), modes of color appearance, and phenomenal transparency (Kanizsa, 1954 (Kanizsa, , 1955a (Kanizsa, , 1955b , although their impact came much later, when he started to publish in English (Kanizsa, 1976 (Kanizsa, , 1979 . In addition to Italy, Gestalt psychology was also strong in Belgium and in Japan. Albert Michotte became famous for his work on the perception of causality (1946/1963), arguing strongly against an inferential, associationist, empiricist account of it, like other Gestalt psychologists had done for other aspects of perception. For him, causality is perceived directly, not derived from more primitive sensations through some cognitive operation, and this percept could be shown to be tightly coupled to specific higher order attributes in the spatiotemporal events presented to observers. He also introduced the notions of modal and amodal completion (Michotte, Thinès, & Crabbé, 1964) , and studied several configural influences on these processes. (For a further discussion of Michotte's heritage, see Wagemans, van Lier, & Scholl, 2006 .) Building on earlier collaborations of Japanese students with major German Gestalt psychologists (e.g., Sakuma with Lewin, Morinaga with Metzger), Gestalt psychology continued to develop in Japan after World War II. For instance, Oyama did significant work on figural aftereffects (e.g., Sagara & Oyama, 1957) and perceptual grouping (e.g., Oyama, 1961). Despite signs of well-deserved respect in the United States and in Germany (e.g., Köhler's American Psychological Association presidency in 1957, Wertheimer's posthumous Wilhelm Wundt Medal in 1983), the ideas of the Gestaltists were received with ambivalence. On the one hand, they were recognized for raising central issues and provoking important debates in psychology, theoretical biology, and other fields, but on the other hand, their 1178 WAGEMANS ET AL. mode of thinking and research style did not sit comfortably in the intellectual and social climate of the postwar world, and they were confronted with vehement criticism. Two sets of explanations have been given for this outcome (Ash, 1995) . The first emphasizes institutional, political, and biographical contingencies. Koffka, Köhler, and Wertheimer all left for the United States and obtained positions where they could do excellent research but could not train doctoral students. The Gestalt school's further expansion was also handicapped by the early deaths of Max Wertheimer in 1943 and Kurt Koffka in 1941, as well as many other Gestalt psychologists of the first and second generations (e.g., Duncker, Gelb, Lauenstein, Lewin, von Restorff). In Germany, Metzger, Rausch, and Gottschaldt did have a large number of doctoral students, but few of them carried on in the Gestalt tradition. A notable exception is Lothar Spillmann, who obtained his doctorate with Metzger in Münster in 1964 and who has pioneered the impact of Gestalt ideas in modern neurophysiology ever since (e.g., Spillmann, 1999 Spillmann, , 2009 . The second set of explanations concerns scientific issues of a methodological and conceptual nature (summarized in the left column of Table 4 ). Compared to the rigor of psychophysics and behaviorism, Gestalt psychology was severely criticized for offering mere demonstrations, using either very simple or confounded stimuli, formulating laws with little precision, and adding new laws for every factor shown to have an influence on perceptual organization. In the 1950s and 1960s, its critics increasingly insisted on causal explanations, by which they meant cognitive operations in the mind that could be modeled as computer algorithms or neural mechanisms that could be attributed to the properties of single cells that were discovered by Hubel and Wiesel in that period. In addition, serious conceptual limitations appeared when Gestalt thinking was extended to other areas such as personality and social psychology (e.g., Richard Crutchfield, Solomon Asch, Fritz Heider, David Krech). The further the metaphors were stretched, the harder it became to connect them to Köhler's concept of a self-organizing brain and his speculations about electromagnetic brain fields. Despite these criticisms, Gestalt thinking did not disappear from the stage completely. In the slipstream of Shannon's information theory, a few researchers tried to provide a quantitative underpinning to the central Gestalt notion of simplicity (e.g., Attneave, 1954; Attneave & Arnoult, 1956; Hochberg & McAlister, 1953; Leeuwenberg, 1969 Leeuwenberg, , 1971 ; for a review, see Hatfield & Epstein, 1985) . A number of independent, original scientists working on perception and information processing kept some Gestalt issues on the research agenda (e.g., Fred Attneave, Wendell Garner, Julian Hochberg, Irvin Rock). These became more prominent again with the discovery of true Gestalt phenomena such as global precedence in hierarchical letters (e.g., Navon, 1977), configural superiority effects based on emergent features (e.g., Pomerantz, Sager, & Stoever, 1977) , and the importance of hierarchical structure in perceptual representations (e.g., Palmer, 1977) . The experimental paradigms were derived from standard methods in cognitive psychology, and the results were incorporated into mainstream information-processing accounts (e.g., J. Beck, 1982; Kubovy & Pomerantz, 1981) . In the major alternative approaches to visual perception-the ecological (e.g., J. J. Gibson, 1971 ) and computational (e.g., Marr, 1982) approaches-the influence of Gestalt thinking has also been acknowledged explicitly. In the last 2 or 3 decades, perceptual grouping and figure-ground organizationthe most central topics of Berlin school research-have returned to center stage (e.g., Kimchi, Behrmann, & Olson, 2003), although the relationship to the original Gestalt theory (e.g., two-sided dependency between wholes and parts, minimum principle) is not always clear. In the remainder of this article, as well as in a second more theoretically oriented article (Wagemans et al., 2012), we review the later developments in more detail (summarized in the right Carefully constructed stimuli, sometimes also richer stimuli (1) -Allowing research of everyday tasks -Allowing research of ecological foundations Grouping principles and laws of perceptual organization studied in isolation Also studying relationships with other processes (1), e.g., -Perceptual grouping in relation to depth perception, lightness perception -Visual contour completion in relation to surface geometry and layout - Figure- Table 4 ). We start with research on perceptual grouping in simple displays (Section 3) and extend this to contour grouping, integration, and completion in more complex shapes and realworld images (Section 4). In the next section, we cover research on figure-ground perception, where many of the factors affecting grouping, in addition to unique factors, exert an influence (Section 5). Although links to neural mechanisms are mentioned throughout, we also provide a more integrated account of the literature on the neural mechanisms of contour grouping and figure-ground organization in a separate section (Section 6). This review demonstrates that research from the last 2 or 3 decades has addressed (and partially solved) some of the major methodological and conceptual shortcomings in old-school Gestalt psychology. Historically, the visual phenomenon most closely associated with perceptual organization is grouping: the fact that observers perceive some elements of the visual field as going together more strongly than others. Indeed, perceptual grouping and perceptual organization are sometimes presented as though they were synonymous. They are not. Grouping is one particular kind of organizational phenomenon, albeit a very important one. Another is figure-ground organization. In general, grouping determines what the qualitative elements of perception are, and figure-ground determines the interpretation of those elements in terms of their shapes and relative locations in the layout of surfaces in the 3-D world. Max Wertheimer first posed the problem of perceptual grouping in his groundbreaking 1923 paper by asking what stimulus factors influence the perceived grouping of discrete elements. He first demonstrated that equally spaced dots do not group together into larger perceptual units, except as a uniform line (see Figure 1A) , and then noted that when he altered the spacing between adjacent dots so that some dots were closer than others, the closer ones grouped together strongly into pairs (see Figure 1B ). This factor of relative distance, which Wertheimer called proximity, was the first of his famous laws or (more accurately) principles of grouping. Wertheimer went on to illustrate other grouping principles, several of which are portrayed in Figure 1 . Figures 1C, 1D , and 1E demonstrate different versions of the general principle of similarity: All else being equal, the most similar elements (in color, size, and orientation for these examples) tend to be grouped together. Another powerful grouping factor is common fate: All else being equal, elements that move in the same way tend to be grouped together. Notice that both common fate and proximity can actually be considered special cases of similarity grouping, with velocity and position as the relevant properties, respectively. Further factors influencing perceptual grouping of more complex elements, such as lines and curves, include symmetry (see Figure 1G) , parallelism (see Figure 1H) , and continuity or good continuation (see Figure 1I ). Continuity is important in Figure 1I because observers perceive it as containing two continuous intersecting lines rather than as two angles whose vertices meet at a point. Figure 1J illustrates the effect of closure: All else being equal, elements that form a closed figure tend to be grouped together. This display also shows that closure can dominate continuity, since the very same elements that were organized as two intersecting lines in Figure 1I are now organized as two angles meeting at a point in Figure 1J . One might think that such grouping principles are mere textbook curiosities only distantly related to normal perception. On the contrary, they pervade virtually all perceptual experiences because they determine the objects and parts that people perceive in the environment. (Hence, they also affect other sensory modalities; for a thorough discussion of grouping principles in audition, see Bregman, 1990 ; for a recent review of Gestalt principles in tactile perception, see Gallace & Spence, 2011.) A practical application of the Gestalt principles is camouflage, which results when the same grouping processes that would normally make an organism stand out from its environment as a separate object cause it to be grouped together with its surroundings instead. For instance, the same leopard that is clearly visible when it is seen in a tree against the uniform sky is difficult to see against a mottled, leafy backdrop-until it moves. Even perfect static camouflage is undone by the principle of common fate. In sum, camouflage and camouflage breaking provide an ecological rationale for the principles of grouping. Since the early days of Gestalt psychology, considerable progress has been made, including (a) the discovery of additional principles, (b) the experimental measurement of the strength of grouping factors and the development of quantitative laws, as well as (c) new insights into the level of processing at which perceptual grouping happens. These new developments are described in the next section, where we also discuss their possible structural and ecological basis. Generalized common fate. One of the most powerful of the classic grouping principles is common fate-the tendency for elements that move together to be perceived as a unitary entity (Wertheimer, 1923) . The possibility that Wertheimer may have had a much broader range of phenomena in mind, however, is suggested by a passage of his seminal article that is not widely known because it was not included in Ellis's translation (Wertheimer, 1923 (Wertheimer, /1938c (2001) presented an extension of common fate to grouping by common luminance changes. They found that when elements of a visual scene become brighter or darker simultaneously, even if they have different luminances throughout, observers have a powerful tendency to group those elements perceptually. It is as though the principle of common fate operates not only for the common motion of elements through 3-D physical space, but through luminance space as well. The structural rationale for generalized common fate is clear: It is another example of similarity grouping, but based on similarity of changes in feature values, such as luminance or position, rather than on the similarity of the feature values themselves. An ecological rationale for grouping by common luminance changes might lie in the simultaneous brightening or darkening that occurs across a spatial area when the level of illumination changes (e.g., with the appearance of sunlight or shadows; see also van den Berg, Kubovy, & Schirillo, 2011) . Synchrony is the tendency for elements that change simultaneously to be grouped together (Alais, Blake, & Lee, 1998; S.-H. Lee & Blake, 1999) . The changes do not have to be in the same direction, however, as they do in generalized common fate. A random field of black and white dots whose luminances change in polarity randomly over time against a gray background, for example, will segregate into two distinct regions if the dots in one area change synchronously rather than randomly. Grouping by synchrony can be considered as an even more general form of common fate in which the simultaneous changes do not have to involve either motion, as in classic common fate, or common direction of change, as in generalized common fate. The structural basis for grouping by synchrony is clear: the simultaneous occurrence of visible changes of the elements that are grouped. Such grouping makes sense because it reflects a strong temporal regularity in the stimulus event. The ecological rationale behind grouping by synchrony is far less clear, however. Objects in the natural environment seldom change their properties in different directions or along different dimensions in temporal synchrony. Indeed, it is difficult even to devise plausible examples of ecological situations that would exhibit this kind of temporal regularity without some form of extended common fate being involved. Nevertheless, synchrony grouping may arise from some very general nonaccidentalness detection mechanism, possibly connected to the perception of causality (e.g., Michotte, 1946 Michotte, /1963 . The argument is that the temporal coincidence of multiple changes is unlikely to be due to chance alone, and so it must have some common underlying cause related to an ecological event that relates the synchronously changing elements. A radically different and quite controversial rationale is that temporal synchrony of changes drives grouping because synchrony of neural firings is the physiological mechanism by which the brain codes all forms of grouping (e.g., Milner, 1974; von der Malsburg, 1981) . The argument is that if the environment drives the neural substrate to produce synchronous firing by virtue of synchronous changes, the changing elements will automatically be grouped because of the synchronous firing. Some researchers report evidence that seems to support this claim (e.g., Gray & Singer, 1989; Singer & Gray, 1995) , but others disagree (e.g., Shadlen & Movshon, 1999) . This issue is discussed further in the second article (Wagemans et al., 2012, Section 4). Further controversy surrounds synchrony grouping because it has been claimed that such grouping effects are actually produced by stimulus artifacts that can be detected by the early visual system (Farid, 2002; Farid & Adelson, 2001 ). These challenges are complex, but the bottom line is that both the existence of grouping synchrony and the mechanism by which it occurs are currently unclear. In general, these controversies show quite clearly that the interest in perceptual grouping principles remains strong in contemporary research. Common region. Common region is the tendency for elements that lie within the same bounded area (or region) to be grouped together (Palmer, 1992 ). An illustration is provided in Figure 1K , where the black dots that lie within the same ovals are likely to be grouped into pairs. The structural basis for grouping by common region appears to be that all the elements within a given region share the topological property of being inside of or contained by some larger surrounding contour. If it is viewed as similarity of containment, it can be related to several other grouping principles based on similarity (e.g., color, orientation, and size). Common region also appears to have an ecological rationale arising from textures and hierarchically embedded parts. When a bounded region encloses a number of image elements, they are likely to be elements on the surface of a single object, such as a leopard's spots or the features of a face, rather than independent objects that just happen accidentally to lie within the same bounding contour. Experimental evidence for the existence of common region as a grouping factor comes from studies using the repetition discrimination time or RDT method (D. M. Beck & Palmer, 2002; Palmer & Beck, 2007) . In a speeded discrimination task, observers were able to report the shape of a repeated element more quickly in a line of otherwise alternating shapes (e.g., squares and circles) when the repeated shapes were located within the same surrounding region than when they were located in two separate regions. Element connectedness. Element connectedness is the tendency for distinct elements that share a common border to be grouped together. The important structural basis for this form of grouping is the topological property of connectedness (Palmer & Rock, 1994) . Connectedness can be considered as the limiting case of the classic factor of proximity, but Palmer and Rock (1994) argued that framing it this way puts the cart before the horse, in the 1181 100 YEARS OF VISUAL GESTALTS: I sense that one needs distinct units to speak meaningfully about their distance in the first place. The compelling rationale for element connectedness is ecological: Pieces of matter that are physically connected to each other in 3-D space are the primary candidates for being parts of the same object, largely because they tend to behave as a single unit. The bristles, metal band, and handle of a paint brush, for example, constitute a single object in large part because of their connectedness, as demonstrated by the fact that when you push one part, the other parts move rigidly along with it. The effectiveness of element connectedness was demonstrated in a behavioral task using the RDT method (Palmer & Beck, 2007) . As was the case for grouping by common region, displays with elements that were connected to each other produced reliably faster responses than displays with unconnected elements. Another behavioral result that provides striking support for the importance of element connectedness comes from a neuropsychological study by Humphreys and Riddoch (1993) . Their patient, who was afflicted with Balint's syndrome-a condition resulting from bilateral damage to parietal cortex that results in a deficit in perceiving more than a single object at any given time-was unable to discriminate between arrays containing many circles of just one color (either all red or all green) and arrays in which half of the circles were red and the other half green. However, if pairs consisting of one red circle and one green circle were connected by lines, the same patient was able to make the discrimination between one-color and two-color arrays. Unifying a pair of circles through element connectedness thus appears to enable these patients to perceive them as a single perceptual object so that they could see two circles at once, a feat that was impossible for them in the absence of the connecting line. Uniform connectedness. This principle represents something of a departure from standard Gestalt ideas about perceptual organization because it addresses the question of how the initial organization into elements might occur. In his classic article on grouping, Wertheimer (1923) never actually mentioned where the to-be-grouped elements came from. Presumably, he believed that they were somehow derived from the grouping principles he articulated, but Palmer and Rock (1994) argued that they arise from the earlier organizational process of uniform connectedness (UC), which is the principle by which the visual system initially partitions an image into a set of mutually exclusive connected regions having uniform (or smoothly changing) properties, such as luminance, color, texture, motion, and depth. The UC elements thus created form the entry level units into a part-whole hierarchy that is created by grouping together different UC regions and, if necessary, by parsing them into lower level elements at deep concavities (e.g., Hoffman & Richards, 1984) . Palmer and Rock's (1994) claims regarding the foundational status of UC have not been uniformly accepted. Peterson (1994) , for instance, argued that UC is one of many properties relevant to partitioning the visual field, and that UC units are not entry-level units. Kimchi (2000) examined the role of UC in experiments designed to reveal the gradual emergence, or microgenesis, of organizational processes using a primed matching task with displays containing connected or disconnected elements. The complex results she obtained were not consistent with UC being the sole determinant of entry-level units in a part-whole hierarchy, as Palmer and Rock proposed. Rather, they showed that collinearity and closure were at least as important, if not more so, in the initial organization that can be tapped by such methods. Nevertheless, the theoretical rationale for some organizational process like UC to contribute to creating a set of potential perceptual units on which further grouping and parsing can operate seems sound. Indeed, something like it is a standard assumption in most theories of computational vision (e.g., Marr, 1982) . Whereas the research on grouping principles, as described above, provides predictions about what elements in a display are likely to be grouped together, it does not reveal how strong each of the grouping principles is. This is the focus of the next sections, covering studies applying static and dynamic stimuli, respectively. Conceptual background. Starting with Wertheimer (1923), researchers have often used dot lattices to quantify grouping. A dot lattice is a collection of dots in the plane that is invariant under at least two translations, a (with length |a|) and b (whose length is |b| Ն |a|). These two lengths, and the angle between the vectors, ␥ (constrained by 60°Յ ␥ Յ 90°), define the basic structure of the lattice by defining the parallelogram between each quartet of dots in the lattice (Kubovy, 1994 , extending the work of Bravais, 1850/1949; see Figure 2A ). The diagonals of this parallelogram are denoted c and d (where |c| Յ |d|). In its canonical orientation, a is horizontal. More generally, the orientation of the lattice can be defined by the angle (measured counterclockwise) and |a| is called the scale of the lattice. Since scale is irrelevant to the invariant properties of the lattice and unimportant for grouping over a reasonable range, the relevant parameters are |b|/|a| and ␥ (see Figure 2B ). With these two parameters, six different types of lattices can be defined, each characterized by their symmetry properties. When grouping by proximity is pitted against grouping by similarity, displays consist of at least two kinds of elements (called motifs), separated by one of the translation components, resulting in dimotif lattices (see Figure 3 ; Grünbaum & Shephard, 1987) . In order to characterize the relation between two grouping principles, one must construct grouping indifference curves (see Figure 4) , similar to the indifference curves used in microeconomics (Krantz, Luce, Suppes, & Tversky, 1971) : Imagine a consumer who would be equally satisfied with a market basket consisting of 1 kg of meat and 4 kg of potatoes and another consisting of 2 kg of meat and 1 kg of potatoes. In such a case, the (meat, potato) pairs (1, 4) and (2, 1) both lie on an indifference curve. With these tools in hand, two important questions regarding perceptual grouping can be formulated. First, when several orientations can be perceived based on grouping by proximity in a particular dot lattice, what determines the preferred grouping? Is the outcome determined by the relative distance alone, or also by the angle between the competing organizations (an aspect that affects the global symmetry of the lattice and the way the overall configuration looks)? Second, when grouping by proximity and grouping by similarity are concurrently applied to the same pattern, what rule governs their joint application? Are these two principles combined additively or not? We briefly review the most important attempts to address these two questions. The initial studies always pitted grouping by proximity against grouping by similarity. Initial attempts to quantify grouping by proximity by pitting it against similarity. The first to systematically study grouping by proximity in interaction with similarity was Rush (1937) . In her experiment, she showed observers sequences of dot lattices in which the distance between dots in one orientation was held constant, and the distance between dots in another orientation was reduced from trial to trial. She assumed-incorrectly, as argued below-that one could measure the strength of the two principles by finding their point of equilibrium, and concluded that "it may be said that Similarity equals about 1.5 cm of Proximity" (Rush, 1937, p. 90). Roughly 2 decades later, Hochberg and Silverstein (1956, unaware of Rush's work, as a footnote in Hochberg & Hardy, 1960, attests) also set out to solve the problem of measuring the strength of grouping by similarity by pitting it against grouping by proximity. In manipulating luminance differences or distances between dots, they produced grouping indifference curves (see Figure 4) . Reanalysis showed that an additive combination of proximity and similarity described their results best. Unfortunately, the logic employed by Hochberg and his colleagues suffered from the same flaw as Rush. Their method produced only one grouping indifference curve-the one for which both groupings are in equilibrium. Their method cannot produce grouping indifference curves for which one principle is 2 times or 3 times as strong as the other, which are needed to measure the relative strengths of the two principles. Quinlan and Wilton (1998) studied the relations between grouping by proximity and two forms of grouping by similarity (by color and by shape). Their stimuli consisted of strips of seven elements, with the center element as the target. They manipulated proximity by slightly shifting the left or right set of three elements, and they also manipulated color and shape similarity. Observers were asked to rate the degree to which the target grouped with the elements on the left or on the right. Although the conception of the experiment is elegant, its reach was curtailed because each grouping principle was either present or absent. Had Quinlan and Wilton used a design in which each type of grouping was a multilevel factor, they could have addressed the additivity question (i.e., the second question introduced above), but they did not. Oyama, Simizu, and Tozawa (1999) presented rectangular dimotif lattices for 3 s and asked observers to indicate continuously with a joystick whether they saw horizontal or vertical grouping. The horizontal separation was increased by 15Ј after a horizontal response, and decreased by that amount after a vertical response. Using a double-staircase method, the ratio of vertical to horizontal distances was determined that matched a particular dissimilarity. This method produced more complete equilibrium grouping indifference curves than were obtained by Hochberg and his colleagues. The pure distance law and the additivity of grouping principles. Oyama (1961) was the first to show that one can measure the strength of grouping by proximity without pitting it against another grouping principle (e.g., grouping by similarity). Using rectangular dot lattices at a fixed orientation, he recorded the amount of time subjects reported seeing the competing horizontal and vertical groupings. The ratio of the time they saw the horizontal and vertical organizations was found to be a power function of the ratio of the horizontal and vertical distances Ϫ␣ , with ␣ Ϸ 2.89. Using dot lattices at near equilibrium, Kubovy and Wagemans (1995) and Kubovy, Holcombe, and Wagemans (1998) demonstrated that grouping by proximity can be understood as the outcome of a probabilistic competition among potential perceptual organizations. The basic idea is simple. If the distances between dots in two orientations of the lattice are equal, the chances of seeing one orientation or the other are equal too. If one distance becomes larger than the other, the relative chance of seeing that orientation decreases. If the ratio of the longer to the shorter vector is larger than about 1.5, grouping along that orientation is almost never seen. Kubovy and colleagues presented different kinds of dot lattices for 300 ms each and asked observers to indicate the perceived orientation. They could then use the frequencies of the perceived orientations over a large number of trials as estimates of the probabilities, and plot the relative frequencies as a function of relative distance. Their results (shown schematically in Figure 5 ) were remarkable. All the values of the log-odds fell on the same line, called the attraction function. Its slope is a person-dependent measure of sensitivity to proximity. Although the (relative) strength of grouping decays as an exponential function of (relative) distance, the attraction function in log-space is linear. The fact that all data points-obtained with all pairs of distances and all relative orientations (i.e., all points in the 2-D lattice space of Figure  2B )-could be fitted well by a single straight line indicates that grouping by proximity depends only on the relative distance between dots in competing organizations, not on the overall configuration in which the competition occurs (i.e., the lattice type, each with its own symmetry properties). Hence, this result, which was called the pure distance law, provided a satisfactory answer to the first question raised above. Once it has been established how grouping varies as a function of relative distance, the effect of conjoined grouping principles can be determined by measuring a family of grouping indifference curves. Kubovy and van den Berg (2008) presented participants with rectangular lattices of dots of different contrasts. Dots with the same contrast were either arranged along the shorter axis of each rectangle of dots within the lattice (similarity and proximity in concert) or arranged along the longer axis (similarity and proximity working against each other). Dot lattices varied across two dimensions: the ratio between the short and long axes of each rectangle of dots within the lattice and the contrast difference between the different arrays of dots. As in the previous studies, each lattice was presented for 300 ms, and participants were asked to indicate which of the four orientations best matched the perceived arrangement of the dots in the lattice. By plotting the log likelihood of reporting the direction of the long axis versus the short axis as a function of the ratio of the length of the long and short axis for different values of the contrast difference between dots (shown schematically in Figure 6A ), a family of grouping indifference curves was then obtained (depicted in Figure 6B ). Because these indifference curves are parallel in log-odds space, the conjoined effects of proximity and similarity are called additive. Using lattices in which dots were replaced by Gabor elements, Claessens and Wagemans (2005) came to similar conclusions regarding proximity and collinearity. These results, therefore, provide a clear answer to the second question raised above. Apparent motion is perceived when an object is presented in two or more successive frames at different spatial locations with proper durations and intervals. As discussed before, Wertheimer (1912) showed that under certain conditions it is possible to perceive pure motion, where motion is perceived without perceiving the moving object itself. The optimal timing and spacing between successively presented object presentations were investigated in more detail by Korte (1915) , who found a direct relationship between the optimal temporal and the optimal spatial intervals for perceived apparent motion. Later studies, however, have shown that the relationship between the optimal temporal and spatial intervals depends on the stimuli used. For example, using horizontal arrays of dots that were displaced on successive frames, Burt and Sperling (1981) found that the spacing of the dots in the array strongly influenced the apparent motion percept in addition to the effects of the temporal interval between frames and the spatial displacement of the entire array. The influence of spatial and temporal factors in apparent motion was further investigated using the Ternus display (Kramer & Yantis, 1997; Pantle & Picciano, 1976; Ternus, 1926; Wallace & Scott-Samuel, 2007) , in which an array of three dots is presented across two frames at different spatial locations. When the two frames are presented in rapid succession (i.e., with a short interstimulus interval), it appears that the outmost dot is displaced while the center two dots appear to be stationary: Element motion occurs. When the temporal interval between the successive frames is longer, the entire array of dots appears to jump: Group motion is perceived. The two different types of perceived apparent motion represent two different solutions to the correspondence problem (Ullman, 1979), referring to the task of matching the objects in the first frame to the (possibly displaced) objects in the second frame. Whether element or group motion was perceived was found to depend on the properties of the individual stimuli in both frames such as their features (Dawson, Nevin-Meadows, & Wright, 1994) , their size or the sharpness of their edges (Casco, 1990) , as well as on the presence of contextual elements affecting how they are grouped (Kramer & Yantis, 1997) or how they are perceived in 3-D space (He & Ooi, 1999) . The interaction between spatial and temporal aspects was further investigated by Gepshtein and Kubovy (2000), who were able to determine the relationship between spatial grouping (determining which elements in each frame belong together) and temporal grouping (determining which elements across frames belong together), by using successive presentations of dot lattices-motion lattices-which allowed them to independently manipulate the strength of spatial and temporal groupings. A motion lattice (see Figure 7) is composed of two identical dot lattices, D 1 and D 2 , displayed in alternation. Two ratios determine the perceived motion: (a) the motion ratio r m ϭ m 2 /m 1 , where m 1 and m 2 are the shortest and the next shortest spatial distances across which the apparent motion could occur between the frames; (b) the baseline ratio r b ϭ b/m 1 , where b is the shortest spatial distance between the dots within D 1 and D 2 to which the apparent motion could apply. The orientation of a virtual line drawn through these dots is called the baseline orientation. As in the classic Ternus display, two classes of motion can be perceived. First, element motion is now apparent motion from each dot in D 1 to a corresponding dot in D 2 (and vice versa as the dot lattices alternate). The log-odds of seeing m 2 rather than m 1 as a function of the ratio of the distances is called an affinity function, by analogy with the concept of an attraction function for static dot lattices (see Figure 8A) . Second, group motion is now apparent motion orthogonal to the baseline orientation (see Figure 7 ). Sequential models predict that if the spatial configuration of a stimulus remains constant, the likelihood of seeing group motion-an indicator of spatial grouping-cannot be affected by manipulations of the temporal configuration of the stimulus. However, the pattern of interaction in Figure 8B between r m , the temporal configuration of the stimulus, and r b , the relative density of the dots along the baseline, clearly refutes the sequential model. How spatial and temporal distances interact to determine the strength of apparent motion has been controversial. Some studies report space-time coupling: If the spatial or temporal distance between successive stimuli is increased, the other distance between them must also be increased to maintain a constant strength of apparent motion (i.e., Korte's third law of motion). Other studies report space-time tradeoff: If one of the distances is increased, the other must be decreased to maintain a constant strength of apparent motion. To establish what determines whether coupling or tradeoff occurs, Gepshtein and Kubovy (2007) generalized the motion lattice of Figure 7 , as illustrated in Figure 9 , showing a temporal component of m 3 , T 3 , of twice the magnitude of the temporal component of m 1 , T 1 . By manipulating the spatial components of these motions, S 3 and S 1 from S 3 Ͼ Ͼ S 1 to S 3 Ͻ Ͻ S 1 , an equilibrium point between the extremes was found at r 31 ϭ S 3 /S 1 , for which the probability of seeing the two motions was the same. If r 31 Ͼ 1, then space-time coupling holds; if r 31 Ͻ 1, then space-time tradeoff holds. This suggests that previous findings on apparent motion were special cases and that the allegedly inconsistent results can be embraced by a simple law in which a smooth transition from tradeoff to coupling occurs as a function of speed: Tradeoff holds at low speeds of motion (below Ϸ 12°/s), whereas coupling (Korte's law) holds at high speeds. The deeper theoretical implications of these results for the visual system's economy principles are discussed in the second review article (Wagemans et al., 2012, Section 4). The above research on perceptual grouping in static and dynamic discrete patterns spans a complete century, from Schumann (1900 , and Korte (1915) up until today. It mainly used well-controlled, parametrically varied stimuli in order to isolate one factor or another, and trying to quantify its strength. In addition, it sparked a renewed interest in understanding the level at which perceptual grouping operates, which was addressed in studies that used somewhat richer stimuli with additional variations, more typical for naturally occurring stimulation.  As described above, Wertheimer (1923) demonstrated powerful grouping effects due to a large number of stimulus variables (e.g., proximity, similarity, good continuation) using flat 2-D displays on the printed page (see Figure 1) . Subsequent researchers have investigated where in the visual system these effects occur (i.e., before or after the construction of a 3-D representation of the image), by using various kinds of 3-D displays with depth cues, shadows, transparency, and other higher level factors. Rock and Brosgole (1964) conducted a classic experiment on this topic to examine whether grouping by proximity operated on retinal 2-D distances or perceived 3-D distances. Observers in a dark room saw a 2-D array of luminous beads either in the frontal plane (perpendicular to the line of sight) or slanted in depth so that the horizontal dimension of the array was foreshortened. The beads were actually closer together vertically than horizontally, so that when they were viewed in the frontal plane, observers always reported seeing them grouped into vertical columns rather than horizontal rows. The critical question was whether or not the beads would be grouped in the same way when the same lattice was viewed slanted in depth such that the beads were retinally closer together in the horizontal direction. When this array was viewed monocularly, so that the beads appeared to be in a frontal plane perpendicular to the line of sight (even though they were actually slanted in depth), observers perceived the grouping to change to a set of rows rather than columns, as one would expect based on retinal distances. However, when viewed binocularly, so that stereoscopic depth information enabled observers to see the beads slanted in depth, they reported grouping them into vertical columns, as predicted by postconstancy grouping based on a 3-D representation of perceived distances in the phenomenal environment (because the beads appeared to be closer in the vertical direction, as was actually the case in the physical world). Rock and Brosgole's results therefore support the hypothesis that the final, conscious result of grouping occurs after binocular depth percep- tion. Several phenomenological demonstrations supporting the same conclusion were provided by Palmer (2002a; Palmer, Brooks & Nelson, 2003) . Rock, Nijhawan, Palmer, and Tudor (1992) later investigated whether grouping based on lightness similarity happened before or after lightness constancy. Using displays that employed cast shadows and translucent overlays, they also found evidence that the final conscious result of grouping depended on a postconstancy representation that reflected the perceived reflectance of surfaces rather than the luminance of retinal regions. Analogous evidence that the final conscious organization resulted from a grouping process that operates on relatively late, postconstancy representations was reported by Palmer, Neff, and Beck (1996) for amodal completion and by Palmer and Nelson (2000) for illusory contours. Further results of Schulz and Sanocki (2003) support the view that prior to achieving the conscious result of perceptual grouping based on a 3-D postconstancy representation, some nonconscious grouping processes operate on a 2-D preconstancy representation. They used the same lightness displays as did Rock et al., but included a brief, masked presentation condition in which they found that observers reported seeing an organization based on the retinal luminance of 2-D regions (see also van den Berg et al., 2011) . Further evidence that grouping operations occur before constancy has been achieved is based on grouping effects that actually influence the achievement of constancy (see Palmer, 2003) . Perhaps the most parsimonious view consistent with the known facts is that grouping principles operate at multiple levels. It seems most likely that provisional grouping takes place at each stage of processing, possibly with feedback from higher levels to lower ones, until a final, conscious experience arises of a grouping that is consistent with the perceived structure of the 3-D environment. Whereas the above findings provide valuable information about the stages at which grouping operates, these studies have mainly employed relatively artificial stimuli. The next section is dedicated to the role of grouping in contour integration and completion, in ways that are closer to the processing of natural stimuli. Contour Integration and Completion Studies in which grouping factors are isolated to quantify their strength are useful but understanding their role in everyday perception requires a different approach. An important task of natural vision is to identify and group together the portions of the 2-D retinal image that project from an object. In the simple case in which the object boundary projects as a single closed curve, the problem reduces to a problem of contour grouping or contour integration. From the 50-year history of computer vision research, however, we know that this is a computationally difficult problem for a number of reasons (e.g., Elder, Krupnik, & Johnston, 2003) . First, occlusions occur generically in natural images, resulting in a projection of the rim of the object as a disconnected set of contour fragments (see Figure 10) . Also, where the figure-ground contrast is low, portions of the contour may not be detected, resulting in further fragmentation. To complicate matters further, natural images are often highly cluttered, such that for any given contour fragment, multiple other fragments could be the correct continuation of the contour. Thus, to effectively exploit contours for object segmentation, the visual system must be able to cope with uncertainty, using a relaxed form of perceptual contour closure that can work reliably even for fragmented contours (e.g., Elder & Zucker, 1993) . Discovering the nature of these mechanisms is a central topic in modern perceptual organization research, involving a range of different methodologies, including psychophysics, neurophysiology, neuroimaging, ecological statistics, and computational modeling. Addressing the role of grouping under natural conditions requires a definition of the grouping primitives: What exactly are the elements being grouped? In the research with dot lattices reviewed above, the primitives were zero-dimensional points or dots, and proximity and similarity were the only cues involved. The study of contour grouping over oriented primitives such as bars or edges expands the grouping cues to also include good continuation. This maps directly onto related computer vision research, where the contour grouping problem is typically defined over local oriented edge elements detected using oriented linear filters (e.g., Canny, 1983 ) that can be loosely identified with receptive fields of simple cells in primate V1 (Hubel & Wiesel, 1968) . Even higher level primitives can be used, for instance, connected contour fragments of arbitrary shape, which may have been separated by occlusions. This higher level of representation may play a role in perceptual completion (see also below), and could be mapped to extrastriate visual areas such as V4, where neurons are known to be selective for higher order properties of shape (Pasupathy & Connor, 1999) . In psychophysics, this has motivated the use of fragmented object pictures, which can be used to study the dynamic interplay between perceptual grouping and object identification (e.g., Panis & Wagemans, 2009 ). In the following subsections, we first review the research on the role of grouping principles for contour integration-research that generalizes properties discovered for individual cues in isolation to more natural conditions where multiple cues are present and the visual stimulus may be quite complex. In addition to psychophys- ical results, we review the ecological foundations of the problem, and discuss computational principles and possible neural mechanisms. We then turn to the specific problem of contour completion in cases of occlusion, before discussing general issues pertaining to both perceptual grouping and contour integration. Proximity. The principle of proximity states that the strength of grouping between two elements increases as these elements are brought nearer to each other, but how exactly does grouping strength vary as a function of their separation? As reviewed above, Oyama (1961) found that this relationship could be accurately described as a power law, whereas Kubovy and Wagemans (1995) employed an exponential model, consistent with random-walk models of contour formation (Mumford, 1992; Williams & Jacobs, 1997) . However, Kubovy et al. (1998) also noted that a power law model could fit their data equally well and found that the proximity cue was approximately scale invariant: Scaling all distances by the same factor did not affect results. Since the power law is the only perfectly scale-invariant distribution, this last result adds strength to the power law model of proximity, which has been used in subsequent studies (e.g., Claessens & Wagemans, 2008) . Perceptual scale invariance is rational if in fact the proximity of elements along real contours in natural images is scale invariantthat is, if the ecological distribution follows a power law. In support of this idea, Sigman, Cecchi, Gilbert, and Magnasco (2001) reported that the spatial correlation in the response of collinearly oriented filters to natural images does indeed follow a power law. Quantitatively, however, the correspondence between psychophysics and ecological statistics is poor here: While Oyama (1961) estimated the perceptual power law exponent to be ␣ Ϸ 2.89, Sigman et al. estimated an ecological exponent of only 0.6, reflective of a much weaker cue to grouping. However, Sigman et al. did not restrict their measurements to pairs of neighboring elements on the same contour of the image. In fact, the measurements were not constrained to be on the same contour, or even on a contour at all, leading to a mixture between strongly related and only weakly related image features. Elder and Goldberg (2002) estimated these distributions more directly, asking human observers to label the sequence of elements forming the contours of natural images, with the aid of an interactive image editing tool. This technique allowed the measurements to be restricted to successive elements along the same contour, and yielded a clear power law with exponent ␣ ϭ 2.92, very close to the perceptual estimate of Oyama. Whether this exponent is independent of orientation in the image remains an interesting open question, but psychophysical data (Claessens & Wagemans, 2008) suggest that at least perceptually this may not be the case. In sum, the convergence between psychophysics and ecological statistics is compelling: Ecologically, proximity follows a power law and exhibits scale invariance, and these properties are mirrored by the psychophysical results. Thus, we have a strong indication that the human perceptual system is optimally tuned for the ecological statistics of proximity cues in natural scenes. Good continuation. A second important grouping principle for contour integration is good continuation, which refers to the tendency for elements to be grouped to form smooth contours (Wertheimer, 1923 (Wertheimer, /1938c . A very effective method for studying the principle of good continuation in cluttered images was developed by Field, Hayes, and Hess (1993) . In this method, a contour formed from localized oriented elements is embedded in a random field of homogeneously distributed distractor elements, in order to eliminate the role of proximity (see Figure 11 ). Aligning the contour elements tangentially to the contour makes the contour easily detected, whereas randomizing the orientation of the elements renders the contour invisible, clearly demonstrating the role of good continuation in isolation from proximity. These findings led Field et al. to suggest the notion of an association field that determines the linking of oriented elements within a local visual neighborhood (see Figure 12) , a construct that is closely related to the machinery of cocircularity support neighborhoods, developed earlier for the purpose of contour refinement in computer vision (Parent & Zucker, 1989) . Ecological data on good continuation have also emerged over the last decade. Krüger (1998) and later Sigman et al. (2001) found evidence for collinearity, cocircularity, and parallelism in the statistics of natural images. Geisler, Perry, Super, and Gallogly (2001) found similar results using both labeled and unlabeled natural image data, in fairly close correspondence with the tuning of human perception to the good continuation cue. Geisler et al. treated contours as unordered sets of oriented elements, measuring the statistics for pairs of contour elements on a common object boundary, regardless of whether these element pairs were close together or far apart on the object contour. In contrast, Elder and Goldberg (2002) modeled contours as ordered sequences of oriented elements, restricting measurements to adjacent pairs of oriented elements along the contours. The likelihood ratios for two Figure 11 . Example of stimuli devised by Field, Hayes, and Hess (1993) to probe the role of good continuation in contour integration. Adapted from "Contour Integration by the Human Visual System: Evidence for a Local 'Association Field'," by D. J. Field, A. Hayes, and R. F. Hess, 1993 , Vision Research, 33, p. 177. Copyright 1993 by Elsevier. Adapted with permission. 1189 100 YEARS OF VISUAL GESTALTS: I oriented elements to be neighboring elements on the same object boundary are much larger for the sequential statistics, reflecting a stronger statistical association between neighboring contour elements. Similarity. The principle of similarity states that elements with similar properties (e.g., brightness, contrast, color, texture) are more likely to group than elements that differ on these dimensions, which has been demonstrated in a number of ways with dot patterns (see above). For oriented elements, studies have generally found a decline in contour integration performance for contrast reversals under certain conditions but not others, suggesting nonadditive interactions with other grouping cues such as proximity and good continuation (e.g., Elder & Zucker, 1993; Field, Hayes, & Hess, 2000; Gilchrist, Humphreys, Riddoch, & Neumann, 1997; Rensink & Enns, 1995; Spehar, 2002) . Elder and Goldberg (2002) explored the ecological statistics of similarity in edge grouping, coding similarity in terms of the difference in brightness and in contrast between the edges, and found that the brightness cue carries useful information for grouping but the contrast cue is relatively weak. Whereas Elder and Goldberg restricted their study to pairs of elements of the same contrast polarity, Geisler and Perry (2009) have more recently studied the ecological statistics of contrast polarity, demonstrating that it is also an informative cue for contour integration. Closure. The role of closure in contour integration has been debated. Whereas Kovács and Julesz (1993) found superior detection performance for closed, roughly circular contours, compared to open curvilinear controls, these findings might also be based, in part, on good continuation alone. In fact, with stimuli more closely controlled for good continuation cues, Tversky, Geisler, and Perry (2004) found only a small advantage for closed contours and argued that this advantage could be due to probability summation rather than closure. While this negative result may seem inconsistent with the emphasis placed on closure in early Gestalt work, it is important to appreciate the exact nature of this early view, as expressed by Koffka (1935, p. 150 Ordinary lines, whether straight or curved, appear as lines and not as areas. They have shape, but they lack the difference between an inside and an outside. . . If a line forms a closed, or almost closed, figure, we see no longer merely a line on a homogeneous background, but a surface figure bounded by the line. The original Gestalt claim was thus not that closure is a grouping cue per se, but rather that it somehow profoundly determines the final percept of form. In the same spirit, Zucker (1993, 1994) argued that the most important role for closure was as a bridge from 1-D contour to 2-D shape, a suggestion that was supported by the finding that small changes in good continuation and closure can yield large changes in shape discriminability. Symmetry and parallelism. The Gestaltists identified symmetry as a factor of good shape (Koffka, 1935) , although it seems to be easily overruled by good continuation and convexity (Kanizsa, 1979) . In the computer vision literature, symmetry has been used in numerous contour integration algorithms (e.g., Mohan & Nevatia, 1992; Stahl & Wang, 2008) . Parallelism has been identified as a factor determining the perceptual simplicity of line configurations (Arnheim, 1967) , and as a grouping cue in computer vision algorithms (e.g., Jacobs, 2003; Lowe, 1985) . In the ecological statistics literature, parallelism has been studied extensively as a cue for the grouping of oriented edge elements into contours (Elder & Goldberg, 2002; Geisler et al., 2001; Krüger, 1998) . Psychophysical evidence for the role of symmetry and parallelism in contour integration has been reported by Feldman (2007) , who showed that comparison of features lying on pairs of line segments is significantly faster if the segments are parallel or mirror symmetric, suggesting a fast grouping of the segments based upon these cues. More recently, Machilsen, Pauwels, and Wagemans (2009) demonstrated enhanced detectability of bilaterally symmetric versus asymmetric closed forms, suggesting a role for more complex, global symmetry processing in contour integration. Physiologically, it is known that bilaterally symmetric patterns differentially activate human extrastriate visual areas V3, V4, V7 and LO, and homologous areas in macaque cortex (Sasaki, 2007) . Convexity. Convexity has long been known as a grouping cue (Rubin, 1927) . In the computer vision literature, Jacobs (1996) also demonstrated its utility for grouping contour fragments that can then be used as features for object recognition. Liu, Jacobs, and Basri (1999) subsequently employed a novel psychophysical Hess, 1993 , Vision Research, 33, p. 190. Copyright 1993 method to demonstrate the role of convexity in contour integration. Their method relies on the observation of Mitchison and Westheimer (1984) that judging the relative stereoscopic depth of two contour fragments becomes more difficult when the fragments are arranged to form a configuration with good continuation and closure. Using an elaboration of this method, Liu and colleagues showed that stereoscopic thresholds are substantially higher for occluded contour fragments that can be completed to form a convex shape, relative to fragments whose completion induces one or more concavities. This suggests that the visual system is using convexity as a grouping cue. In sum, research on contour integration, using oriented elements or shape fragments, has demonstrated important roles for the principles of proximity, good continuation, similarity, closure, symmetry, and parallelism. This research thus can be seen as an elaboration of early Gestalt work that established these principles phenomenologically. Importantly, however, work on contour integration has provided quantitative measures that have led directly to computational models and algorithms, and that have allowed direct comparison to the underlying ecological statistics of the problem and to neurophysiological results. Whereas the preceding section discussed research on the integration of contour fragments, the next section turns to the specific problem of contour completion in cases of occlusion, which brings us another step closer to understanding the role of grouping in more complex tasks of natural vision. Modal and amodal completion. Whereas contour integration refers to the integration of discrete elements such as dots or oriented elements, contour completion refers to the integration of smooth extended contours, separated by gaps due to occlusion or camouflage. Stimuli used in the study of contour completion often include cues to relative depth or occlusion, such as T junctions (see Figure 13 ). In Figure 13A , for example, the perceived unity of the black fragments and the perceived shape of the black surface behind the gray occluder appear to result from visual contour completion. This form of completion of the black shape behind the gray occluder is referred to as amodal completion (Michotte et al., 1964) . Although one has a compelling sense of continuity of the boundaries of the black surface behind the occluder, one does not actually see a contour. By contrast, illusory contours constitute an example of modal completion. They generate a percept of a contrast border in image regions that are physically homogeneous, such as the illusory edges of the white wedge in Figure 13B . Grouping and shape problem. For contour completion, the visual system must solve two problems (see Figure 14) . First, it must determine whether or not the two contour fragments are part of a single continuous contour: the grouping problem. Second, it must determine the shape of the missing portion of the contour: the shape problem. As a solution to the grouping problem, Kellman and Shipley (1991) proposed a relatability criterion. This criterion refers to the coding of contour geometry in terms of the positions and orientations of the edges of the contours. Two inducing contours are grouped if they satisfy two conditions. First, if extended linearly, these extensions must intersect, and second, the turning angle of the two edges should not exceed 90°. Evidence for the role of contour relatability has been found by means of observer ratings (Kellman & Shipley, 1991) , shape (fat/thin) discrimination performance (Ringach & Shapley, 1996; J. Zhou, Tjan, Zhou, & Liu, 2008) , depth discrimination performance (Liu et al., 1999; Yin, Kellman, & Shipley, 2000) , and interpolation settings (Fulvio, Singh, & Maloney, 2008) . The shape problem involves determining the shape of the occluded portion of the contour. This is a highly underconstrained problem, since an infinite number of possible shapes could be hidden behind the foreground shape (see Figure 14C ). Human observers typically perceive only a small subset of these. This suggests that the visual system imposes strong constraints when generating and selecting the set of possible shapes. Different methods have been used to examine how the visual system solves the shape problem. For example, several studies have asked participants to draw the perceived trajectory of visually completed Figure 13 . A: Amodal completion of the black shape behind the gray shape. B: A white shape seen on top of three black shapes. The perceived contours of this white shape have a sensory quality (hence, modal completion), although they are completely illusory. Adapted from "Bayesian Contour Extrapolation: Geometric Determinants of Good Continuation," by M. Singh and J. M. Fulvio, 2007, Vision Research, 47, p. 784 (Takeichi, Nakazawa, Murakami, & Shimojo, 1995; Ullman, 1976 ). Other studies have asked observers to mark the farthest point along the interpolated contours (Fantoni, Bertamini, & Gerbino, 2005; Guttman & Kellman, 2004; Takeichi et al., 1995) , to match the perceived interpolated shape from a parametric family (Singh, 2004) , or to rate its overall degree of roundedness (Fantoni & Gerbino, 2003) . More recently, Fulvio et al. (2008) used a method that obtains interpolation settings (position and orientation) at multiple locations along the length of a partly occluded contour. An examination of the precision and consistency of these settings showed that observers can interpolate a single, stable (self-consistent), smooth contour when the inducing contours are relatable, but not when they require an inflecting interpolating curve. An empirically successful model that addresses the grouping problem and the shape problem simultaneously has been proposed by van Lier (1999; van Lier, van der Helm, & Leeuwenberg, 1994 . In line with the descriptive simplicity principle (see Wagemans et al., 2012, Sections 5 and 6), this model postulates that an interpretation is judged not only by the complexities of the potentially occluding and occluded shapes but also by the complexity of the relative positions of these shapes. The combination with the lowest overall complexity is then taken to predict whether occlusion occurs, and if so, how the occluded shape looks. Contour interpolation and extrapolation. Good continuation is an important criterion in shape interpolation, but it is not perfectly clear what is meant by this term. Dating back to Wertheimer (1923, especially his Figures 16 -19), two aspects have been distinguished: (a) What geometric properties of the visible contours are used by human vision (e.g., orientation, curvature, rate of change of curvature, higher order derivates), and (b) how are they combined to define the shape of the contour? These questions were addressed in studies of contour extrapolation (e.g., Singh & Fulvio, 2005 , in which observers adjusted the position and orientation of a line probe on the other side of an occluder (see Figure 15 ) at multiple distances from the point of occlusion in order to optimize the percept of smooth continuation. The findings suggested that observers use contour orientation and curvature, but not rate of change of curvature. The shape of visually extrapolated contours was best characterized by a decaying curvature. The results were modeled by a Bayesian interaction between a tendency to extend contour curvature and a prior tendency for straight contours.
We tune our method especially towards this aim by setting the model hyperparameters to produce clusters of superpixels that have a strong link to human object perception as described by the Gestalt principles of human object perception REF .
A Century of Gestalt Psychology in Visual Perception: I. Perceptual Grouping and Figure–Ground Organization
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