Length and area estimation with visual and tactile stimuli more

PROCEEDINGS of the HUMAN FACTORS AND ERGONOMICS SOCIETY 48th ANNUAL MEETING—2004 1875 LENGTH AND AREA ESTIMATION WITH VISUAL AND TACTILE STIMULI Merrill Sapp and Douglas J Gillan New Mexico State University Las Cruces, New Mexico Why do the psychophysical functions for line length (linear) and area (compressive) differ and do they differ for both the tactile and visual modalities? Experiments 1A and B examined the effects of a twodimensional perception on psychophysical functions for visual perception. Participants used magnitude estimation to judge the diameter, area, and circumference of a set of 14 circles. The psychophysical functions for diameter was approximately 1.0, for area was approximately .60, and for circumference was above 1.0, indicating that two-dimensional perception, per se, does not cause the compressive function for area. Obtaining spatial information without vision can be important for people with demanding graphically based decision-making tasks and people with visual impairments. Tactile interfaces provide an alternative way to display and obtain information. Do the tactile and visual modalities process spatial information in similar ways? Experiment 2 examined the correspondence between visual and tactile perception. Participants touched, but did not see, a series of circles. For each circle they judged diameter, area, and circumference. Psychophysical functions for diameter length, circumference length, and area of a circle estimated by tactile perception in Experiment 2 were comparable to those for visual perception. INTRODUCTION Decision-making tasks often require multiple sources of information. Interfaces typically rely on visual displays to convey information to a user, who may have to make a choice based on a combination of elements, from a variety of sources. When a user’s eyes are busy, tactile interfaces can provide additional information without adding to the visual load. In addition, persons with visual disabilities may use tactile interfaces for graphical information displays, such as maps (Ungar, Blades, and Spencer, 1997), with presentation structures that are similar to visual graphics. Is tactile information processed in the same way as visual information? Are tactile interfaces a viable alternative for the people with visual disabilities or other users that have a high visual load? If so, information can be presented in comparable ways in visual or tactile displays. If not, we need to find the best way to translate visual information into tactile information, so that “eyes busy” and users with visual disabilities can have accurate access to information. Stevens’ Law describes the psychophysical functions for line and area perception with a relationship between the physical stimuli and sensation that can be expressed by S = kIb. S represents the sensation, k is a constant that represents the units of measurement (grams, etc.), I is the stimulus intensity, and b is the exponent to which the intensity is raised (Stevens, 1961). The exponent value can be used to describe the nature of a particular sensory modality. For example, judgments for visual length typically have an exponent value of approximately 1.0. This means that there is a direct relationship between the size of the physical stimulus and people’s perception of that stimulus. On the other hand, area perception usually has an exponent value of .60 - .70. This is a compressive relationship, i.e., to double a sensation it takes more than double the stimulus intensity. Compressive relationships compress large amounts of physical energy into smaller amounts of physical response. The exponent for a certain sense modality may provide important information about how that sense processes and uses incoming stimuli. Given the importance of accurate visual information, you might expect that all spatial perception would accurately and exactly reflect physical reality. That linear perception is usually very accurate may be a testament to the biological importance of distance perception. The fact that area is directly computable from the length of a figure, makes the difference between the psychophysical functions relating the physical stimulus to sensation for line length and area seem paradoxical. If the visual system proceses linear information accurately, it seems that it could use that linear information to produce accurate area perception, and then it would use the area information to produce accurate volume perception. In fact, magnitude judgments get progressively worse from linear, to area, to volume judgments. What happens when people judge area and volume? Is it an entirely different process than linear judgment? Some of the variation between the psychophysical functions of line and area judgments (Cleveland, 1983) can be explained by differences in stimulus range (Parducci, 1968; Gillan & Sapp, 2002). However, even when the stimulus ranges, i.e. the corresponding physical values in each stimulus set (length and area), are identical, the psychophysical function for area is less than that for line length (Gillan et al, 2002). Thus, different judgment processes may influence the two types of stimuli. A key difference between perceiving a line and an area is that area perception requires a viewer to look at an object in two dimensions. Perhaps some aspect of the process of viewing a stimulus in two dimensions results in response compression. If two-dimensionality underlies the compressive function for area, then other tasks that require perception in two dimensions should yield a compressive PROCEEDINGS of the HUMAN FACTORS AND ERGONOMICS SOCIETY 48th ANNUAL MEETING—2004 1876 psychophysical function. The circumference of a circle is interesting in that regard – it involves a judgment of line length, but requires perception in two dimensions. Thus, if two dimensional perception is the basis for the compressive psychophysical function for area, the circumference of a circle should have a Stevens’ Law exponent like area. For the present experiments, participants estimated one of the three features of a circle on each trial -- its diameter, circumference, or area. In Experiment 1A, the three types of judgments were interspersed randomly throughout the session; in Experiment 1B, the types of judgments were organized into three separate blocks. Experiment 2 examined the judgments of diameter, circumference, and area for circles presented tactilely. EXPERIMENT 1 Method Participants. Experiment 1A had 30 participants and Experiment 1B had 20 participants. All participants were undergraduates at New Mexico State University. Participants received class credit for their participation. Table 1. Diameter, circumference, and area of each circle used in Experiment 1. Diameter (in cm) 0.5 1 2 3 4 5 6 7 8 9 10 11 12 16 Circumference (in cm) 1.57 3.14 6.28 9.42 12.56 15.7 18.84 21.98 25.12 28.26 31.4 34.54 37.68 50.24 Area 2 (in cm ) 0.196 0.785 3.14 7.065 12.56 19.625 28.26 38.465 50.24 63.585 78.5 94.985 113.04 200.96 diameter of 4 cm, a circumference of 12.56 cm, and an area of 12.56 cm2. Procedure Experiment 1A. Participants were asked to make estimations of diameter, circumference, or area depending on the condition. They were asked to rate each target in a ratio with the standard and were given examples of ratio scaling. They were told that there was no upper limit to the numbers they could assign the stimuli. The participants were instructed to estimate the size of the target as quickly and accurately as possible. They were told that they would be judging the diameter, circumference, or area of the target circles and were then shown examples of diameter, circumference, and area. They were instructed that one circle would serve as the standard to use as a comparison for the three types of judgments, and the standard was shown to them highlighting each dimension to be used. In Experiment 1A, the three trial types were randomly presented during one session. In addition, each participant received a different random order of stimulus size. On each trial, the participant was presented with a circle, which was labeled with “diameter”, “circumference”, or “area” to indicate which aspect of the circle was to be judged on that trial. When participants were ready to enter a judgment, they would click the mouse, which would take them to the response screen. Then, on the response screen, they would enter a value into the response field and click “READY” to move on to the next screen. Procedure Experiment 1B. The procedure for Experiment 1B was the same as that in Experiment 1A except that judgment type was blocked, rather than randomly presented. Participants were shown only one standard at a time, depending on the judgment type for that block of trials. In other words, each judgment type was completed before beginning another type (e.g., all diameter judgments were completed before beginning the area block). The order of the blocks of judgment type was counterbalanced. Results and Discussion The psychophysical functions for diameter, circumference, and area estimates are displayed in Figures 1A (for Experiment 1A) and 1B (for Experiment 1B). These figures show the typical compression functions for area and a Steven’s Law exponent close to 1.0 for the straight line component of diameter, much like the exponents typically observed for a straight line in isolation. Circumference does not appear to have a compressive psychophysical function. In fact, where the psychophysical functions of the two linear elements of a circle differ most, in Experiment 1A, circumference has a strongly expansive psychophysical function - with an exponent more than two times that of area. The pattern of results in these experiments produced a significant Judgment Yype x Intensity interaction, (Experiment 1A, F[2, 58] = 42.91, p < .0001; Experiment 1B, F[2, 38] = 136.97, p =.0001). In addition, the psychophysical functions for all 30 participants in Experiment 1A and all 20 participants in Experiment 1B had a larger Stevens’ Law exponent for circumference than their exponent for area, both Apparatus. The stimuli were created using Deneba Artworks and Hypercard, and were displayed on a Macintosh Quadra with a 17 inch monitor. Stimuli were presented and responses were recorded by a specially-designed Hypercard program. Stimuli. Participants viewed 14 circles with the dimensions shown in Table 1. The standard circle had a PROCEEDINGS of the HUMAN FACTORS AND ERGONOMICS SOCIETY 48th ANNUAL MEETING—2004 1877 A. Diameter 800 Mean Estimated Length Mean Estimated Length Est = 3.15(Diameter) R2 = .997 1.08 600 800 600 Circumference Mean Estimated Area Est = 1.88(Circumference) R2 = .986 1.13 B Area 800 Est = 3.17(Area).60 R2 = .993 B 600 J 400 J J J 400 B B B B B J 400 B B B B B 200 JJ J J J J J J J 200 B BB 0B B B B B 200 B 0 0 60 B B B B B B B 0 4 8 12 Diameter Length (in cm) 16 0 10 20 30 40 50 Circumference (in cm) 0 50 100 150 200 Area (in squared cm) 250 B. Diameter 1200 Mean Estimated Diameter 1000 800 600 400 200 0 0 2 4 6 8 10 12 14 16 Diameter (in cm) Est = 2.97(Diameter) 1.21 R2 = .995 Mean Estimated Circumference 1200 1000 800 600 400 200 0 0 Circumference 1200 Mean Estimated Area Est = 1.26(Circumference) 1.73 R2 = .997 1000 800 600 400 200 0 0 Area Est = 3.20(Area).66 R2 = .987 10 20 30 40 50 Circumference (in cm) 60 50 100 150 200 Area (in squared cm) 250 Figure 1. A. Experiment 1A: Mean estimated length as a function of the length of the diameter of various circles; mean estimated length as a function of the circumference of those circles; and mean estimated area as a function of the area of those circles. B. Experiment 1B: Mean estimated length as a function of the length of the diameter of various circles; mean estimated length as a function of the circumference of those circles; and mean estimated area as a function of the area of those circles. p’s < .001, Sign test. The results of both Experiments 1A and B -- particularly the Stevens’ Law exponent for circumference -- indicate that perception in two dimensions does not necessarily produce a compressive function. Thus, the difference in psychophysical functions for line length and area is not due to the two-dimensionality of the area. EXPERIMENT 2 Experiment 1 showed that a second dimension did not necessarily result in response compression for visual stimuli. If the tactile system processes one and two-dimensional information in the same way as the visual system, then the psychophysical functions for the length of a straight line (e.g., a diameter of f circle), the length of a circle’s circumference, and the area of a circle should be comparable for a circle perceived by touch and a circle perceived visually. Method Participants. Experiment 2 had 11 participants, all of whom were undergraduates at NMSU. Apparatus. The stimuli were a set of 14 circles and a standard stimulus created with .25 inch foam board mounted on pieces of 8.5 x 11 inch paper. Stimuli. The circle sizes were the same as those in Experiment 1 (see Table 1). The standard circle had an area of 12.56 cm2. Procedure. Participants were read similar instructions to those in Experiment 1. They were blindfolded and given examples of diameter, circumference, and area of circles (the experimenter moved a participant’s preferred hand over a circle indicating the three features -- diameter, circumference, and area). Participants were instructed to touch the circles and make the appropriate judgment, judgment type was blocked as in Experiment 1B. In the Passive condition, the experimenter moved the participants’ hand over the circle. In the Active condition, the participants were given the appropriate stimulus and then were allowed to move their hand over the circle freely. PROCEEDINGS of the HUMAN FACTORS AND ERGONOMICS SOCIETY 48th ANNUAL MEETING—2004 1878 800 Mean Estimated Length l Mean Estimated Area 600 l 600 Estimated Area = 2.83(Area) .69 R 2= .984 l l l l Mean Estimated Circumference Estimated Length = 2.56(Length) 1.39 R2= .996 Diameter 800 Area l 800 Estimated Circumference = .99(Circumference) 1.41 l R 2= .996 Circumference 600 l l l 400 l l l 400 l 400 l 200 l l l 0 ll l l l l 200 ll 0ll l l l l 200 l l 0 ll l l l l l 0 4 8 12 Diameter Length (in cm) 16 0 40 80 120 160 Area (in cm-squared) 200 0 10 20 30 40 Circumference (in cm) 50 Figure 2. Mean estimated length as a function of diameter length of various circles; mean estimated area as a function of the area of those circles; and mean estimated length of the circumference as a function of the circumference of those circles in Experiment 2. Results and Discussion The active and passive conditions showed no differences (F[1, 9] <1.0) and were combined for the analysis. The psychophysical functions for diameter, circumference, and area estimates are shown in Figure 2. They are very similar to the corresponding functions found for the visual stimuli in Experiment 1. Circumference and diameter both show a slightly expansive functions, but area shows a very typical compressive function. The pattern of results produced a significant judgment type x intensity interaction, F(2, 16) = 53.75, p < .0001. Circumference did not show compression as was predicted by the hypothesis that two-dimensional perception causes compression. GENERAL DISCUSSION The present research was designed to examine the effect of dimensionality on psychophysical judgments. Specifically, three experiments addressed the question, does twodimensional perception cause a compressed psychophysical function? If so, the psychophysical function for circumferemce judgments should be similar to that for area judgments. However, Experiments 1A, 1B, and 2 showed that two-dimensional perception does not necessarily result in compression; a line in two dimensions (i.e., a circumference) has a Stevens’ Law exponent of 1.0 or higher, whereas an area has a Stevens’ Law exponent less than 1.0. This indicates that while the perceptual system treats area and circumference information differently and that the compressive function for area is not merely a function of dimensionality. What then can explain the differences found for line, area, and circumference judgments? As discussed above, Gillan et al, (2002) showed that stimulus range -- across a set of the same circles, the range of the linear dimensions like diameter and circumference tend to be much loweer than that of the area -cannot account for the entire difference between line and area perception. Another possibilty, related to the two dimensions of area judgment task, focuses on competion between processing linear elements of a circle (diameter and circumference). Basically, as viewers judge the area of an object, such as a circle, they automatically process the line that delinates the object. Part of that automatic processing of the line might involve judging its length. The judgement of the length of the circumference might compete with and interfere with the viewers’ ability to judge the area, with the result being that the overt area judgment involved a combination of relatively accurate assessments of the area and the circumference. To test this hypothesis, we reanalyzed the data from Experiment 1A, using a multiple regression model, Area Estimate = a + b1(area) + b2(circumference). The competition model predicts that a significant proportion of the variance in area estimates should be uniquely related to the circumference. The 2 reanalysis of Experiment 1A found that the semipartial r for circumference was substantial, .58, and substantially greater 2 than the semipartial r for area, .05. In other words, the circumference uniquely accounts for more than 10 times more variance in area estimates than does area. This finding is consistent with the compeition hypothesis. In addition, the idea of priviledged processing of the linear element of an object is consistent with theories of object preception (e.g., Biederman, 1987) The other question addressed by the present research, does the tactile system process one- and two- dimensional spatial information the same way as the visual system, was the focus of Experiment 2. Experiment 2 showed that the psychophysical functions for line length, circle circumference length, and circle area are comparable for tactile perception and visual perception. Accordingly, the results of Experiment 2 suggests that tactile displays could be designed to provide graphical information in the same way as visual graphic displays (e.g., Kaczmarek and Bach-y-Rita, 1995). This is valuable information for the design of displays, especially in multi-task environments (see Jones, 2003). Visual information can translate into tactile information without modifying algorithms. In modern task environments, the limiting factor may be more commonly a users’s lack ability to use incoming information rather than lack of information. The present research indicates that haptic displays could be a solution to overload. By using both visual and haptic displays, PROCEEDINGS of the HUMAN FACTORS AND ERGONOMICS SOCIETY 48th ANNUAL MEETING—2004 1879 in a sense the load is dispersed across modalities, and perhaps could be better utilized. Instead of relying solely on the capacity of the visual system, the tactile system can take on some of the responsibility of dealing with incoming information. At a more basic level, the present findings raise the following questions: are the visual and tactile system similar because they have both evolved in response to the same environment? Or does each system feed into a single higher level mechanism that controls judgments of perceptual intensity? Acknowledgements Prepared through participation in the Advanced Decision Architectures Collaborative Technology Alliance sponsored by the U.S. Army Research Laboratory under Cooperative Agreement DAAD19-01-2-0009. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U. S. Government. References Biederman, I. (1987). 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