Priming for symmetry detection of three-dimensional figures: Central axes can prime symmetry detection separately from local components

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1 VISUAL COGNITION, 2006, 13 (3), 363±397 Priming for symmetry detection of three-dimensional figures: Central axes can prime symmetry detection separately from local components Takashi Yamauchi Psychology Department, Texas A&M University Lynn A. Cooper, H. John Hilton, and Nicholas J. Szerlip Department of Psychology, Columbia University, New York Hsin-Chin Chen and Terrence M. Barnhardt Psychology Department, Texas A&M University The image properties that are crucial for priming for symmetry perception in threedimensional line drawings were examined in four experiments. In all experiments, participants first engaged in a study task, in which they determined the left/right facing direction of individual objects. Following the study task, priming (facilitation in accuracy and/or speed of performance) of symmetry judgements was analysed for objects whose image properties were modified at the time of test. The results of the experiments indicated that (a) priming was present even when local components of objects were modified between study and test, so long as the axis of symmetry of the objects was unchanged, and (b) priming was also present even when studied objects had completely different configurations of local components. These results suggest that the symmetric axis of objects can prime symmetry detection separately from local components and their configurations. Visual symmetries have a special status in perception. Symmetric patterns are aesthetically pleasing, they evoke perceived ``goodness'' of figures, they facilitate figure±ground segregation, and they are detected spontaneously without much effort (Barlow & Reeves, 1979; Baylis & Driver, 1994; Corballis & Roldan, 1974; Driver, Baylis, & Rafal, 1992; Palmer, 1991; Palmer & Hemenway, 1978; van der Helm & Leeuwenberg, 1996; Wagemans, 1995). Please address all correspondence to: Takashi Yamauchi, Department of Psychology, Mail Stop: 4235, Texas A&M University, College Station, TX , USA. tya@psyc.tamu.edu The research was supported by Air Force Office of Scientific Research Grant , to Lynn A. Cooper. We wish to thank Taosheng Liu, Jeana Frost, David Krantz, and Arthur Markman for their helpful suggestions. # 2006 Psychology Press Ltd DOI: /

2 364 YAMAUCHI ET AL. Symmetry also plays a crucial role in computational models of object representation and recognition (Biederman, 1985; Hummel & Biederman, 1992; Marr, 1981; Marr & Nishihara, 1978; Tarr, 1995; Ullman, 1996, 1998; Vetter & Poggio, 2002). What mechanism mediates symmetry perception in three-dimensional figures? How is symmetry perception intertwined with the process of object representation? This paper focuses on bilateral (or ``mirror-image'') symmetries and explores these questions by examining the relative roles that the central axis of symmetry and the local components of an object play in priming associated with symmetry detection. We chose these two properties for our investigation because of their centrality in object representation and recognition (see Biederman, 1985; Hummel & Biederman, 1992; Marr & Nishihara, 1978). SYMMETRY AND OBJECT REPRESENTATION A number of theoretical and empirical findings converge on the idea that the perception of symmetry is linked to the basic processes of object representation (Baylis & Driver, 1994, 1995a, 1995b; Bertamini, Friedenberg, & Kuboy, 1997; Palmer, 1991; van der Helm & Leeuwenberg, 1996). In the field of object recognition research, both structural description models and view-based models make use of symmetries as a building block of representation. For example, in Marr and Nishihara's (1978) structural description model, the global structure of an object is characterized by hierarchically arranged axes of symmetries, which are obtained from the boundaries of individual components. In a view-based model, Vetter and Poggio (2002) have shown that symmetry in an object provides valuable information to extract the three-dimensional structure of an object with a single view (see also Ullman, 1998; Vetter, Poggio, & Bulthoff, 1994). Tarr and his colleagues (Tarr, 1995; Tarr & Gauthier, 1998; Tarr & Pinker, 1989, 1990, 1991; Tarr & Vuong, 2002) also demonstrated that the orientation of an object, which is specified by the elongation and axes of symmetries, is integrated into the process of object recognition. Consistent with these theoretical positions, research has shown that visual symmetries provide strong cues for image segmentation, such as distinguishing a figure from its background (Driver et al., 1992). If symmetry perception is linked to the basic function of object representation, how do they interact with each other? Despite the centrality of symmetry perception in object representation, to our knowledge, few studies have systematically addressed this question (but see Baylis & Driver, 1994). One possibility is that the detection of symmetry in three-dimensional figures occurs separately from the formation of structural representations of objects. In the structural-description theories of object recognition (Biederman, 1985; Hummel & Biederman, 1992; Marr, 1981; Marr & Nishihara, 1978), the symmetry of objects is used to derive and specify the structure of objects. For example, in

3 SYMMETRY PERCEPTION AND CENTRAL AXES 365 Biederman's (Biederman, 1985; Hummel & Biederman, 1992) recognition-bycomponents theory, the visual system first extracts two-dimensional edge properties such as curvature, colinearity, symmetry, parallelism, and/or cotermination from image data, and then constructs three-dimensional geometric primitives from these edge features (see also Layer 2 of ``JIM'' in Hummel & Biederman, 1992, p. 486). Thus, some form of symmetry detection is likely to occur before or separately from the representation of local components and their configurations. Similarly, in the Marr and Nishihara model, axes of symmetry are computed in the service of generating a structural description of object shape. Thus, some aspect of symmetry detection should be achieved prior to the representation of local components and their structure. Research in symmetry perception and object representation generally agrees with this view. Studies have shown that the construction of object structure by three-dimensional local components requires binding of image features to objects, and this binding process is often incomplete unless attention is given to relevant locations (Stankiewicz, Hummel, & Cooper, 1998; Treisman & Kanwisher, 1998). Although forming component-based structural descriptions requires attention, the perception of symmetry is spontaneous, and it does not involve spatial attention (Driver et al., 1992; but see Olibers & Helm, 1998). Moreover, research has shown that the complexity of local image features hardly interferes with the speed and accuracy of symmetry perception of two-dimensional figures (Baylis & Driver, 1994). These empirical phenomena imply that symmetry perception can arise separately from the representation of local components and their overall structures. In other words, the complete component-based structural descriptions of objects may not be necessary for some form of symmetry perception. Although this suggestion is consistent with a number of empirical studies, to our knowledge this proposal has not been empirically tested. In this paper, we focus on the role that local components and central axes of an object play in symmetry perception. In so doing, we intend to clarify the relative role that these visual features play in priming associated with symmetry detection. BACKGROUND OF EXPERIMENTS We created three-dimensional line drawings that were composed of three types of componentsðcubes, triangular solids, and rectangular solids (Figure 1a). We employed a priming technique to examine the extent to which the representation of local components affects symmetry perception. Priming refers to a shift in task performance that is attributable to prior experience with the same or related stimuli and tasks. Priming is also known to stem from changes in internal processes and representations associated with study and test tasks (Biederman & Cooper, 1991a, 1991b; Cooper, Schacter, Ballesteros, & Moore, 1992; Liu &

4 366 YAMAUCHI ET AL. Figure 1. Samples of the stimuli used in the experiments. (a) All objects were composed of the three basic components, a cube, a triangular solid, and a rectangular solid, and four samples of symmetric objects and four samples of asymmetric objects were shown in (b) and (c). Cooper, 2001; Stankiewicz, & Hummel, 2002; Stankiewicz et al., 1998; Williams & Tarr, 1997, 1999). Previous studies concerning implicit and explicit forms of memory have shown that inspecting left±right directions of three-dimensional line drawings results in substantial priming in the judgement of the structural ``possibility'' of three-dimensional figures (Cooper et al., 1992; Schacter, Cooper, & Delany, 1990; Schacter, Cooper, Delany, Peterson, & Tharan, 1991). In a typical experiment, participants first engaged in a left/right direction task, in which they judged if each stimulus faced primarily to the left or to the right. After the left/ right direction task, participants were given a possible/impossible decision task, in which they judged whether briefly presented objects were structurally possible or impossible. Priming occurred only for structurally possible objects but not for impossible objects. Priming was preserved even when the size or reflection of objects was modified at the time of test, as long as the left/right direction task was given at study (Cooper et al., 1992; Cooper, Schacter, & Moore, 1991). When local or semantic elements of objects were studied, priming did not occur (see Cooper & Schacter, 1992, for review).

5 Following the Schacter and Cooper studies, Liu and Cooper (2001) further found that the left/right direction task facilitates symmetry detection. In their experiments, participants first carried out the left/right direction task, and then a symmetry detection task. The results of their study showed that there was substantial facilitation of symmetry detection for studied stimuli as compared to nonstudied stimuli (i.e., priming), indicating that some of the visual properties that were assessed in the left/right direction task facilitated subsequent symmetry detection of the same or related figures. In our study, we employed the same experimental setting as developed by Liu and Cooper (2001) and tried to identify critical properties underlying symmetry perception. Specifically, we modified central axes and/or local components of line drawings at the time of test, and measured whether or not these modifications would affect priming for symmetry detection. We reasoned that if modifications of particular visual properties eliminate priming, then that property is critical for the priming task; likewise, if modifications do not affect priming, then that property is not crucial for the priming task (see, for similar reasoning, Biederman & Cooper, 1991a, 1991b; Cooper et al., 1992; Schacter et al., 1990, 1991; Stankiewicz & Hummel, 2002; Stankiewicz et al., 1998; Williams & Tarr, 1997, 1999). Following this logic, if the representation of local components is crucial for a priming task, then modifying local components at the time of test should eliminate priming. In contrast, if central axes of objects are crucial for the priming task, then modifying central axes of objects should eliminate priming. GENERAL METHOD This section summarizes the general method employed in the four experiments that will be described later. Materials SYMMETRY PERCEPTION AND CENTRAL AXES 367 The stimulus materials used in the experiments were variations of 80 threedimensional line drawings similar to those shown in Figures 1b and 1c. All stimuli were composed of arrangements of three types of local componentsða triangular solid, a rectangular solid, and a cube (see Figure 1a). Of the 80 objects, half were symmetric (Figure 1b) and half were asymmetric (see Figure 1c). A symmetric object contains imaginary planes that divide the object into mirror-image halves; an asymmetric object has geometric properties that make it impossible to divide the object in this way. Each object was differentiated from the others by the number, arrangement, and/or types of the components in its construction. Stimulus objects were selected to meet the following criteria: (1) Intersubject agreements as to the symmetry or asymmetry of individual objects are, on average, 95% or greater in a study using an unlimited exposure duration; (2) baseline performance for determining the symmetry/asymmetry of objects is

6 368 YAMAUCHI ET AL. approximately 60% when objects were displayed for brief durations in the absence of study (see Cooper et al., 1992). To meet these criteria, we conducted two independent pilot studies. In the first study, 20 participants observed each object on a computer screen without any time limitation and determined whether the object appeared symmetric or asymmetric. The average level of agreement for their judgements was 96.4%. The minimum level of agreement across the entire object set was 80% and the maximum was 100%. In the second pilot study, 26 college students participated in an object-decision test without a study task. With 45 ms exposure times, participants classified 57% of symmetric and 61% of asymmetric objects correctly. The stimuli were produced by Adobe Illustrator 3.0 and were presented by an Apple Quadra 950 computer on an NEC XP17 monitor as well as Dell OptiPlex GX110 with Pentium III processor on a Dell 17 P780 Ultra, 16.0 VIS monitor coupled with NVDIA M64 16MB PCI video card. The stimuli subtended approximately 4.0 degrees of visual angle. Procedure All experiments consisted of two phasesða study phase and a test phaseðgiven in sequence. During the study phase, symmetric objects and asymmetric objects were randomly presented one at a time at the centre of the screen for five seconds each. Participants examined each object as a whole for the entire 5 s and judged whether the object faced primarily to the right or to the left by pressing one of two specified keys (see Schacter et al., 1990, for this task). No mention was made at this point of either object symmetry or asymmetry, or of the subsequent symmetry/asymmetry judgement task. After completing the study phase, participants proceeded to the test phase, during which they determined whether an object presented on the screen was symmetric or asymmetric by pressing one of two specified keys. Each stimulus was displayed on the centre of the computer screen. The definition of symmetric and asymmetric objects and two examples of each were shown in the instructions. Five practice trials were included at the beginning of the test task. Data analysis procedures Among the symmetric and asymmetric objects that were shown in the test phase, half had been previously presented in the study phase (i.e., studied objects), while the remaining half were shown only in the test phase (i.e., nonstudied objects). The magnitude of priming was assessed by calculating the difference between performance for studied objects and performance for nonstudied objects. The primary dependent measure in Experiment 1 was response times for symmetry/asymmetry judgement. The primary dependent measure in Experiments 2 and 3 was detection accuracy, which was defined by hit minus false

7 SYMMETRY PERCEPTION AND CENTRAL AXES 369 alarm scores. Specifically, we defined ``hit'' as responding ``symmetry'' given symmetric objects, and ``false alarm'' as responding ``symmetry'' given asymmetric objects (see, for a similar procedure, Barlow & Reeves, 1979; Wenderoth, 1997). The ``detectability'' of symmetry was then compared across the studied and nonstudied status of objects. Calculated this way, these measures help control possible response bias associated with priming performance (Ratcliff & McKoon, 1995; Roediger & McDermott, 1994; and see Appendix A for the rationale). For our response time analyses, we followed closely the procedures suggested by Luce (1986), Ratcliff (1993), and van Zandt (2000, 2004). Specifically, the following steps were adopted: (1) The response time data that corresponded to the correct responses were selected. (2) Based on the data identified in (1), a Gaussian Kernel estimator was applied to the data obtained from the symmetric objects and the asymmetric objects separately, and probability density functions were estimated (see Appendix B). (3) On the basis of (2), all responses that exceeded 4000 ms were removed uniformly across the conditions. (4) The 4000 ms cutoff point was selected because this cutoff point preserves approximately 90±95% of the correct responses and the effects observed with this cutoff point were consistent with the analyses made with other nonextreme cutoffs; to verify the validity of the cutoff, the inverse transformation of the data was also applied and the data were reanalysed with transformed values (i.e., 1/RT). In Experiment 1, we modified some local components of the standard stimuli at the time of test. Experiments 2a and 2b manipulated the orientation of central axes of objects between study and test. In Experiment 3, two completely different sets of objects were presented in the study task and in the test task, and we examined if priming would be observed when two different sets of objects have the same orientation of axes of symmetry, but have different configurations of local components. EXPERIMENT 1 Experiment 1 employed two between-subjects conditionsðan original condition and a transformed condition. The study phase was identical in the two conditions. In the test phase of the original condition, half of the objects had been presented in the study phase, and the other half had not been presented in the study phase. In the test phase of the transformed condition, in every stimulus, some of its local components were replaced with other type of components (Figure 2). The two conditions were identical except for this single point. If the complete representation of local components is not critical for the priming task, then priming should be present in the transformed condition as much as in the original condition.

8 370 YAMAUCHI ET AL. Figure 2. Three types of transformation of local componentsðtwo cubes were replaced with two triangular solids (left), two rectangular solids were replaced with two cubes (centre), and two triangular solids were replaced with two rectangular solids (right). Method Participants A total of 104 participants participated in Experiment 1. Among those, 50 participants from the Columbia University community received $4.00 in payment for their participation, and 54 undergraduate students from Texas A&M University participated for course credit. All had normal or corrected-to-normal vision. The data from 12 participants were removed from analysis. Among those, 3 participants responded no better than a chance level, 1 and 9 participants responded almost exclusively with one of the two designated keys. 2 Overall, the data from 92 participants (original condition = 45 and transformed condition = 47) were analysed. Materials Stimuli were 72 original objects and 72 transformed objects. To construct original objects, 72 objects were selected from the 80 basic objects (see the General Method section). 3 Each object was then rotated in the 1 The average accuracy scores of these participants were.41,.37, and.11, respectively. 2 These nine participants responded with either the asymmetry or symmetry key for at least 47 out of the 72 stimuli; p <.005 (binomial distribution test). 3 Four symmetric objects were not selected because the transformation of local components was not possible without violating the transformation criteria. Four other asymmetric objects were not selected to balance the number of symmetric and asymmetric objects. These asymmetric objects were chosen randomly.

9 SYMMETRY PERCEPTION AND CENTRAL AXES 371 picture plane in one of the 20 randomly assigned angles ranging from 0 to 180 degrees. This procedure was adopted to introduce a degree of variability in axis orientation into the stimulus set. Transformed objects were modifications of the original objects. For each of the original objects, one of the three types of components (cubes, rectangular solids, triangular solids) was exchanged for one of the other types of components with the constraints that (a) the symmetric axis of the object had to remain unchanged after replacement, and (b) the number of components used to depict the object had to remain the same after replacement. Thus, there were six different types of transformation: (1) Cubes to rectangular solids, (2) cubes to triangular solids, (3) rectangular solids to triangular solids, and (4±6) the reverse of these three types of replacement (cf. Figure 2). Each of the original objects was pseudorandomly assigned to one of these six transformation types. Of the 72 objects, 36 were symmetric objects and the remaining 36 were asymmetric objects. Altogether, 144 objects (72 original objects, 72 transformed objects) were divided into four versions for counterbalancing, and each object was arranged to appear in the original condition and in the transformed condition, and in the studied condition and in the nonstudied condition equally often. In the study phase, which was identical in the two conditions, participants were presented with 36 stimuli (18 symmetric objects and 18 asymmetric objects). In the test phase of the original condition, participants received 72 stimuli (36 studied objects, 36 nonstudied objects). In the test phase of the transformed condition, participants received 72 transformed stimuli. Procedure The same study task was used in the original and transformed conditions (see the General Method section). The test task in the transformed condition was identical to that in the original condition, except that transformed objects were shown in the transformed condition. Each object remained on the computer screen until participants responded. Priming was measured as the reduction in time required to evaluate studied relative to nonstudied objects (see William & Tarr, 1997, for the use of response time in a similar setting). The response time measure was employed in order to eliminate a potential confusion effect. Measurements of accuracy in object decision performance require a brief presentation of stimuli. However, if a brief presentation was used, it seemed possible that priming in transformed objects could occur simply because participants were unable to distinguish transformed and original objects when stimuli were shown briefly. In order to avoid this potential confusion effect, each stimulus was presented until participants made a response.

10 372 YAMAUCHI ET AL. Design The design of this experiment was a 2 (object type: Symmetric vs. asymmetric) 6 2 (study status: Studied vs. nonstudied) 6 2 (transformation condition: Original vs. transformed) 6 4 (object version: Version 1, version 2, version 3, version 4) mixed factorial. The first two factors, object type and study status, were within-subjects manipulations, and the last factor, transformation condition, was a between-subjects manipulation. Object version did not interact with transformation condition; therefore this factor was collapsed for subsequent analyses. The stimulus set was divided into four object versions for counterbalancing. Each object set contained an equal number of symmetric and asymmetric objects with an equal number of the total components used to depict objects. Each object served as both an old and a new object, and both an ``original'' and a ``transformed'' object in different object versions. The dependent measure on the symmetry detection task was the time required for judgements. Results Response time data. Figures 3a and 3b summarize overall results of Experiment 1. Consistent with previous studies (Kersteen-Tucker, 1991; Liu & Cooper, 2001), there was a large disparity between response times obtained from symmetric objects and those obtained from asymmetric objects, F(1, 90) = 101.0, MSE = 159,189.8, p <.01, Z 2 = A significant priming effect was apparent in symmetric objects but not in asymmetric objects, as revealed in an interaction effect between study status and object type, F(1, 90) = 6.18, MSE = 35,329.4, p <.05, Z 2 = The origin of this disparity is not clear. As suggested by Liu and Cooper (2001), the decision mechanism underlying ``asymmetry'' responses might correspond to ``No'' responses in a binary yes/ no identification task. For this reason, we focused our analyses on symmetric objects, and response time data were analysed separately for symmetric objects and for asymmetric objects. For the symmetric objects, a large priming effect was present both in the transformed condition and in the original condition. The mean response time obtained in studied objects was significantly shorter than that in the nonstudied objects, F(1, 90) = 10.34, MSE = 30,839.1, p <.01,Z 2 = There was no interaction effect between study status and transformation condition (original vs. transformed), F < 1.0; nor a main effect of transformation condition, F < 1.0. These results suggest that studying left±right orientations of objects helped subsequent symmetry/asymmetry judgements irrespective of the transformation status of objects. T-tests that were applied separately to the two conditions revealed that the mean response time obtained in the studied symmetric objects was significantly shorter than that from the nonstudied symmetric objects in the original as well as

11 SYMMETRY PERCEPTION AND CENTRAL AXES 373 Figure 3. Summaries of the results from Experiment 1. (a) Symmetric objects, and (b) asymmetric objects. Each error bar represents two standard error units. transformed conditions; the original condition, studied, M = ms, SD = 405.8, nonstudied, M = ms, SD = 426.6, t(44) = 2.08, p <.05, d = 0.31; the transformed condition, studied, M = ms, SD = 325.5, nonstudied, M = ms, SD = 411.9, t(46) = 2.47, p <.05, d = The magnitude of priming, which was calculated for each participant by subtracting the response times in nonstudied symmetric objects from those in studied symmetric objects, was not statistically different in the two conditions; the original condition, M = 76.0 ms, SD = 244.3, the transformed condition, M = 90.6 ms, SD = 252.1, t(90) = 0.28, p =.78, d = These additional analyses confirm that a significant priming effect was present both in the original condition and in the transformed condition, and the level of priming in the two conditions was statistically indistinguishable. For asymmetric objects, neither a main effect of study status nor an interaction between study status and transformation condition was significant; for both measures, Fs < 1.0. The two conditions were marginally different in their

12 374 YAMAUCHI ET AL. TABLE 1 Mean accuracy scores in Experiment 1 Symmetry Asymmetry Nonstudied Studied Nonstudied Studied Original M SD Transformed M SD M = mean, SD = standard deviation. overall response times; the original condition, M = , SD = 445.4; the transformed condition, M = , SD = 480.9, F(1, 90) = 3.64, MSE = 430,378.5, p =.06, Z 2 = Accuracy data. A summary of the accuracy data is shown in Table 1. Note that accuracy in this experiment was deliberately set at an asymptotic level. For this reason, no meaningful priming effects were observed due to a ceiling effect. There was no main effect of transformation condition nor of study status, Fs < 1.0. An interaction between transformation condition and study status was not significant, F < 1.0. Thus, the priming effect observed in the response time data cannot be attributed to accuracy±time tradeoff. Object type and study status was marginally significant, F(1, 90) = 2.89, MSE = 0.004, p =.09, Z 2 = Discussion The results from Experiment 1 indicate that studying left/right facing directions of stimuli facilitated subsequent symmetry detection. Because priming for symmetry/asymmetry judgements was present even in the transformed objects, 4 In addition to the 4000 ms cutoff point, we analysed the response time data by using the inverse transformation (1/RT). Overall results of this analysis were consistent with those found with the 4000 ms cutoff point. Given symmetric objects, the main effect of study status was significant, F(1, 90) = 8.41, MSE = ±8, p <.01, Z 2 = An interaction between study status and transformation condition was not significant, F(1, 90) = 1.15, MSE = ±8, p =.29, Z 2 = 0.013, nor a main effect of transformation condition, F(1, 90) = 2.337, MSE = ±7, p =.13, Z 2 = Given asymmetric objects, study status was marginally significant, F(1, 90) = 2.81, MSE = ±8, p =.097, Z 2 = However, an interaction between study status and transformation condition was not significant, F < 1.0. A main effect of transformation condition was marginally significant, F(1, 90) = 3.61, MSE = ±7, p =.06, Z 2 = 0.04.

13 SYMMETRY PERCEPTION AND CENTRAL AXES 375 transformations of local components did not interfere with priming associated with symmetry detection. None of the objects in the transformed condition appeared during the study phase. The transformed objects replaced some of the local components of original objects, while their global axes of symmetry were kept unchanged. In this sense, central axes of objects, as compared to local components, are likely to be a crucial mediator for the priming effect in Experiment 1. A potential problem with this interpretation is that original objects and transformed objects are highly similar. The transformed objects were created by replacing one type of components in each of the original objects. The overall arrangements of the two types of objects were the same (Figure 2). Because priming is highly susceptible to the relationship between study and test tasks (Srinivas, 1993), it is difficult to claim that central axes of symmetry caused priming on the basis of the results from Experiment 1 alone. The next three experiments were designed to clarify this ambiguity. EXPERIMENTS 2A AND 2B Palmer and Hemenway (1978) examined the relationship between symmetry detection and shape orientations with two-dimensional figures. They demonstrated that symmetries with vertical orientations are easy to detect as compared to symmetries with horizontal or diagonal orientations (but see also Wenderoth, 1994, 1997). Tarr (1995) has also suggested that the orientation of objects is incorporated in the system of object representation and recognition. In this regard, we hypothesized that the central axis of an object may be defined with respect to its overall orientation. In Experiment 2a, we first measured priming in an object set that had varying axis orientations. Then, in Experiment 2b, we measured priming with an object set in which a majority of the symmetric objects were arranged with similar vertical orientations (Figures 4b and 4c). The logic of these experiments was as follows. Assume that the priming effect for symmetry detection arises primarily from the representation of axis structures. Now, consider that all symmetric objects, both those that appear in the study task and those that appear in the test task, have a uniform axis orientation. If a priming experiment is carried out with these objects, then nonstudied objects should be ``primed'' as much as studied objects, if, as hypothesized, shared axis structures were indeed the main source of priming in the transformed condition in Experiment 1. In this case, our conventional method of calculating priming should result in a null effect, because priming is defined by the difference between the performance for studied objects and the performance for nonstudied objects. In this regard, a priming effect should be present in Experiment 2a, but not in Experiment 2b, if activating axis structures was indeed the major source of priming in symmetry detection.

14 376 YAMAUCHI ET AL. Figure 4. (a) Samples of the symmetric objects used in Experiment 2a; (b) samples of asymmetric objects used in Experiment 2a. These objects had heterogeneous axis orientations. (c) Samples of the symmetric objects used in Experiment 2b; (d) samples of asymmetric objects used in Experiment 2b. Note that all symmetric objects have vertical planes that can bisect the objects into mirror-image halves. For example, the symmetric planes of the first two objects in (c) are faced directly to the centre, those of the next two objects in (c) are directed 30 degrees to the right, and those of the last two objects in (c) are directed 150 degrees to the left. Method Participants One hundred undergraduate students at Columbia University and Texas A&M University participated in Experiments 2a (N = 46) and 2b (N = 44). The data from one participant in Experiment 2a was removed from analysis because this participant misunderstood the instructions. All participants had normal or corrected-to-normal vision. Materials The materials for Experiment 2a were analogous to those used in the original condition of Experiment 1. We first adopted the 80 basic objects (see the General Method section) and rotated each object in the picture plane to one of 20 angles ranging from 9 to 180 degrees (increments of 9 degrees; see Figures 4a

15 SYMMETRY PERCEPTION AND CENTRAL AXES 377 and 4b). Four objects (two symmetric and two asymmetric ) were assigned pseudorandomly to each of 20 different angles of rotation. This procedure was adopted to introduce variability in axis orientation into the stimulus set. The materials employed in Experiment 2b were also the 80 basic objects (see the General Method section). These objects were nearly homogeneous in their orientations of symmetric axes. Among the 40 symmetric objects, 37 had at least one vertical axis of symmetry (see Figures 4c and 4d). Two versions of stimuli were created for counterbalancing. Procedure The procedure of Experiments 2a and 2b was identical. Participants received 40 objects (20 symmetric and 20 asymmetric objects) in the study phase, and 80 objects (40 symmetric and 40 asymmetric objects) in the test phase. Among these 80 objects, 40 objects appeared both in the study task and in the test task; the remaining 40 objects appeared only in the test task. In the test task, each object flashed on the computer screen for 45 ms, and was followed by a mask, which remained until a response was made. Design The main dependent measure of the two experiments was hit minus false alarm scores. The design of the two experiments was a 2 (object type: Symmetric vs. asymmetric) 6 2 (study status: Studied vs. nonstudied) 6 2 (object version: Version 1, version 2) factorial. Results As predicted, a significant priming effect was present in Experiment 2a. Participants' hit minus false alarm scores were higher for studied objects, M = 0.33, SD = 0.26, d' = 0.85, c (criterion) = , than for nonstudied objects, M = 0.25, SD = 0.26, d' = 0.63, c (criterion) = ; t(44) = 2.97, p <.01, d = 0.44 (Figure 5). In essence, this finding was a replication of the results in the original condition of Experiment 1 with a hit minus false alarm measure. In Experiment 2b, the average hit minus false alarm score for studied objects, M = 0.44, SD = 0.30, d' = 1.16, c = ±0.079, was only marginally different from that for nonstudied objects, M = 0.39, SD = 0.31, d' = 1.01, c = ; t(43) = 1.74, p =.09, d = Note that the effect size in Experiment 2a was 0.44 and that in Experiment 2b was However, the magnitude of priming was not different between those observed in Experiment 2a and in Experiment 2b, t(97) = 0.85, p =.40, d = The average hit minus false-alarm score was higher in participants in Experiment 2b than that in Experiment 2a, t(97) = 2.17, p <.05, d = This disparity probably stemmed from the fact that detecting symmetries

16 378 YAMAUCHI ET AL. Figure 5. A summary of the results from Experiments 2a and 2b. Each error bar represents two standard error units. with vertical orientations was easier than detecting symmetries with varying orientations (Palmer & Hemenway, 1978). The response time data were analysed separately for symmetric and asymmetric objects (Table 2). Note that this experiment was designed to examine priming in accuracy, not in response times by setting average accuracy slightly above a threshold level. Because the response time data were analysed only for correct responses, not many data points were left for this analysis. For this reason, any interpretation of the response time data should be made with caution. In Experiment 2a, studied objects did not have any advantage over nonstudied objects either in symmetric objects, t(43) = 0.01, p =.99, d = 0.002, or in asymmetric objects, t(44) = 0.30, p =.76, d = In Experiment 2b, the mean response time of studied symmetric objects was significantly faster than that for nonstudied symmetric objects, t(43) = 2.39, p <.05, d = For asymmetric objects, a marginally significant advantage for the studied condition was found, t(44) = 1.91, p =.06, d = 0.15 (Table 2). 5 Discussion The results from the two experiments were mixed. Experiment 2a employed objects with heterogeneous axis orientations, and a robust priming effect was observed. Experiment 2b employed objects with homogeneous axis orientations, 5 A response time data analysis with the inverse transformation showed a similar picture as described with those using the 4000 ms cutoff. In Experiment 2a, the mean response times obtained from the studied symmetric objects and that from the nonstudied symmetric objects were not statistically different, t(43) = 0.55, p =.58, d = The same trend was apparent in the data obtained from the asymmetric objects, t(44) = 1.47, p =.15, d = In Experiment 2b, there was a significant priming effect in the symmetric objects, t(43) = 2.55, p <.05, d = 0.40, and in the asymmetric objects, t(43) = 3.09, p <.01, d = 0.50.

17 SYMMETRY PERCEPTION AND CENTRAL AXES 379 TABLE 2 Mean response times in Experiments 2a and 2b Symmetry Asymmetry Nonstudied Studied Nonstudied Studied Experiment 2a M SD Experiment 2b M SD The response time data were presented in milliseconds. M = mean, SD = standard deviation. and a marginally significant priming effect was observed. Although the magnitude of priming appear considerably larger in Experiment 2a than in Experiment 2b, the difference was not statistically significant. Furthermore, the results from the response time measure were inconsistent with our predictionðthe mean response time in Experiment 2b was shorter in the studied symmetric objects than in the nonstudied symmetric objects. On one hand, it appears that there is a strong possibility that one group of symmetric objects can elevate the symmetry detection of other groups of objects as long as these objects share axes of symmetry; on the other hand the results from Experiments 2a and 2b were not conclusive enough to support this hypothesis. Experiment 3 combined the baseline conditions (i.e., nonstudied conditions) in Experiment 2a and 2b, and tested this hypothesis directly in a single experiment. EXPERIMENT 3 Three between-subjects conditionsða same-axis condition, a different-axis condition, and a different-axis-same-object conditionðwere developed to test whether or not one group of objects that have vertical axes of symmetry can prime another group of completely different objects, which also have vertical axes of symmetry. Table 3 summarizes the manipulations introduced in Experiment 3. Participants in the three conditions received the same stimuli in the test task. All of these stimuli had vertical orientations (Figure 6a). In the same-axis condition, the stimuli in the study task (Figure 6b) had vertical orientations just as those shown in the test task. However, the stimuli that were shown in the study task were different from those that were presented in the test task in their configurations of local components. In the different-axis condition, the axis orienta-

18 380 YAMAUCHI ET AL. TABLE 3 Three experimental conditions employed in Experiment 3 Conditions Stimulus number Study task Test task Same-axis Symmetric objects s1, s2, s3... s14 (vertical) s15, s16, s17... s28 (vertical) Asymmetric objects a1, a2, a3... a14 (vertical) a15, a16, a17... a28 (vertical) Different-axis Symmetric objects s1, s2, s3... s14 (rotated) s15, s16, s17... s28 (vertical) Asymmetric objects a1, a2, a3... a14 (rotated) a15, a16, a17... a28 (vertical) Different-axis-same-object Symmetric objects s15, s16, s17... s28 (rotated) s15, s16, s17... s28 (vertical) Asymmetric objects a15, a16, a17... a28 (rotated) a15, a16, a17... a28 (vertical) tions of the studied objects were rotated to one of 14 predetermined angles. The two conditions were equivalent except for this single point. In the different-axissame-object condition, participants received the same stimuli in the study task and in the test task. However, the orientations of individual stimuli in the study task were modified in the same manner adopted in the different-axis condition (Figure 6d). If, as hypothesized, objects with vertical axes of symmetry can activate different objects that also have vertical axes of symmetry, the performance in the same-axis condition should be better than the performance in the different-axis condition. Furthermore, if shared configurations of local components are not as important as shared axis structures, then the performance in the different-axissame-object condition should be no better than the performance in the differentaxis condition. Method Participants One hundred and sixty-seven undergraduate students at Texas A&M University participated in this experiment. Twenty-two participants received $5.00 in payment for their participation. The other participants received course credit. The data from one participant were excluded for statistical analyses because that person did not follow the instructions. The participants were assigned randomly to one of three conditionsðthe same-axis condition (N = 53), the different-axis condition (N = 58), or the different-axis-same-object condition (N = 55). All participants had normal or corrected-to-normal vision.

19 SYMMETRY PERCEPTION AND CENTRAL AXES 381 Figure 6. (a) Samples of symmetric objects shown in the test task in Experiment 3. All symmetric objects had vertical orientations of symmetry, and participants in the three conditions received the same stimuli in the test task. (b) Samples of symmetric objects shown in the same-axis condition. These objects were different from those shown in the test task in their configurations of local components, but they also had vertical orientations of symmetry. (c) Samples of symmetric objects shown in the different-axis condition. These objects were rotations of the objects shown in the study task of the same-axis condition. (d) Samples of symmetric objects shown in the study task in different-axis-same-object condition. Participants in this condition received the same objects as those shown in the test task, but the orientation of individual objects was modified at study. Materials Materials were 28 symmetric objects and 28 asymmetric objects that were selected from the basic object set (see the General Method section). All 28 symmetric objects had a vertical axis of symmetry (see Figure 6). Asymmetric objects were chosen randomly from the basic object set (see the General Method section). From the 56 objects, two versions of the study-test materials were created such that for every participant who was presented with one subset of objects (14 symmetric and 14 asymmetric objects) at study was shown the other subset of objects at test. The assignment of individual objects to each version was determined randomly. In the same-axis condition, the objects shown in the study task had the same vertical orientations as those shown in the test task. However, these objects were

20 382 YAMAUCHI ET AL. completely different in their configurations of local components (Figure 6b). In the different-axis condition, the objects shown in the study task were different from the objects shown in the test task both in their configurations of local components and in their orientations of central axes. Individual objects were rotated to one of 14 predetermined angles, which ranged from 12 to 168 degrees (increments of 12 degrees). The assignments of individual objects to each of the 14 angles were determined pseudorandomly so that there was one symmetric object and one asymmetric object in each assignment. The same-axis condition and the different-axis conditions were identical except for this critical point. In the different-axis-same-object condition, the objects shown in the study task and the objects shown in the test task had the same configurations of local components but their orientations of central axes were different. The orientations of these objects were modified in the same manner adopted in the different-axis condition (Figure 6d). Procedure The basic procedure of Experiment 3 was analogous to that described in Experiments 2a and 2b. Design The design of the experiment was a 3 (Axis structure: same-axis, differentaxis, different-axis-same-object) 6 2 (object type: Symmetry vs. asymmetry) 6 2 (stimulus version: Version 1, version 2) factorial. The factor, stimulus version, was collapsed for data analyses because this factor did not interact with the other independent variables. Results Figure 7 summarizes the main results of Experiment 3. Overall, participants in the same-axis condition were most accurate in their symmetry detection. A oneway ANOVA applied to hit minus false alarm scores indicated that there was a main effect of axis structure, F(1, 163) = 4.43, MSE = 0.09, p <.05, Z 2 = Planned t-tests revealed that participants in the same-axis condition, M = 0.54, SD = 0.32, d' = 1.50, c = 0.13, were significantly more accurate than participants in the different-axis condition, M = 0.38, SD = 0.29, d' = 1.06, c = 0.37, t(109) = 2.79, p <.05, d = 0.53 (Bonferroni), indicating that studying objects with vertical orientations helped symmetry judgements of completely different objects that also had vertical orientations. The performance in the different-axis condition, M = 0.38, SD = 0.29, d' = 1.06, c = 0.37, and the performance in the different-axis-same-object condition, M = 0.41, SD = 0.29, d' = 1.11, c = 0.22, were not statistically different, t(111) = 0.57, p >.5, d = This result confirms the view that shared axes were more important than shared objects in

21 SYMMETRY PERCEPTION AND CENTRAL AXES 383 Figure 7. A summary of the results from Experiment 3. Each error bar represents two standard error units. our priming task. The impact of shared vertical axes was also notable even when it was compared to the data taken from the objects in the different-axis-sameobject condition. Participants in the same-axis condition made correct detections more often than participants in the different-axis-same-object condition, t(106) = 2.22, p =.09, d = Although this difference was only marginally significant due to a Bonferroni adjustment (i.e., an alpha level of.05/3 was employed for multiple comparisons), the effect size for this difference was reasonably large (d = 0.43) (see Cohen, 1988). The response time data analyses were applied separately to the symmetric objects and asymmetric objects (Table 4). Given symmetric objects, there was a significant impact of axis structure, F(2, 147) = 3.08, MSE = 389,408.0, p <.05, Z 2 = Among the three conditions, the mean response time in the sameaxis condition was shorter than that in the different-axis condition, t(95) = 2.49, p <.05, d = The different-axis condition and the different-axis-same-object condition were statistically indistinguishable in their response times, t(101) = 0.94, p =.34, d = The difference between the same-axis condition and the different-axis-same-object condition was not significant, t(98) = 1.71, p =.25, d = For asymmetric objects, a clear advantage for the same-axis condition was observed. Participants in the same-axis condition were significantly faster than participants in the different-axis condition, t(103) = 3.81, p <.01, d = Participants in the different-axis condition and participants in the different-axissame-object condition were not statistically different, t(110) = 1.56, p =.36, d = The difference between participants in the same-axis condition and those 6 The degree of freedom employed in the response time data analysis is different from the degree of freedom employed in the accuracy data analysis because the response time data were collected only from correct responses and the data below the 4000 ms cutoff point were excluded for this analysis.

22 384 YAMAUCHI ET AL. TABLE 4 Mean response times in Experiment 3 Symmetry Asymmetry Same-axis M SD Different-axis M SD Different-axis-same-object M SD The response time data were presented in milliseconds. M = mean, SD = standard deviation. in the different-axis-same-object condition did not reach a significant level, t(103) = 2.17, p =.11, d = This response time analysis clearly indicates the advantage of the same-axis condition over the different-axis condition. Discussion Every symmetric object that was shown in the study task of the same-axis condition had vertical axes of symmetry, while the symmetric objects that were shown in the study task in the different-axis conditions had varying axis orientations. The two conditions were identical except for this single point, and no objects were shown both in the study task and in the test task. Nevertheless, participants in the same-axis condition were significantly more accurate than participants in the different-axis condition in their symmetry detection. This result is consistent with the hypothesis that vertical axes of symmetry, which were processed in the study task, can facilitate the detection of symmetry of other objects that also have vertical axes of symmetry. 7 The result from an analysis with response time data with the inverse transformation agreed with those using the 4000 ms cutoff. Given the symmetric objects, there was a significant main effect of axis structure, F(2, 151) = 3.66, MSE = ±7, p <.05, Z 2 = Planned t-test showed that the mean response time obtained from participants in the different-axis condition was significant longer than that from the same axis condition, t(99) = 2.61, p <.05, d = 0.51 (Bonferroni). The mean response times from the different-axis condition and from the different-axis-same-object condition were not statistically different, t(102) = 1.54, p =.39, d = A similar tendency was observed between participants in the same-axis condition and those in the different-axis-same-object condition, t(101) = 1.28, p =.60, d = Given asymmetric objects, there was no main effect of axis structure, F(1, 164) = 1.42, MSE = ±7, p =.24, Z 2 =