1

Dynamic grouping motion: A method for determining

perceptual organization for objects with connected surfaces

Howard S. Hock

Department of Psychology and the Center for Complex System and Brain Sciences,

Florida Atlantic University, Boca Raton FL 33431 U.S.A.,email: hockhs@fau.edu

To appear in: Oxford Handbook of Perceptual Organization Oxford University Press Edited by Johan Wagemans

1. Overview

Rather than focusing on a particular aspect of perceptual organization, the purpose of this chapter is to

describe and extend a new methodology, dynamic grouping, which cuts across and addresses a wide

variety of phenomena and issues related to perceptual organization. The need for this new methodology,

which was introduced by Hock and Nichols (2012), arises from its relevance to the most common stimulus

in our natural environment, objects composed of multiple, connected surfaces. Remarkably, and despite

Palmer and Rock’s (1994) identification of connectedness as a grouping variable, there has been no

systematic research concerned with the perceptual organization of connected surfaces. This chapter

demonstrates the potential of the dynamic grouping method for furthering our understanding of how

grouping processes contribute to object perception and recognition. It shows how the dynamic grouping

method can be used to identify new grouping variables, examines its relevance for how the visual system

solves the “surface correspondence problem” (i.e., determines which of an object’s connected surfaces are

grouped together when different groupings are possible), and provides a concrete realization of the

classical idea that the whole is more than the sum of the parts. The chapter examines the relationship

between dynamic grouping and transformational apparent motion (Tse, Cavanagh & Nakayama, 1998) and

provides insights regarding the nature of amodal completion and how it can be used to examine classical

Gestalt grouping variables entailing disconnected surfaces (e.g., proximity). Finally, it demonstrates that

perceptual grouping should have a more prominent role in theories of object recognition than is currently

the case, and proposes new theoretical approaches for characterizing the compositional structure of

objects in terms of ‘multidimensional affinity spaces’ and ‘affinity networks’.

2. The lattice method

Grouping laws, which were originally delineated by Wertheimer (1923), characterize the effect of various

stimulus variables on perceptual organization. How the components of a stimulus are grouped together

depends on such variables as closure, proximity, similarity, movement direction (common fate), and good

continuation (Brooks, this volume). The predominant method for studying grouping variables has entailed

the perceived orientation of 2-D lattices composed of disconnected surfaces (Wertheimer, 1923; Rush,

1937; Kubovy & Wagemans, 1995; Palmer, Neff & Beck, 1996; Gori & Spillman, 2011; Kubovy, this volume).

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This method is appropriate for the large volume of research concerned with the recovery of objects from

surface fragments that have become disconnected as a result of degraded viewing conditions (e.g., Lamote

& Wagemans, 1999; Shipley & Kellman, 2001; Fantoni, Hilger, Gerbino & Kellman, 2008). Under non-

degraded conditions, however, objects always are composed of connected surfaces. It would not be

surprising, therefore, if a different set of grouping variables applied. Nor would it be surprising that a

substantially different methodology would be required in order to study these grouping variables.

The great success of the lattice method stems from the isolation of grouping variables and the

determination of their effects from competition between alternative perceptual organizations. Similarity in

shape is isolated for the Wertheimer (1912) lattice in Figure 1a; parallel rows are perceived because the

surfaces composing alternating rows are more similar than the surfaces composing columns, so there is

greater grouping strength horizontally than vertically. Proximity is isolated for the lattice in Figure 1b;

parallel columns are perceived because the surfaces composing each column are closer together than the

surfaces composing each row, so there is greater grouping strength vertically than horizontally. Finally,

shape similarity competes with proximity for the lattice in Figure 1c. Parallel columns are perceived

because grouping strength due to proximity is greater than grouping strength due to shape similarity.

Significantly, however, the outcome of this competition between proximity and shape similarity is not true

in general. It holds only for the particular differences in proximity and the particular differences in shape

for the stimulus depicted in Figure 1c.

What is needed for significant progress in our understanding of perceptual organization, especially as it

applies to the connected surfaces of objects, is the development of a new empirical tool for assessing

grouping strength for pairs of adjacent surfaces, and the determination of how the effects of cooperating

grouping variables are combined to establish overall grouping strength (affinity) for pairs of adjacent

surfaces. The prospect for a methodology meeting these requirements is a fully described compositional

structure for an object (i.e., the pair-wise affinities for all the object’s surfaces), and the determination that

the compositional structure is central to the recognition of the object.

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Figure 1. (a,b,c) Examples using Wertheimer’s (1912) lattice method to identify grouping

variables and determine their relative strength by the outcome of competition between two

perceptual organizations. (d,e) Examples of stimuli for which dynamic grouping (DG) motion is

perceived. (f,g) Nonlinear functions relating the combined effect of grouping variables to the

affinity of the surfaces in panels d and e. Because of super-additivity, changes in affinity are

larger and therefore, DG motion is stronger, when pre-perturbation luminance similarity is

greater. (h) Example of a stimulus from Tse, Cavanagh and Nakayama (1998) for which

transformational apparent motion (TAM) is perceived in relation to the square. (i) A version of

Tse et al.‘s (1998) stimulus for which DG motion also is perceived in relation to the square. (j,k)

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Nonlinear functions relating the combined effect of grouping variables to affinity for the two

pairs of surfaces in panel i. Because of super-additivity, changes in affinity are larger and

therefore, DG motion is stronger, for the surface pairs that benefit in pre-perturbation

grouping strength from good continuation.

3. Dynamic grouping: methodology and concepts

A method with the potential to meet these requirements has recently been reported by Hock and Nichols

(2012). It entails the perception of motion due to dynamic grouping (DG).1 In their experiments, 2-D objects

composed of two or more adjacent surfaces are presented in a randomly ordered series of two-frame trials.

The first frame’s duration is on the order of one second, allowing sufficient time for the perceiver to focus

attention on the fixation dot located in the center of the target surface. Preliminary testing has indicated

that this duration is sufficient to establish the compositional structure for simple geometric objects (i.e., the

affinity relationships among the object’s surfaces). However, it remains to be determined whether different

compositional structures would be obtained for other frame durations as a result of differences in the rate

with which affinities are established for different grouping variables (see Section 3.5).

The target in the dynamic grouping paradigm is the surface for which an attribute is changed during the

second frame, the duration of which is on the order of half a second. The luminance of the target surface

always is greater than the luminance of the surfaces with which it is connected. While some grouping

variables remain the same during the transition from Frame 1 to Frame 2, dynamic grouping variables

change in value as a result of changes to the target surface. The change (say in luminance) increases or

decreases the affinity of the target surface with each of the surfaces adjacent to it, without qualitatively

changing the perceptual organization of the geometric object. Changes (perturbations) in surface affinities

that are created by dynamic grouping (DG) variables, when large enough, elicit the perception of motion

across the changing target surface.2 3The direction of the DG motion is diagnostic for the affinity

relationships among the stimulus’ surfaces that were established during Frame 1, prior to the change in the

target surface during Frame 2.

3.1 The direction of dynamic grouping motion

For the 2-D objects depicted in Figures 1d and 1e, connectivity (Palmer & Rock, 1994), co-linearity of

horizontal edges (i.e., good continuation) and luminance similarity are grouping variables that combine to

determine the affinity of the two surfaces during Frame 1. Changing the horizontal bar’s luminance

1 Watt and Phillips (2000) use the term ‘dynamic grouping’ in a much different sense. Rather than motion induced by changing values of grouping variables, their emphasis is on the dynamical, self-organizational aspect of perceptual grouping for both moving and static stimuli. 2 Previous experiments concerned with perceptual grouping and motion perception have studied the effects of unchanging grouping variables on the perceptual organization of motions elicited by the displacement of surfaces (e.g., Kramer & Yantis, 1997; Martinovic, Meyer, Muller & Wuerger, 2009). Dynamic grouping differs in that the perception of motion is across a changing surface that is not displaced, and is elicited by changes in grouping variables. 3 Dynamic grouping motion, although weaker, is phenomenologically similar to the line motion illusion that is obtained when the changing surface is darker than the surfaces adjacent to it (Hock & Nichols, 2010). For the latter, motion perception results from the detection of oppositely signed changes in edge and/or surface contrast (i.e., counterchange). The avoidance of counterchange-determined motion is why the dynamic grouping method requires the target surface to be lighter than surfaces adjacent to it.

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during Frame 2 changes its luminance similarity with the unchanged square surface next to it; i.e., luminance similarity is the dynamic grouping (DG) variable. The change in the surfaces’ luminance similarity perturbs the surfaces’ affinity, inducing the perception of motion across the changing target surface. It can

be seen in Movie 1 (part 1) http://gestaltrevision.be/pdfs/oxford/movies/Hock/Movie1.mov that the motion perceived across the changing surface is toward the boundary when the affinity of the two surfaces decreases; the boundary is momentarily more salient, as if for the moment the grouping of the surfaces is weaker (Figures 1d and 1e). The motion is away from the boundary when their affinity increases; the boundary is momentarily less salient, as if for the moment the grouping of the surfaces is strengthened (Movie 1, part 2). These directions are characteristic for DG induced motion. In viewing these movies, and the movies that follow, it is important to immediately fixate on the dot in the center of the target surface and to closely maintain fixation and attention on the dot for the entire trial. The implications of fluctuations in eye position or covert attention shifts without eye movements (Posner, 1980) are discussed in Section 6.0.

3.2 Affinity and the surface correspondence problem

The term affinity is the conceptual lynchpin for the dynamic grouping method. It entails any variable

affecting the likelihood of two surfaces being grouped together. The term is derived from Ullman's (1979)

“minimal-mapping” account of how the visual system solves the motion correspondence problem, which

arises when there are competing possibilities for the perception of apparent motion from an initially

presented surface to one of two or more surfaces that replace it. Ullman shows that such ambiguities in

how surfaces are grouped over time can be resolved by differences in the affinity of the initially presented

surface with each of the subsequently presented surfaces that replace it.

Like Ullman’s (1979) minimal mapping, the dynamic grouping (DG) method stipulates that differences in

affinity resolve ambiguities, but now for ambiguities entailing the alternative ways in which adjacent

surfaces can be grouped. Rather than solving the motion correspondence problem in time, the objective is

to solve this surface correspondence problem in space (the latter is called “instability of structural

interpretation” by Edelman, 1997). In contrast with Ullman, changes in affinity result in the perception of

motion within one of two or more adjacent surfaces rather than motion between two or more non-

adjacent surface locations. In addition, Ullman’s concept of affinity is extended to account for the

combined effect of multiple grouping variables on the affinity of surface pairs; i.e., how they cooperate in

determining over-all grouping strength.

3.3 State-dependence and super-additivity

Hock and Nichols (2012) found, for pairs of adjacent surfaces, that the frequency with which motion is

perceived in DG-determined directions depends on the affinity state of the surfaces (during Frame 1), prior

to the perturbation in affinity produced by the dynamic grouping variable (during Frame 2). Although other

grouping variables could serve as DG variables, for example, hue similarity and texture similarity in Hock

and Nichols (2012), the focus in this chapter is on the luminance similarity of pairs of surfaces (as measured

by their inverse Michelson contrast). Thus, the greater the luminance similarity for a pair of surfaces during

Frame 1 (their pre-perturbation luminance similarity), the more often DG-specified motion is perceived

when luminance similarity is changed (perturbed) during Frame 2. Hock and Nichols (2012) showed that

these results were consistent with the affinity of these surfaces depending on the nonlinear summation of

the affinity values ascribable to individual grouping variables (connectivity, good continuation, and

luminance similarity). This is illustrated in Figures 1f and 1g by power functions (the curved gray lines),

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although the only requirement is for the accumulated effects of individual grouping variables on affinity to

be super-additive; i.e., the combined effects of individual variables on affinity must be greater than their

linear sum.

It can be seen in these figures that the strength of DG motion induced by perturbing a surface-pairs’ affinity

depends on the Frame 1, pre-perturbation affinity state of the surfaces. It lies on a steeper segment of the

nonlinearly accelerating grouping/affinity function when the pre-perturbation affinity of the surfaces is

larger (in this case because of greater luminance similarity prior to the perturbation). As a result of this

advantage in pre-perturbation affinity, the same Frame 2 perturbation in luminance similarity produces a

larger change in the affinity of the two surfaces, and thereby elicits a stronger signal for motion across the

changing surface in characteristic DG-determined directions (i.e., away from the boundary of the surfaces

when their affinity increases, and toward the boundary when their affinity decreases.

3.4 Compositional structure: solving the surface correspondence problem

An example stimulus from Tse, Cavanagh and Nakayama’s (1998) study of “transformational apparent

motion” (TAM) is presented in Figure 1h (see also Blair, Caplowitz & Tse, this volume). A horizontal bar

connects the square and vertical bar, which are spatially separated during Frame 1, during Frame 2. The

square then appears to be transformed into an elongated horizontal bar (Movie 2, part 1)

http://gestaltrevision.be/pdfs/oxford/movies/Hock/Movie2.mov . Tse et al. (1998) conclude that this

occurs because the square and horizontal bar are preferentially grouped as a result of good continuation.

Hock and Nichols (2012) studied a version of this stimulus for which all three surfaces are always visible

(Figure 1i). For this stimulus, the square and horizontal bar can be grouped to form a subunit, and the

subunit grouped with the vertical bar. However, an alternative compositional structure also is possible.

That is, the vertical and horizontal bars could be grouped to form a subunit, and the subunit grouped with

the square. How this surface correspondence problem is solved depends on the pre-perturbation affinity

relationships among the surfaces composing the object. On this basis, good continuation is decisive for the

stimulus depicted in Figure 1i because of asymmetry in the pre-perturbation affinity of the horizontal bar

with its two flanking surfaces; luminance similarity and connectivity contribute to the pre-perturbation

affinity of the horizontal bar with both flanking surfaces, whereas good continuation only contributes to the

horizontal bar’s affinity with the square (Figures 1j and 1k).

The asymmetrical effects of good continuation mean that the pre-perturbation affinity state for the

horizontal bar and square is located on a steeper segment of the accelerating grouping/affinity function

compared with the pre-perturbation affinity state for the horizontal bar and vertical bar. Consequently, the

same perturbation in luminance similarity produces a larger perturbation in the horizontal bar’s affinity

with square than its affinity with the vertical bar, and unidirectional DG motion is perceived in relation to

the square rather than the vertical bar. That is, the DG motion that is perceived across the horizontal bar is

away from the square when their luminance similarity increases (Movie 2, part 2), and is toward the square

when it decreases. The dominance of the stronger affinity relationship of the horizontal bar and the square

is confirmed by the perception of the same DG motion directions when a gap separates the horizontal and

vertical bars, but not when the gap separates the horizontal bar and square.

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Figure 2. (a) A version of Tse et al.’s (1998) stimulus for which unidirectional dynamic grouping

motion is perceived in the direction determined by hue similarity. (b) A similar stimulus, but

with the horizontal bar presented only during Frame 2. Transformational apparent motion is

perceived in the direction determined by good continuation. (c,d) Nonlinear functions relating

the combined effect of grouping variables to affinity for the two pairs of surfaces in panels a

and b. Both are consistent with hue similarity more strongly affecting grouping strength than

good continuation. (e) For relatively long boundary lengths, dynamic grouping (DG) motion is

perceived across the changing surface on the left when its luminance is increased. (f) For the

same change in luminance, either no motion or symmetrically divergent motion is perceived

when the boundary is shorter. (g) The perception of DG motion across the surface on the left is

restored when the luminance of the surface on the right is raised, increasing the luminance

similarity and thereby the pre-perturbation affinity of the two surfaces.

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3.5 Dynamic grouping motion versus transformational apparent motion

Another version of the Tse et al. (1998) stimulus indicates that good continuation does not necessarily

dominate in resolving the surface correspondence problem. In this example (Figure 2a), the presence of

hue similarity strengthens the pre-perturbation affinity of the horizontal and vertical bars sufficiently for

their over-all affinity to frequently predominate in determining the direction of DG motion, and therefore,

the pre-perturbation compositional structure of the stimulus. That is, when luminance similarity increases,

unidirectional DG motion is perceived across the horizontal bar, away from the vertical bar rather than

away from the square (Movie 3, part 1) http://gestaltrevision.be/pdfs/oxford/movies/Hock/Movie3.mov .

This asymmetry in motion perception can again be traced to the nonlinear grouping/affinity function. That

is, the pre-perturbation affinity state is greater when hue similarity contributes to the grouping of the

horizontal and vertical bars, compared with when good continuation contributes to the grouping of the

horizontal bar and square (Figure 2c). As a result of the affinity for the horizontal and vertical bars being

located on a steeper segment of the grouping/affinity function, the perturbation of luminance similarity

produces a greater change in affinity, and therefore, stronger DG motion across the horizontal bar in

relation to the vertical bar than in relation to the square. (It is noteworthy that this difference in grouping

strength between good continuation and hue similarity for this stimulus would not be discernible without

something like the DG method.)

When the horizontal bar is presented only during the second frame (Figure 2b), as in Tse et al.’s (1998)

TAM paradigm, good continuity predominates despite the apparently stronger affinity of the horizontal and

vertical bars because of their hue similarity; i.e., the square appears to expand into a long horizontal bar

(Movie 3, part 2). As illustrated in Figure 2d, there is minimal pre-perturbation affinity during the first frame

for this stimulus (the effect of proximity grouping for the separated surfaces is assumed to be negligible),

and the insertion of the horizontal bar results in a larger change in affinity for the grouping of the

horizontal and vertical bars compared with the horizontal bar and square. If the perception of motion

depended only on the size of the affinity change, TAM, like DG motion, would have been in relation to the

vertical bar. This is the opposite of what is actually perceived.

The perceptual differences between DG and TAM for the stimuli in Figures 2a and 2b indicate that they do

not always reflect identical aspects of perceptual organization. What then is the relationship between

them? A dynamical model (Hock, in preparation) demonstrates that DG and TAM can entail the same

processing mechanisms, with both depending on differences in the rate of change in affinity that results

from changes in grouping variables. DG and TAM function differently in the model in that TAM depends on

different grouping variables having different rates of change in affinity, whereas DG motion depends as

well on rates of change varying according to the level of stable, pre-perturbation affinity. The perceptual

results described above suggest that hue similarity may have a stronger effect on surface affinity than good

continuation, but the contribution of good continuation to surface affinity may emerge more rapidly.

3.6 Identifying new grouping variables

Although there are many stimulus variables that might affect the appearance of two surfaces, they do not

necessarily affect their affinity. That is, a stimulus variable may or may not function as a grouping variable.

This is an important consideration because it would affect the likelihood that surfaces would be grouped

together when they are embedded in a more complex, multi-surface object.

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The DG method can be used to identify new grouping variables by testing different values of a stimulus

variable and determining whether each value requires a different amount of pre-perturbation luminance

similarity in order for motion to be perceived in directions characteristic of DG. For example, if the length of

the boundary separating two surfaces is a grouping variable that affects their affinity, different levels of

luminance similarity would be required in order for unidirectional DG motion to be perceived for different

boundary lengths. When the boundary is relatively long, the pre-perturbation luminance similarity for the

stimulus in Figure 2e and Movie 4 (part 1) http://gestaltrevision.be/pdfs/oxford/movies/Hock/Movie4.mov

is sufficient to perceive DG motion across the target surface on the left. When the boundary is shorter, this

level of luminance similarity results in either the perception of no motion or the perception of symmetrical,

diverging motion (Figure 2f and Movie 4, part 2). Additional pre-perturbation luminance similarity is

required (luminance is raised for the surface on the right) in order for DG motion to be perceived for the

shorter boundary (Figure 3g and Movie 4, part 3), indicating that the strength of the grouping variable

increases with increases in the length of the boundary separating pairs of adjacent surfaces.

3.7 Implications of super-additivity

Super-additivity, according to which the combined effects of cooperating grouping variables on the overall

affinity of two surfaces exceeds their linear sum, is a concrete realization of the principle that the whole is

more than the sum of the parts (von Ehrenfels, 1890; Wagemans, this volume). An important consequence

of super-additive nonlinearity is that the effect of a particular grouping variable on the affinity of a pair of

adjacent surfaces is context dependent. That is, it will vary, depending on the presence or absence of other

cooperating grouping variables. This contrasts with Bayesian analyses indicating that the effects of

grouping variables are independent, or additive (e.g., Elder & Goldberg, 2002). Although Bayesian

independence was confirmed by Claessens and Wagemans (2008) using the lattice method, they also

found, inconsistent with Bayesian-determined independence, that the relative strength of proximity and

co-linearity depended on whether their lattice aligned with cardinal axes or was oblique.

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Figure 3. (a) A stimulus for which the perception of dynamic grouping (DG) motion is indicative

of amodal completion behind the occluding cube. The direction of the motion is consistent

with the implied presence of a discontinuous luminance boundary separating surfaces A and C.

(b) Unidirectional DG motion is perceived across the square surface on the right when its

luminance is decreased and the occluding surface is relatively narrow (the squares are

relatively close together). (c) For the same change in luminance, DG motion is not perceived

when the occluding surface is relatively wide (the squares are further apart). (d) The

perception of DG motion across the square on the right is restored when the luminance of the

square on the left is lowered, increasing the luminance similarity and therefore the pre-

perturbation affinity of the two physically separated surfaces. (e) Variation of a stimulus from

Biederman (1987). The dynamic grouping motion that is perceived when the luminance of

surface B is decreased is consistent with its grouping with surface A, perhaps to form a

truncated cone, a ‘geon’ which contributes to the recognition of the object as a lamp in

Biederman’s (1987) recognition-by-components theory.

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4. Amodal completion

The DG method can be used to gain further insights into amodal completion, which is typically concerned

with the continuity of unseen stimulus information in time (e.g., Yantis 1995; Joseph & Nakayama, 1999)

and space (e.g., Michotte, Thiinès, & Crabbè, 1964; Tse, 1999; van Lier & Gerbino, this volume). It also can

be used to establish the strength of grouping variables for disconnected surfaces.

4.1 Hidden boundaries

For the stimulus in Figure 3a, a partially occluded light gray bar composed of surfaces A and C is readily

perceived during the first frame of a two-frame trial. When surface A’s luminance is decreased during the

second frame, its luminance similarity with surface C decreases, resulting in diagonally upward DG motion

across A, toward an amodal hidden boundary with C (Movie 5)

http://gestaltrevision.be/pdfs/oxford/movies/Hock/Movie5.mov .

In addition to its effect on the affinity of surfaces A and C, the luminance decrease for surface A increases

its similarity with surface B, so if DG motion were determined strictly on the basis of whether surfaces are

adjacent on the retina, the motion across surface A would have been in the opposite direction, away from

surface B. That the direction of DG motion is consistent with the grouping of surfaces A and C is important

because: 1) it shows that amodal completion can entail discontinuous luminance boundaries, not just

continuity, 2) the DG method can be diagnostic for the grouping of surfaces even when their common

boundaries are hidden, and 3) it enables the measurement of affinity for non-adjacent surfaces. The latter

feature is the basis for the measurement of proximity effects, which is described next.

4.2 The effects of proximity

Pairs of co-linear squares that are separated by an occluding surface can be used to measure proximity

effects, which would be expected to decrease as the width of the occluding surface is increased. For the

relatively narrow occluder in Figure 3b, the perception of unidirectional DG motion across the target square

on the right requires relatively little pre-perturbation luminance similarity (Movie 6, part 1)

http://gestaltrevision.be/pdfs/oxford/movies/Hock/Movie6.mov . However, proximity grouping is weaker

when the width of the occluder is increased, so DG motion is not perceived (Figure 3c and Movie 6, part 2).

It is perceived across the square on the right when luminance is lowered for the square on the left (Figure

3d and Movie 6, part 3). This is because the change in luminance increases the pre-perturbation luminance

similarity of the two square surfaces, which are physically separate but nonetheless perceptually grouped.

The pre-perturbation luminance similarity required in order to perceive motion in DG-determined

directions increases (the Michelson contrast of the physically separated surfaces decreases) with successive

increases in the distance between the squares. Precise psychophysical measurements with systematically

varied pre-perturbation luminance similarity will make it possible to determine whether the ratios based on

the equivalent luminance similarity for each proximity value (including a proximity value of zero) will be

consistent with the distance ratios measured by Kubovy and Wagemans (1995) in their experiments using

the lattice method.

5.Implications for object recognition

The most prominent theories of object recognition are based on the spatial arrangement of 3-D geometric

primitives (Marr & Nishihara, 1978; Pentland, 1987; Biederman, 1987). Much of the research evaluating

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these theories has addressed their limitations with respect to viewpoint invariance (e.g., Tarr, Williams,

Hayward & Gauthier, 1998), Ieading to alternative models entailing the encoding of different views of the

same object (e.g., Ullman, 1989). However, these image-based models have their own limitations with

respect to category invariance; i.e., they are problematic for the classification of other objects belonging to

the same category (Edelman, 1997; Tarr & Bultoff, 1998). A further limitation is that in contrast with the

computer vision literature (e.g., Lowe, 1987; Arseneault, Bergevin & Laurendeau, 1994; Jacobs, 1996; Iqbal

& Aggarwal, 2002), grouping properties have not been incorporated into psychological theories of object

recognition (Palmer, 1999). A possible reason for this has been the absence, until now, of a suitable

empirical method for identifying grouping variables specific to the connected surfaces of objects and

determining the combined effect of these grouping variables. Described below is the use of the DG method

to demonstrate the potential for perceptual grouping to play a more significant role in theories of object

recognition, like Biederman’s (1987) recognition-by-components theory (Biederman, this volume).

Biederman’s (1987) theory entails edge extraction, the parsing of surfaces based on their concavities, and

the recognition of objects on the basis of whether the parsed surfaces match 3-D geometric primitives

(geons) in memory. The stimulus depicted in Figure 3e is similar to one of Biederman’s (1987) examples.

The object is presumably recognized as a lamp based on the presence and relative locations of geons

corresponding to the lampshade (a truncated cone), the stem (a cylinder) and the base (a truncated

cylinder). However, surface B by itself does not evoke a truncated cone or any other geon. A truncated

cone is formed only after surface B (corresponding to the lampshade’s outer surface) is grouped with

surface A (the elliptical shadow corresponding to the inside of the lampshade). Hock and Nichols (2012)

used the DG method to show that surfaces A and B are indeed grouped together. When the luminance of

surface B decreases, its luminance similarity with both black surfaces adjacent to it increases, and motion

across the changing surface is downward and to the right, consistent with the outer lampshade having a

greater pre-perturbation affinity with the ellipse (due to good continuation and perhaps boundary length)

than with the cylindrical stem of the lamp (Movie 7).

http://gestaltrevision.be/pdfs/oxford/movies/Hock/Movie7.mov

This example is consistent with a theory of object recognition in which surface-grouping operations

precede the activation of object parts in memory (possibly geons, but other primitives are not excluded),

with the object’s parts serving as the basis for its recognition. (See Jacot-Descombes & Pun [1997] for an

artificial vision model along these lines.) A processing sequence in which surface grouping precedes

comparison with component information in memory would reduce the complexity of object recognition

(Jacobs, 1996; Feldman, 1999), but it also is possible that the affinity values for all pairings of the surfaces

composing an object are unique, and therefore sufficient for the recognition of the object. In either case,

the ultimate test for dynamic grouping, or any other method for assessing the compositional structure of a

multi-surface object, is that the compositional structure is determinative for the recognition of the object.

6. Further implications

The example in Figure 3e and Movie 7 shows that grouping processes should have an explicit role in

theories of object perception, but it is quite another thing to specify what the role should be. The approach

taken in this chapter is that grouping variables determine the affinity of pairs of surfaces, and thereby, the

compositional structure of the object comprising those surfaces. Experiments and demonstrations with

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simple, 2-D objects composed of two or three surfaces have provided evidence for the usefulness of the

dynamic grouping method for the determination of affinity. Extending the method to multi-surface, 3-D

objects creates opportunities for discovering new grouping variables, and determining how ambiguities in

perceptual grouping are resolved (the ‘surface correspondence problem’) in the context of the other

surfaces composing a complex object.

The key theoretical concepts are: 1) the affinity of a pair of surfaces belonging to an object depends on the

nonlinear (super-additive) summation of the affinity values ascribable to individual grouping variables, and

2) the compositional structure of the object is revealed by embedding the pairwise affinity relationships

among the surfaces composing the object into a multidimensional affinity space. This would entail

multidimensional scaling (MDS) based on matrices of DG-measured affinity for all the pairwise

combinations of an object’s surfaces. Points in the space would represent the surfaces composing an

object, and the distance between the points would represent the affinity of the surfaces. In contrast with

multidimensional models of object recognition that specify particular features, like color, shape and texture

(e.g., Mei, 1997), the compositional structures determined with the dynamic grouping method will be

based on an abstract entity, affinity, so they will not be specific to the particular features of familiar objects.

They therefore would have the potential to exhibit a degree of invariance; i.e., generalize to other objects

with different features but a similar compositional structure, and to new viewpoints for the same object.

Using MDS methods, the compositional structure of an object can be determined without restrictions or

pre-conceptions; e.g., without the typical assumption that the structure is hierarchical (Palmer (1977);

Brooks (1983); Cutting (1986), Feldman (1999); Joo, Wang & Zhu, this volume). Although there are no

restrictions in the compositional structure’s form, the existence of parts could be indicated by the

clustering of surfaces in multidimensional affinity space, and significant relations between the parts,

including possible hierarchical relations, could be indicated when pairs of surfaces from different clusters

are relatively close in that abstract space.

An important consideration is the extent to which affinity relationships indicated by the dynamic grouping

method are definitive. In the experiments and demonstrations discussed in this chapter, instructions have

emphasized fixating on a dot placed in the center of the target surface and maintaining attention on the

dot for the entire two-frame trial. The purpose is to establish relatively unbiased conditions for determining

the direction of dynamic grouping motion. However, it is as yet undetermined whether fluctuations in eye

position or covert attentional shifts without eye movements (Posner, 1980) will alter the compositional

structures that are indicated by the dynamic grouping method. Indeed, when the stimuli like those in

Figures 1i and 2a are freely examined there is the sense that the surfaces can be grouped in more than one

way.

These uncertainties do not undermine the usefulness of the dynamic grouping method for objects with

more complex surface relationships. That is, changes in fixation or shifts of attention that reduce the

measured affinity of a target surface with another surface would be likely to also change its affinity with the

other surfaces composing the object. Such changes can be conceived of as the equivalent of the

perturbations in luminance similarity that that can result in the perception of dynamic grouping motion.

That is, they can temporarily alter the multidimensional compositional structure of an object, but the

structure is nonetheless restored after the perturbation.

14

The relationships among the surfaces composing an object also could be characterized as an ‘affinity

network’ in which each surface is represented by an activation variable and the coupling strength for pairs

of activation values is determined by their affinity. Changes in luminance, eye position or attention could

perturb coupling strengths, but the inherent stability of the network would restore the couplings to their

stable values. Exceptions are bistable objects for which perturbations could result in new couplings among

the object’s surfaces that qualitative change the compositional structure of the object (e.g., the Necker

cube). As in the case of bistable motion patterns (Hock, Schöner & Giese, 2003; Hock & Schöner, 2010),

such bistable objects may provide an ideal vehicle for investigating the nature of compositional structure

for static objects.

15

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