Feature localization and identification

Acta Psychologica 106 (2001) 97±119

www.elsevier.com/locate/actpsy

Feature localization and identi®cation Mieke Donk a

a,b,*

, Cristina Meinecke

c

Department of Cognitive Psychology, Vrije Universiteit, De Boelelaan 1111, Amsterdam 1081 HV, Netherlands b Max-Planck-Institut f ur psychologische Forschung, M unchen, Germany c Ludwig-Maximilians-Universit at, M unchen, Germany Received 24 December 1998; accepted 17 August 1999

Abstract Theories on visual search di€er substantially with respect to the relationship they assume between localization and identi®cation processes. The aim of the present study was to rigorously compare the alternative theoretical notions on how localization and identi®cation processes are related. In two experiments, participants searched for a target with a unique line orientation among distractors containing another orientation. Localization and identi®cation performance were measured in combination, as function of display size and target eccentricity. To compare the alternative theories, formal binomial models were developed and compared with respect to their goodness of ®t to the individual data. The formal analyses showed that the model assuming identi®cation processes to be conditioned on localization processes provided the best ®t to the individual data. Furthermore, maximum likelihood estimates of the parameter corresponding to identi®cation processes were di€erently a€ected by display size than identi®cation performance was. The results were discussed in terms of their implication for current theories on visual search. Ó 2001 Elsevier Science B.V. All rights reserved. PsycINFO classi®cation: 2300; 2323; 2340 Keywords: Localization; Identi®cation; Visual search; Binominal models

*

Corresponding author. Tel.: +31-20-4448797; fax: +31-20-4448832. E-mail address: [email protected] (M. Donk).

0001-6918/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 1 - 6 9 1 8 ( 0 0 ) 0 0 0 2 8 - 7

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Andries Sanders may be considered as one of the chief guardians of the serial stage structure of information processing (e.g., Sanders, 1980, 1990, 1998). Apart from his continuing involvement in the discovery of processing stages, he has also been working on what is going on during a particular stage (e.g., Van Duren & Sanders, 1988). This last issue has prompted the interest of several of his students (see also Los in the present issue). The present paper is an attempt to investigate what is going on at two consecutive stages of information processing during visual search. Major theories on visual search suggest that human vision operates in two sequentially arranged stages in which the operation of the second attentive stage is conditioned on the output of the ®rst preattentive stage (e.g., Sagi & Julesz, 1985a; Treisman & Gelade, 1980; Wolfe, Cave & Franzel, 1989). Generally, the ®rst stage is assumed to operate in parallel over the visual ®eld. That is, visual information presented across the visual ®eld is believed to be processed at the same time. The second stage whose operation is conditioned on the output of the ®rst one, presumably operates in a serial manner. In this stage, the amount of visual information processed per time unit is assumed to be limited (but see Townsend, 1974, 1990). Although theories on visual search generally agree on the above notions, they di€er considerably with respect to the capabilities they ascribe to both stages. Initially, it was suggested that the preattentive stage performs a feature analysis whereas the attentive stage is involved with localization and feature binding. According to the original feature integration theory (FIT), visual information is ®rst analyzed into separate features (e.g., red or vertical) which are represented in distinct feature maps (Treisman & Gelade, 1980). Thus, in preattentive vision, primitive features are detected and identi®ed (Folk & Egeth, 1989; Green, 1991; Treisman & Gelade, 1980; Treisman & Gormican, 1988). Basically, preattentive processes signal what the identity is of a feature without signaling where it is. To localize a feature in the visual ®eld the involvement of the second attentional stage is required. The attentional stage allows features that are initially Ôfree-¯oatingÕ to be tied to their location and to each other. A second theoretical approach to visual search was provided by Sagi and Julesz (1985a, b) who suggested that the preattentive stage is capable of detection and localization whereas computations like discrimination and identi®cation require the operation of the attentive stage. This notion is just opposite to the original notion of Treisman and Gelade (1980). Sagi and Julesz (1985a, b) claimed that the preattentive stage is not able to identify features. Instead, the identi®cation of even simple visual features is assumed to require the allocation of attentional resources. The preattentive stage is capable to detect feature gradients if the display density is high enough. That is, feature di€erences or discontinuities can be computed in parallel if the distance between adjacent elements is relatively small. Apart from the detection of discontinuities, preattentive vision is also able to localize these discontinuities. Thus, according to this view, the preattentive system can signal where without knowing what the target is, except that it is di€erent. Whereas Treisman and Gelade (1980) assume localization processes to be conditioned on feature identi®cation processes,

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Sagi and Julesz (1985a) presume identi®cation processes to be conditioned on localization processes (Nothdurft, 1992; Sagi & Julesz, 1985b). More recently, a third theoretical point of view has been proposed (Cave & Wolfe, 1990; Treisman & Sato, 1990; Wolfe, 1994; Wolfe, Cave & Franzel, 1989). Like in the original FIT, it is assumed that the preattentive stage in human vision is capable of detecting simple features across the visual ®eld (Treisman & Gelade, 1980). In contrast to the original FIT, in this view, features cannot be preattentively identi®ed. Instead, localization as well as feature identi®cation processes are assumed to be under attentional control, i.e., both processes are assumed to be performed by the attentive stage and conditioned on the output of the preattentive stage which only signals the presence of activity. Activity levels above some threshold indicate that some feature is present somewhere in the visual ®eld. The identity and location of a feature can be reported only if attention is allocated (Cave & Wolfe, 1990; Treisman & Sato, 1990; Wolfe, 1994; Wolfe, Cave & Franzel, 1989). In other words, no conditional relationship is assumed between localization and identi®cation processes. Evidence for one or the other theory primarily derives from studies directly comparing localization with identi®cation performance. For example, Treisman and Gelade (1980) reported two experiments (Experiments VIII and IX) in which they had participants indicate the identity and location of a target that was concurrently presented with multiple distractors during a brief presentation time. One major ®nding was that feature identi®cation was well above chance, even when major location errors were made. Furthermore, location responses were generally at chance when the target was wrongly identi®ed. Their conclusion was that the identi®cation of features can be performed preattentively but that the localization of elements requires the utilization of focused attention. Atkinson and Braddick (1989) came to a di€erent conclusion. They showed that when in a localization task only ``coarse'' localization was required, performance was superior to that in an identi®cation task. When in the localization task ``®ne'' localization was required, localization and identi®cation accuracies were equal. They concluded that processes related to ``coarse'' localization are preattentive and that processes of feature identi®cation and ``®ne'' localization are attentive. Saarinen (1996a) also manipulated a localization task. He reported the results of three experiments indicating that by manipulating the localization task, it is possible to obtain data suggesting that localization processes precede identi®cation processes, localization processes follow identi®cation processes, or in which there seems to be no priority of one over the other. 1 Finally, Green (1992) had participants perform in a detection, localization, and identi®cation task. His basic ®nding was that observers detected, localized, and identi®ed targets with similar accuracies (Green, 1991, 1992). 1 It should be noted that in Saarinen (1996a) experiments reaction time has been used as dependent variable. It is very likely that his results were a€ected by response factors like compatibility. Indeed, in Experiment 2, participants had to indicate the `up' or `down' position of a target by using the left hand for `up' and the right hand for `down'. Only in this experiment, reaction time in the localization task was found to be longer than in the identi®cation task. When stimulus response compatibility was high, like in Experiment 1, identi®cation performance was found to be inferior to localization performance.

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Apparently, the published data do not provide unequivocal evidence for one or another theory (Saarinen, 1996b). Instead, whereas in some studies it is suggested that localization processes are conditioned on identi®cation processes, the results of other studies seem to provide evidence for unconditional processing or for the idea that identi®cation processes are conditioned on localization processes. A major reason for this disagreement might be related to the fact that in previous studies di€erences between localization performance and identi®cation performance were directly interpreted in terms of which process precedes the other one. In other words, the relationship between localization processes and identi®cation processes was directly inferred from di€erences in performance. This is, however, not appropriate. A performance superiority in one task over the other does not justify the conclusion that processing related to the second task is conditional on processing related to the ®rst one. Instead, it might as well be the case that both processes are not conditioned on each other (e.g., when they occur in parallel) but that the former is just faster than the latter resulting in better performance. In addition, neither does the absence of any di€erence in performance imply that both processes are unconditioned. Basically, a ®nding of equal performance levels in a localization and an identi®cation task is not conclusive at all with respect to the underlying architecture of processes since most theories of visual search would be compatible with such a result (see below). The purpose of the present study was to investigate the relationship between feature localization and feature identi®cation processes by developing formal binomial models of the alternative theoretical accounts. In contrast to previous studies, the method utilized in the present study should permit appropriate conclusions concerning the underlying architecture of information processing in a visual search task. 1. The models Following Batchelder and Riefer (1986, 1990) and Riefer and Batchelder (1988) formal multinomial tree structures were developed enabling direct comparison of the various theoretical approaches to visual search. In the present study, participants were brie¯y presented with search displays containing one target and multiple nontargets. Participants had two tasks concurrently. In the localization task, they had to indicate whether the target occurred to the left or right of central ®xation. In the identi®cation task, they had to indicate whether the target contained a tilted line to the left or a tilted line to the right. Each combination of target location and target identity occurred equally often. The dependant variable was the proportion responses per response category, i.e., correct identi®cation and correct localization response (CICL), correct identi®cation and false localization Response (CIFL), false identi®cation and correct localization response (FICL), and false identi®cation and false localization response (FIFL). If the simultaneous perception of location and identity occurs in a statistically independent fashion and participants gain all-or-none information about the loca-

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tion and the identity of a target (Link, 1982; Lord & Novick, 1968), the probability of a certain outcome should be predictable on the basis of the tree diagrams as illustrated in Fig. 1. Fig. 1 delineates three tree diagrams depicting all possible theoretical states and how they lead to speci®c response types separate for three alternative theoretical notions. The ®rst model, the feature model, states that localization processes are conditioned on identi®cation processes. This model is basically a formalization of the original FIT of Treisman and Gelade (1980). The second model, the localization model, assumes identi®cation processes to be conditioned on localization processes. This model is the formal equivalent to the theory of Sagi and Julesz (1985a, b). Finally, in the third model, the unconditional model, it is assumed that localization and identi®cation processes are not conditioned on each other. This model is equivalent to the later theories of visual search (Cave & Wolfe, 1990; Schneider, 1995; Treisman & Sato, 1990). On the basis of these tree diagrams, the expected proportion for every response category is given by the sum of the paths corresponding to that response category. For example, in the localization model, the expected proportion of a correct identi®cation response in combination with a correct localization response (CICL) is given by

Fig. 1. Three tree diagrams corresponding to the three alternative theoretical notions. Each diagram depicts the outcome on every trial as a function of the product of the probability that the target localization processes are ®nished, i.e., l, and the probability that the target identi®cation processes are ®nished, i.e., i (CICL ˆ correct identi®cation and correct localization response; CIFL ˆ correct identi®cation and false localization response; FICL ˆ false identi®cation and correct localization response; FIFL ˆ false identi®cation and false localization response). See text for further explanation.

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       1  1 ‡ …1 ÿ l† ; p…CICL† ˆ‰l iŠ ‡ l …1 ÿ i† 2 4 in which l corresponds to the probability that the target localization processes are ®nished, and i corresponds to the probability that the target identi®cation processes are ®nished. In general, the diagrams in Fig. 1 state that the expected proportion of a response in a certain response category depends on these two probabilities. If feature localization processes are conditioned on feature identi®cation processes as assumed by FIT, it is expected that the feature model provides the best ®t to the data. Furthermore, at a performance level, identi®cation performance may never be worse than localization performance (see Appendix A). If feature identi®cation processes are conditioned on feature localization processes as presumed by the theory of Sagi and Julesz (1985a), it is expected that the localization model provides the best ®t to the data. Furthermore, localization performance may never be worse than identi®cation performance (see Appendix B). It is important to note that both conditional models, i.e., the feature model and the localization model, allow localization performance to be equal to identi®cation performance. This occurs when the conditioned probability, i.e., l in the feature model and i in the localization model, equals one. In that case, the di€erence between the proportion of correct identi®cation responses, p(CI), and the proportion of correct localization responses, p(CL), equals zero. This implies that a ®nding of no di€erence between localization performance and identi®cation performance does not necessarily imply that both corresponding processes are unconditioned. Finally, if feature localization processes and feature identi®cation processes are not conditioned on each other, it is expected that the unconditional model provides the best ®t to the data. Moreover, at a performance level, localization performance may be equal, worse, or better than identi®cation performance dependent on the individual probabilities that the localization and identi®cation processes are ®nished (see Appendix C). From the foregoing it should be clear that in contrast to the belief of previous studies, a di€erence between localization and identi®cation performance is only preliminary indicative for the underlying architecture. That is, performance superiority of one over the other does not necessarily imply that the processing of the latter is conditioned on the processing of the former. Instead, it might as well be that both processes are not conditioned on each other. Actually, equal performance levels are not necessarily the result of unconditional processing but might as well occur if one of the conditional models is true. Basically, directly interpreting di€erences between localization performance and identi®cation performance in terms of the relationship between the underlying processes, requires assumptions concerning the eciency of the processes related to localization and identi®cation. That is, one has to assume that the probability that the target localization processes are ®nished, l, is equal to the probability that the target identi®cation processes are ®nished, i. Only in this case one may directly infer the underlying architecture from overt behavior. However, the validity of this assumption is very questionable since there is no good reason to assume both processes to be equal ecient. Indeed, various studies suggest that

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dependent on the accidental diculty of the localization task and the identi®cation task, the relative eciency of both processes may strongly change (Atkinson & Braddick, 1989; Saarinen, 1996a). Utilization of the present approach circumvents this problem. The unconstrained parameters in the models, i.e., l and i, make any prior assumptions about these values super¯uous since the values of these parameters may vary freely. The present approach has at least two advantages over previous approaches. First, the binomial modeling technique allows a formal comparison between alternative theoretical notions. That is, alternative theories can be directly compared with respect to their goodness of ®t to the individual data. In previous studies, the alternative theoretical notions were not formalized providing less opportunity to precisely compare the possible theories. Second, apart from the possibility to determine which architecture provides the best ®t to the data, additionally, the present modeling approach provides estimates of the psychologically meaningful parameters l and i. This allows us to examine the processes related to l and i more directly as has been the case in earlier studies. One may, for instance, investigate how variables like display size and target eccentricity, which are typically manipulated in visual search experiments (Geisler & Chou, 1995; Jo€e & Scialfa, 1995; Kehrer, 1987; Treisman & Gelade, 1980; Wolfe, Cave & Franzel, 1989), exert their e€ect on performance. That is, one may study which processes are a€ected by these variables and how these changes in processing a€ect performance. As previously mentioned, overt behavior does not directly re¯ect the relationship between underlying processes. In a similar vein, behavioral e€ects of variables like display size and target eccentricity do not immediately allow one to conclude which process they a€ect. Utilizing the present approach provides an opportunity to formally decide where in the chain of information processing these variables exert their e€ects. The aim of Experiment 1 was to provide a formal test of the alternative theoretical accounts to visual search. A further goal was to investigate how display size and target eccentricity a€ect processes of localization and identi®cation.

2. Method Participants: Twelve participants were recruited for the present experiment. Each participant had normal or corrected to normal vision. They received DM 12 per hour for participation. Task and Stimuli: On each trial, participants were brie¯y presented with a display containing either 47 or 431 identical elements composed of three straight lines and one deviant element, the target, which could be either a `N' or a mirror `N' (see Fig. 2). 2 To attain a broad range of performance for each individual participant, 2 The values of display size were chosen such as to relate to previous studies on element search (e.g., Treisman & Gelade, 1980) as well as to prior studies on texture segmentation (e.g., Nothdurft, 1992).

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Fig. 2. One sample display with 48 elements (upper panel) and one sample display with 432 elements (lower panel).

there were three display exposure durations, i.e., approximately 55 ms (4 raster cycles), 83 ms (6 raster cycles), or 110 ms (8 raster cycles). After presentation, the search display was masked by a whole-screen mask containing all properties of the discriminating features between target and background. Elements were always presented in a region that subtended 19:7  3:6 cm which is 21:50  4:12 of visual angle at an observation distance of 50 cm. In 50% of the trials the target contained a line tilted the left and in 50% of the trials it contained a line tilted to the right. Furthermore, targets were equally probable presented to the left or right of the central ®xation point with the constraint that they could only occur on the horizontal midline at a distance of 0.65, 1.95, 3.25, 4.55, 5.85, 7.15, and 8.45 cm from the central ®xation point which equals 0.74°, 2.23°, 3.72°, 5.20°, 6.67°, 8.14°, and 9.59° of visual angle. Elements were 0:35  0:35 cm (0:40  0:40 of visual angle). In the 48-elements condition, interitem distance was 0.90 cm (1.03° of visual angle) and in the 432-elements condition interitem distance was 0.13 cm (0.15° of visual angle). Participants had two sequential tasks. In the localization task, they had to indicate whether the target occurred to the left or right of central ®xation. In the identi®cation task, they had to indicate whether the target contained a tilted line to the left or a tilted line to the right. Each combination of target location and target identity occurred equally often. Responses were made by means of the two mouse keys. That is, for the localization task, participants had to press the left mouse key if the target occurred to the left of central ®xation and the right mouse key if the target occurred to the right of central ®xation. For the identi®cation task, they had to press the left mouse key if the target contained a tilted line to the left and the right mouse key if the target contained a tilted line to the right. Design: A within subject design was used. Target eccentricity (0.65, 1.95, 3.25, 4.55, 5.85, 7.15, and 8.45 cm from the central ®xation point), target identity

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(`N' versus mirror `N'), target position (left of central ®xation point versus right of central ®xation point), and exposure duration (55, 83, and 110 ms) were varied within blocks. Display size (48 versus 432 elements) was varied between blocks. The sequences of block presentation as well as the required sequences of responses with respect to the localization and identi®cation task were counterbalanced over participants. The dependent variable was the proportion of responses per response category. There were four di€erent response categories, i.e., correct identi®cation and correct localization response (CICL), correct identi®cation and false localization response (CIFL), false identi®cation and correct localization response (FICL), and false identi®cation and false localization response (FIFL). Procedure: Each trial started with the presentation of a tone (6000 Hz, 200 ms) immediately followed by the presentation of a central ®xation point. After 500 ms, the search display was presented during approximately 55, 83, or 110 ms immediately followed by the mask. After the ®rst response, the mask changed in a central ®xation point that disappeared after the second response. The next trial started after an interval of 1 s. Participants were required to give two responses at every trial. If they did not perceive the location or the identity of the target, they were instructed to guess. Participants were seated in a dimly illuminated room with their heads ®xed in a head-chin rest. Every participant took part in one session of about 1.5 h. Each session consisted of two blocks corresponding to the two display sizes. Each block was preceded by an instruction and 84 practice trials corresponding to that block. After practice, which took about 10 min, the experimental part started which consisted of 588 trials and took about 35 min. Participants were free to take a break every 196 trials.

3. Results Behavioral analysis: Fig. 3 shows the average proportions of correct localization and identi®cation responses separate for each combination of display size, target eccentricity, and exposure duration. Generally, localization performance is better than identi®cation performance, F …1; 11† ˆ 15:60; p < 0:002. A MANOVA 3 on the individual mean proportions of correct localization responses shows that performance is a€ected by display size, F …1; 11† ˆ 17:10; p < 0:002, and target eccentricity, F …6; 6† ˆ 56:18; p < 0:001. Furthermore, performance is strongly a€ected by exposure duration, F …2; 10† ˆ 86:74; p < 0:001. A MANOVA on the individual mean proportions of correct identi®cation responses shows the same pattern. That is, performance is a€ected by display size, F …1; 11† ˆ 22:50; p < 0:001, and target eccentricity, F …6; 6† ˆ 22:84; p < 0:001. In 3

As the experiment is based on repeated measurements, multivariate analyses of variance were performed on the data when the independent variable had more than two levels. Furthermore, Wilks' lambda was used, and the reported F-values represent approximate values (Stevens, 1992).

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Fig. 3. Average proportions of correct localization responses (a) and correct identi®cation responses (b) as a function of display size, target eccentricity, and exposure duration in Experiment 1.

addition, performance is strongly a€ected by exposure duration, F …2; 10† ˆ 113:98; p < 0:001. Theoretical analysis: To investigate whether the present data are better described by a feature model, a localization model, or an unconditional model, each model was separately ®t to the data of each participant. For each model maximum likelihood estimates of the free parameters were obtained using an iterative search procedure

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Table 1 Individual goodness-of-®t values (lnL values) for Experiment 1 Participant

Model

1 2 3 4 5 6 7 8 9 10 11 12

Feature model

Localization model

Unconditional model

)1061.78 )1314.23 )1154.45 )1283.71 )1379.54 )747.72 )1155.29 )639.46 )845.85 )1321.38 )1230.07 )1153.02

)1048.54 )1286.07 )1138.94 )1282.49 )1371.94 )739.73 )1090.20 )614.45 )821.50 )1304.57 )1214.38 )1148.73

)1058.58 )1287.38 )1140.12 )1316.12 )1379.27 )754.02 )1086.19 )616.72 )835.89 )1313.93 )1234.41 )1158.74

(Hu & Batchelder, 1994). The maximum likelihood estimates are those parameter values that minimize the absolute value of the log likelihood (lnL). The lnL is given by lnL ˆ

n X

fi lnPi ;

i

in which fi is the observed response frequency in cell i of the data matrix, and Pi is the probability of this type of response as predicted by the model. Log Likelihood is always a negative value. The closer the value to zero, the better the model ®t. The absolute value of lnL depends on the goodness of ®t of the model and the number of observations. Since there were 2 display sizes, 3 exposure durations, 7 eccentricities, and 4 possible responses, there were 168 cells in the data matrix for each participant (2  3  7  4) and 126 degrees of freedom. Each model was separately ®t to the data of each individual participant. Table 1 shows the individual goodness-of-®t values for the alternative models. For 11 out of 12 participants, the localization model provided the best ®t to the data. Fig. 4 shows the average parameter estimates of l and i of the best ®tting localization model as a function of display size, target eccentricity and exposure duration. A MANOVA on the individual parameter estimates of the localization model shows that the probability that the target localization processes are ®nished, l, is a€ected by display size, F …1; 11† ˆ 24:45; p < 0:001, target eccentricity, F …6; 6† ˆ 48:11; p < 0:001, and exposure duration, F …2; 10† ˆ 154; 35; p < 0:001. The probability that the target identi®cation processes are ®nished, i, is not a€ected by display size, F …1; 11† ˆ 2:22; p < 0:05, but is a€ected by target eccentricity, F …6; 6† ˆ 15:83; p < 0:002 and exposure duration, F …2; 10† ˆ 15:73; p < 0:001. Furthermore, there was an interaction between display size and target eccentricity, F …6; 6† ˆ

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5:29; p < 0:031. 4 Since according to the best ®tting model, i was conditioned on l, estimates of i were rather unreliable when l was small. This was in particular the case for a presentation duration of 55 ms and the further target eccentricities.

4. Discussion Experiment 1 shows that the localization model provides the best ®t to the data for 11 out of 12 participants. This suggests that at least in the present experiment, identi®cation processes are conditioned on localization processes. Apparently, observers are not able to indicate the identity of a simple feature without knowing (at least coarsely) where that feature is. This ®nding is in strong agreement with the ideas of Sagi and Julesz (1985a, b) that localization precedes identi®cation. On a behavioral level, both localization and identi®cation performance are affected by display size and target eccentricity. It interesting that the maximum likelihood estimates derived from the best ®tting model, i.e., l and i, show a somewhat di€erent pattern. Whereas l is a€ected by display size as well as target eccentricity, i is only a€ected by target eccentricity. Apparently, di€erences in identi®cation performance as a function of display size were due to di€erences in localization processes instead of identi®cation processes. Since i was found to be conditioned on l, estimates of i were not reliable. This was in particular the case when l was small (e.g., for the shortest presentation duration). To closer examine possible e€ects of target eccentricity on i, a second experiment was designed. Another aim of Experiment 2 was to further test the alternative models. Experiment 2 was basically a replication of Experiment 1 with two major changes. First, exposure duration was constant at a value of approximately 83 ms. Second, display size was further manipulated by adding one condition in which the target was the only element presented. The one-element condition provided a situation in which the probability that target localization processes are ®nished, l, was maximized, allowing reliable estimation of i if the localization model would be the best ®tting model.

5. Experiment 2 5.1. Method Participants: Twelve new participants took part in the present experiment. Each participant had normal or corrected to normal vision. They received DM 12 per hour for participation. 4 Since i was found to be conditioned on l, maximum likelihood estimates of i were partly extremely high. The interaction was therefore probably due to a ceiling e€ect at the high exposure duration. Indeed, a MANOVA on the individual maximum likelihood estimates of i excluding the highest exposure duration, shows no interaction between display size and target eccentricity, F …6; 6† ˆ 2:55; p < 0:050.

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Fig. 4. Average parameter estimates for the probability that the target localization processes are ®nished, l (a) and the probability that the target identi®cation processes are ®nished, i (b) as function of display size, target eccentricity, and exposure duration in Experiment 1.

Task and Stimuli: Task and stimuli were the same as in Experiment 1, except that on each trial, elements were presented during approximately 83 ms (6 raster cycles). Furthermore, a third condition was added in which only one element was presented. Design: See Experiment 1. Procedure: Every participant took part in one session of about 1 h. Each session consisted of three blocks corresponding to the three display sizes. In Experiment 2,

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the experimental part of each block consisted of 196 trials. Further procedures were identical to those in Experiment 1.

6. Results Behavioral analysis: Fig. 5 shows the average proportions of correct localization and identi®cation responses separate for each combination of display size and target eccentricity. Considering the data of the multiple element conditions only shows that localization performance was better than identi®cation performance, F …1; 11† ˆ 6:58; p < 0:026. This was also the case in the single element condition, F …1; 11† ˆ 63:67; p < 0:001.

Fig. 5. Average proportions of correct localization responses (a) and correct identi®cation responses (b) as a function of display size and target eccentricity in Experiment 2.

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A MANOVA on the individual mean proportions of correct localization responses in the multiple element conditions shows an e€ect of display size, F …1; 11† ˆ 32:44; p < 0:001 and target eccentricity, F …6; 6† ˆ 19:07; p < 0:001. In the single element condition the mean proportion of correct localization responses was not a€ected by target eccentricity, F …6; 6† ˆ 0:63. A MANOVA on the individual mean proportions of correct identi®cation responses in the multiple element conditions shows that identi®cation performance is also a€ected by display size, F …1; 11† ˆ 26:56; p < 0:001 and target eccentricity, F …6; 6† ˆ 12:70; p < 0:003. In the single element condition, the mean proportion of correct identi®cation responses was also a€ected by target eccentricity, F …6; 6† ˆ 15:52; p < 0:002. Theoretical analysis: To further investigate whether the present data are better described by a feature model, a localization model, or an unconditional model, each model was separately ®t to the data of each individual participant. In Experiment 2, there were 3 display sizes, 7 target eccentricities, and 4 response categories resulting in 84 cells in the data matrix for each participant (3  7  4) and 63 degrees of freedom. Table 2 shows the individual Goodness-of-Fit values for the alternative models. For 10 out of 12 participants, the localization model provided the best ®t to the data. Fig. 6 shows the average parameter estimates of l and i of the best ®tting localization model as a function of display size and target eccentricity. To compare the present data with those of Experiment 1, analyses were performed on the individual parameter estimates of the localization model in the multiple element conditions only. The probability that the target localization processes are ®nished, l, is a€ected by display size, F …1; 11† ˆ 33:97; p < 0:001 and target eccentricity, F …6; 6† ˆ 43:81; p < 0:001. The probability that the target identi®cation processes are ®nished, i, is

Table 2 Individual goodness-of-®t values (lnL values) for Experiment 2 Participant

1 2 3 4 5 6 7 8 9 10 11 12

Model Feature model

Localization model

Unconditional model

)543.82 )543.71 )600.99 )390.85 )786.09 )638.64 )455.45 )543.71 )691.62 )406.75 )328.44 )657.44

)506.04 )518.61 )559.37 )339.47 )708.93 )592.36 )378.03 )497.20 )626.66 )363.75 )299.85 )615.07

)509.71 )520.00 )564.97 )341.89 )706.53 )599.21 )387.48 )500.79 )629.96 )366.49 )302.81 )611.04

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Fig. 6. Average parameter estimates for the probability that the target localization processes are ®nished, l (a) and the probability that the target identi®cation processes are ®nished, i (b) as function of display size and target eccentricity in Experiment 2.

not a€ected by display size, F …1; 11† ˆ 3:52; p < 0:050 and only marginally a€ected by target eccentricity, F …6; 6† ˆ 3:95; p < 0:059. Including the single element condition in the analyses shows that i was smaller in the single element condition than in the multiple element conditions, F …1; 11† ˆ 34:58; p < 0:001. Furthermore, i was a€ected by target eccentricity, F …6; 6† ˆ 15:94; p < 0:002.

7. Discussion The major result of Experiment 2 is that for 10 out of 12 participants, the localization model provided the best ®t to the data. This result is basically a replication

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of the previous result in Experiment 1. Furthermore, the behavioral data as well as the theoretical data are in general agreement with those obtained in Experiment 1. Considering the multiple element conditions only, at a behavioral level, both localization and identi®cation performance were a€ected by target eccentricity. Generally, performance tended to increase up till an eccentricity of about 3° of visual angle and decrease gradually at the further eccentricities. This ®nding is not surprising regarding the results of previous studies. It has repeatedly been shown that search performance tends to be worse in the fovea than in the parafoveal areas in particular if display density is high (Jo€e & Scialfa, 1995, Kehrer, 1987, 1989; Meinecke, 1989; Meinecke & Kehrer, 1994). Furthermore, previous studies repeatedly demonstrated that search performance gradually declines as function of target eccentricity (e.g., Geisler & Chou, 1995). However, the results of these studies do generally not allow any inference as to whether localization or identi®cation processes are a€ected by target eccentricity. In the present study, this inference can be made by investigating how the maximum likelihood estimates corresponding to localization and identi®cation processes change as a function of target eccentricity. Maximum likelihood estimates of l derived from the multiple element conditions show that l increases up till about 3° of visual angle and decreases at the further eccentricities. Likewise, maximum likelihood estimates of i show the same pattern suggesting that some common mechanism underlies both processes. The e€ects of display size are less uniform. Considering the multiple element conditions only, localization as well as identi®cation performance are a€ected by display size. Performance was generally better in the 432-element condition than in the 48-element condition. At a theoretical level, l was also found to be larger in the 432-element condition than in the 48-element condition. In contrast, i was not found to be di€erent in both conditions. Apparently, the eciency of localization processes increases if display size becomes larger whereas this is not the case for identi®cation processes. Basically, these results are in accordance with those predicted by a localization model. According to Sagi and Julesz (1987), localization processes should become more ecient when display size increases (see also Kehrer, 1989; Meinecke, 1989; Nothdurft, 1985, 1990). A larger display size results in a higher display density allowing the preattentive system to e€ortlessly locate feature gradients. It should be noted that neither FIT (Treisman & Gelade, 1980) nor the more recently developed theories on visual search (Treisman & Sato, 1990; Wolfe, Cave & Franzel, 1989) predict localization processes to become more ecient as display size increases. It is interesting to note that whereas display size does not a€ect i in the multiple element conditions, i is a€ected when comparing the single element conditions with the multiple element conditions. That is, the eciency of identi®cation processes is smaller in the one element condition than in the multiple element conditions. Apparently, identi®cation processes pro®t from the presence of other elements irrespective of their quantity. This allows observers to more instantly identify the target element compared to a condition in which no other elements are presented.

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8. General discussion The present experiments show that it is possible to formally decide between alternative theoretical notions of visual search by comparing the goodness of ®t of the corresponding binomial models to the individual data. The results unequivocally show a superior ®t of the localization model over the feature model and the unconditional model. In the multiple element conditions, analyses of the maximum likelihood estimates corresponding to localization and identi®cation processes show that whereas the eciency of localization processes is a€ected by both target eccentricity and display size, the eciency of identi®cation processes appears to be only a€ected by target eccentricity. Furthermore, identi®cation processes are generally less ecient in the single element condition than in the multiple element conditions. The present results are not in accordance with any account assuming that identi®cation processes precede localization processes. Even at a behavioral level, localization performance is generally superior to identi®cation performance. Nevertheless, a major claim of FIT (Treisman & Gelade, 1980) is that preattentive feature identity information can be accessed through pooled signals permitting feature identity perception without location perception (see also Treisman & Gormican, 1988). Major support for this claim derived from two sources of empirical evidence. First, in the Experiments VIII and IX of Treisman and Gelade (1980) it was shown that localization accuracy was superior to identi®cation accuracy. This ®nding has, however, not been replicated (Green, 1991). Moreover, as already pointed out by Johnston and Pashler (1990), Treisman and Gelade (1980) experiments might have su€ered from the ``negative information problem''. Since the targets they utilized were likely not equally visible, participants might have used the strategy of guessing the less visible target when no target was detected. As a result, superior identi®cation performance might not have been due to identi®cation processes preceding localization processes but to subjects guessing the identity of the target better than chance. A second argument favoring a feature model is that many studies suggest the existence of illusory conjunctions (e.g., Treisman & Schmidt, 1982). Illusory conjunctions are percepts in which features are correctly perceived but falsely combined (Treisman & Schmidt, 1982). The ®nding that participants more often report false combinations of presented features (e.g., reporting `red T' when a `red O' is presented concurrently with a `blue T') than features that are not presented at all (e.g., reporting `green T' when a `red O' is presented concurrently with a `blue T') was taken as prime evidence for the belief that the processing of a feature's identity precedes the processing of a feature's location. The existence of illusory conjunctions would obviously be a major argument against any theory assuming identi®cation to be conditioned on localization. However, a recent study shows that previous reports of illusory conjunctions were likely to be due to errors of target-nontarget confusion instead of imperfect feature binding (see Donk, 1999). The results of the present study are also not compatible with any model assuming identi®cation processes and localization processes not to be conditioned on each other. Recent theories of visual search assume that in search, all responses are made after attention ®nds the target item (e.g., Wolfe, 1994). In other words, those theories

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do not assume identi®cation processes to be conditional upon localization processes or the other way around. The present study shows that it is not likely that identi®cation and localization processes operate in an unconditional fashion. Experiments 1 and 2 generally show that a model assuming identi®cation processes to be conditioned on localization processes provides a better ®t to the data than a model assuming both processes not to be conditioned on each other. As mentioned before, the relevance of the conclusions in the present experiments strongly depends on the validity of the utilized models. The binomial models used here all rely on the independence assumption. According to this assumption, localization and identi®cation processes are assumed to occur in a statistically independent fashion. It is imaginable that this assumption is not true. Possibly, computational mechanisms take advantage of whichever process ®nishes ®rst, localization or identi®cation, to guide the output of the other process. 5 Given a coarse localization task like in the present experiments, a localization model might provide the best ®t to the data due to the localization processes being ®nished faster than the identi®cation processes. Increasing the diculty of the localization task may possibly shift the balance resulting in a better ®t of the feature model. According to this view, whichever process ®nishes ®rst, directs the other process analysis. In a logical sense, this idea is a viable alternative however, in the present context it is not the most parsimonious one since one assumes the functional organization of processes to be modulated by the relative eciency of both corresponding tasks. Furthermore, there is good evidence that the independence assumption holds if participants make separate decisions with respect to the identity and the location of the target (Ashby & Townsend, 1986). Since there is much evidence that identi®cation and localization occur in di€erent visual systems (Ungeleider & Mishkin, 1982), it seems reasonable to assume that in the present experiments, localization and identi®cation processes occurred in a statistically independent fashion. The present ®ndings generally ®t in with the theory proposed by Sagi and Julesz (1985b) according to which preattentive processes are able to detect and localize changes in feature gradients whereas the analysis of feature identities requires the operation of a subsequent stage of processing. According to Sagi and Julesz (1987), the eciency of localization processes increases if more elements are presented due to an increased ability of the preattentive system to localize discontinuities in feature gradients. The present experiments show that l is a€ected by display size suggesting indeed that localization processes pro®t from high display density. Furthermore, l and i were both a€ected by target eccentricity. Although Sagi and Julesz's (1985a, b) theory does not contain any speci®cation with respect to possible e€ects of target eccentricity, these results are not incompatible with their view. The spatial resolution of the visual system declines dramatically with retinal eccentricity primarily due to decreases in retinal cell density (e.g., Banks, Sekuler & Anderson, 1991). It is likely that this di€erence in the neuronal characteristics across the retina results in both

5

This possibility was raised by one of the reviewers.

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changes in the eciency of localization processes and changes in the eciency of identi®cation processes (Jo€e & Scialfa, 1995). In sum, the present study shows that it is possible to formally decide which model of visual search provides the best ®t to the data. The data provide unequivocal evidence for the localization model assuming that identi®cation processes are conditioned on localization processes. Apart from the possibility to formally decide between alternative theoretical notions, the present approach also allows one to directly investigate where in the functional architecture variables like display size and target eccentricity exert their e€ect. This provides further opportunities to discriminate between alternative theoretical notions.

Acknowledgements This research was supported by the Max-Planck-Institut f ur psychologische Forschung, Munich, Germany. We would like to thank Willem Verwey, Jan Theeuwes, and an anonymous reviewer for their helpful comments on an earlier version of this article. We would also like to thank G unther Heilmeier for performing the experiments. Appendix A If feature localization processes are conditioned on feature identi®cation processes as assumed by the FIT (Treisman & Gelade, 1980), identi®cation performance may never be worse than localization performance. This becomes apparent when comparing the expected proportion of correct identi®cation responses, CI, with the expected proportion of correct localization responses, CL. According to the feature model:     1 ; p…CI† ˆ ‰i lŠ ‡ ‰i …1 ÿ l†Š ‡ …1 ÿ i† 2       1 1 ‡ …1 ÿ i† ; p…CL† ˆ ‰i lŠ ‡ i …1 ÿ l† 2 2     1 ; p…CI† ÿ p…CL† ˆ i …1 ÿ l† 2 in which l corresponds to the probability that the target localization processes are ®nished, and i corresponds to the probability that the target identi®cation processes are ®nished. Appendix B If feature identi®cation processes are conditioned on feature localization processes as presumed by the theory of Sagi and Julesz (1985a), localization performance may never be worse than identi®cation performance which is evident when calculating the

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di€erence between the expected proportion of CI and the expected proportion of CL. According to the localization model:     1 p…CI† ÿ p…CL† ˆ ÿ l …1 ÿ i† 2 in which l corresponds to the probability that the target localization processes are ®nished, and i corresponds to the probability that the target identi®cation processes are ®nished. Appendix C If feature localization processes and feature identi®cation processes are not conditioned on each other, localization performance may be equal, worse, or better than identi®cation performance dependent on the individual probabilities that the localization and identi®cation processes are ®nished. According to the unconditional model, the expected di€erence between the proportion of CI and CL is           1 1 1  1  ÿ …1 ÿ i† l ˆ iÿ l p…CI† ÿ p…CI† ˆ i …1 ÿ l† 2 2 2 2 in which l corresponds to the probability that the target localization processes are ®nished, and i corresponds to the probability that the target identi®cation processes are ®nished.

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