Running head : PERCEPTUAL GROUPING OF LINE SEGMENTS Spatial relations inducing perceptual grouping of line segments : a microgenetic study

Perceptual grouping is the process by which elements in the visual image are aggregated into larger and more complex structures, i.e. “objects.” Grouping is thought to be promoted by certain types of spatial relations among image elements, but the relative binding strength of different relations is not well understood, nor is the chronology of the grouping process. This paper reports a comprehensive study measuring grouping of visual elements in many geometric configurations, including nonaccidental properties such as collinearity, cotermination and parallelism, contour relatability, Gestalt factors such as symmetry and skew symmetry, and others. The study used an “objective” methodology capable of very fine temporal precision, allowing a detailed account of the time-course of grouping, and of each specific grouping factor. Generally, the data reveal that objects bind the most effectively due to local good continuation, as well as highly regular spatial relations such as parallelism and symmetry. Configurations whose structure suggests two distinct objects—e.g. T-junctions, which cue occlusion boundaries—undergo an initial period (about 125msec) of provisional grouping, and then (125–200msec) begin to progressively break up or “ungroup.” The data paint a vivid picture of the chronology of object formation, as fully bound visual objects progressively develop over the first two hundred milliseconds of processing. Perceptual grouping of line segments 3 Spatial relations inducing perceptual grouping of line segments: a microgenetic study The organization of the initially inchoate visual field into coherent units or “objects,” called perceptual grouping or binding, is of fundamental importance in visual perception, influencing the perception of lightness (Adelson, 1993; Gilchrist, 1977), motion (Shimojo, Silverman, & Nakayama, 1988), and recognition of objects (Biederman, 1987; Tarr, 1995). Much has been learned about the grouping factors originally identified by the Gestaltists, such as spatial proximity (Compton & Logan, 1993; Kubovy & Wagemans, 1995), collinearity (Caelli & Umansky, 1976; Feldman, 1997a, 2001; Foster, 1979, 1983; Pizlo, Salach-Golyska, & Rosenfeld, 1997; Smits, Vos, & Oeffelen, 1985),and parametric similarity (Geisler & Super, 2000; Zucker, Stevens, & Sander, 1983). Yet surprisingly little is known about the role of more complex geometric factors on grouping, notwithstanding a large number of conflicting theoretical proposals. One particularly important and often-discussed case is grouping of line segments, because simple oriented elements are thought to be the basic units in the early visual system. But even the minimal case of two line segments is poorly understood. What spatial relations between two line segments tend to induce binding? Many answers to this question have been proposed, with surprisingly little direct psychophysical evidence to adjudicate. One very influential proposal is that grouped configurations tend to be nonaccidental properties (Lowe, 1987; Witkin & Tenenbaum, 1983), that is, configurations that seem unlikely to have occured by accident—or, in Horace Barlow’s phrase, “suspicious coincidences” (Barlow, 1994). Such configurations, including (at least) collinearity , cotermination (b), and parallelism (c), probabilistically imply the presence of stable structure in the 3D world (Jepson & Richards, 1992), and hence make promising candidates for grouping. Biederman (1987) provided some initial empirical evidence that nonaccidental groupings are perceptually important and highly detectable. However more recent experimental investigations (Wagemans, 1992) have yielded more equivocal results, leaving open the question of Perceptual grouping of line segments 4 whether nonaccidental properties actually do in fact promote grouping, and if so, to what degree, and how the binding induced by the three best-known nonaccidental properties compare to each other. Insert Figure 1 about here Moreover, several other geometric factors have been proposed as candidate grouping cues. Prominent among these are realizations of the Gestalt notion of good continuation, including cocircularity (Ullman, 1976; Parent & Zucker, 1989) and relatability (Kellman & Shipley, 1991) . (These two relations approximatly coincide in the case of line segment pairs, and in what follows I will use the term relatability to encompass either one.) Two line segments are relatable if a smooth curve can be passed from the end of one to the beginning of the other without loops or inflections (Singh & Hoffman, 1999). Relatability is not strictly equivalent to any nonaccidental property, though it is of course closely related to collinearity. It is thought to play a major role in early visual completion (Field, Hayes, & Hess, 1993), but its its tendency to promote grouping of line segments, and in particular relative to other potential grouping cues, is not well known. The field of potential grouping factors expands considerably more when one considers more global or configural factors such as bilateral symmetry  skew symmetry (i.e., bilateral symmetry as viewed from a slant), and even biaxial skew symmetry . Symmetry (Wagemans, 1995, 1993) and other kinds of global regularity (Boselie & Wouterlood, 1989; Kanizsa, 1979; Leeuwenberg, 1971) have long been invoked as organizational principles in the visual system, and have even been found to override local cues when the two are put in conflict (Sekuler, Palmer, & Flynn, 1994). However local cues are more amenable to early computation by the visual system, raising the question of how their relative time-courses of local and global cues might differ. Several other types of line segment configurations are of particular interest. Perpendicularity Perceptual grouping of line segments 5 (i) is another special configuration that has been thought to have an early role in assigning local 3D structure (Enns & Rensink, 1991). One also naturally wonders whether actual contact (Fig. 1j) matters, as would be predicted by the principle of “uniform connectedness” (Palmer & Rock, 1994) (but not corroborated by recent findings (Kimchi, 2000))—but not if nonaccidentalness were the sole factor, because transverse crossing of lines (as in the figure) is not nonaccidental. Contraposed to all of these regular and potentially binding-inducing configurations is the case of totally irregular or generic line segment pairs  (“none of the above” cases), which bear no apparent structural relationship. Such configurations constitute the natural baseline against which more regular candidate configurations ought to be compared. Finally, one particularly interesting question is the case of T-junctions , which are thought to signal occlusion boundaries (Clowes, 1971). These are in effect an anti-grouping cue, in that the head and stem of the T would normally be interpreted as respectively the occluding and occluded boundaries of two distinct objects (though of course in particular situations other interpretations are possible). Hence the question of whether T-junctions induce binding is particularly urgent. To complicate matters further, many of the above-mentioned categories overlap, raising the question of how multiple cues might combine in influencing binding, a difficult question recently of great theoretical interest (Feldman, 1997b; Landy, Maloney, Johnston, & Young, 1995). Hence a thorough investigation would include not only cases of each of the above properties but would range over the entire space of possible line segment pairs, including all geometrically possible combinations of the relations of interest. Chronology of perceptual grouping. The time-course of perceptual grouping is also very little understood. Debate exists over whether grouping is pre-attentive, and thus presumably early (Prinzmetal & Banks, 1977; Treisman, 1982), or post-attentive and thus presumably late (Mack, Tang, Tuma, Kahn, & Rock, 1992). Simple scene classification may be substantially complete by 150msec of processing (Thorpe, Fize, & Marlot, 1996), though some visual illusions do not Perceptual grouping of line segments 6 become completely effective until as much as 250msec of exposure (Reynolds, 1978). Subjective contours have been found to be computed as early as about 100msec (Ringach & Shapley, 1996). Amodal completely (i.e. completion of a contour behind a visible occluder) has been found to be substantially complete by 200msec of processing (Sekuler & Palmer, 1992), with a more recent study with more precise methodology indicating as early as 75-100msec (Murray, Sekuler, & Bennett, 2001). An important contribution are the studides of Kimchi (1998, 2000), which have charted the time-course of early completion processes using objective methodology (primed matching), although not directly testing the contribution of the various two-segment geometric factors considered here. These diverse findings raise the possibility that grouping might involve a number of different rules or mechanisms, each with their own timing profiles, making it difficult to map out the chronology without a temporally fine-grained methodology and systematic manipulation of cues. The current paper reports the results of a large experiment testing the degree of binding induced by a wide variety of line segment configurations, including examples of all of the above-mentioned special categories and combinations. The experiment used a new psychophysical methodology capable of very accurate and chronologically precise estimates of the magnitude of binding. Measurements of grouping strength for each configuration type were taken at a finely sampled sequence of time-slices, yielding an unprecedentedly detailed look at the chronology of perceptual grouping in perhaps its most basic case. Experimental paradigm Historically, experiments on visual grouping have often used