The Persistence of Vision in Spatio-Temporal Illusory Contours formed by Dynamically-Changing LED Arrays

Transcription

1 The Persistence of Vision in Spatio-Temporal Illusory Contours formed by Dynamically-Changing LED Arrays Damian Gordon * and David Vernon Department of Computer Science Maynooth College Ireland ABSTRACT LED displays produce anomalous spatio-temporal (moving) illusory contours involving the apparent (perceived) shift in the position of physical stimuli and resulting in an apparent tilt of the displayed pattern. This illusion may be explained by a spatio-temporal grouping which is dependent on the persistence of vision associated with illusory contours. Empirical measurements corroborate existing results on the relationship between the duration of persistence, on the one hand, and period of stimulation, on the other. In addition, these results extend existing knowledge by providing empirical data for persistence and stimulus time intervals which have not so far been addressed. Specifically, Meyer and Ming report a non-linear but regular relationship between duration of stimulus and persistence, with stimulus duration ranging from 50ms to 1000ms. In this paper we present results for stimulus duration in the range 0ms to 25ms; these results fit well with an extrapolation of Meyer and Ming s results. 1 Introduction Most people are familiar with LED array display systems (see figure 1). These are electronic display devices which consist of an array of light-emitting diodes (LEDs) which allow the display of text or graphics. Usually, the text is displayed as a moving sequence of characters, scrolling horizontally across the LED array. Since the individual characters being displayed are formed by straight, upright, sequences of individual LEDs, one would expect the moving characters to appear upright as well. However, in many LED displays, the orientation of the scrolling text appears to change to an angle of approximately 10 decrees off vertical. This illusion does not occur with static text and the orientation reverts to the expected vertical. * Visiting Researcher

2 Figure 1. An LED Array Display System Whilst most people do not notice this phenomenon, it is remarkable because the apparent position of the stimulus (i.e. the individual LED) does not correspond to its physical location. In essence, the human perceptual system forms a spatio-temporal grouping of scrolling LEDs and, in the right conditions, the percept is a distortion, albeit a consistent distortion, of the physical structure of the LED array. This illusion may be explained by a spatio-temporal grouping which is dependent on the persistence of vision associated with illusory contours. While this illusion is quite interesting in itself, the primary focus of this paper is to exploit the very short time intervals over which one can present an LED stimulus in order to investigate the relationship between the period of stimulation and the duration of persistence in a hitherto uninvestigated range of stimulus durations. Empirical measurements corroborate previously published results regarding this relationship. It is important to note that this apparent tilt is not related to the tilt after-effect (investigated with respect to illusory contours by Smith and Over, 1975) which is due to adjustment of the visual system to a persistently presented stimulus and the subsequent perception of an opposing effect when the stimulus is removed. It was in 1904 that Schumann first introduced the concept of illusory contours (variously called subjective contours, cognitive contours, and ambiguous contours [Halpern, 1981], anomalous contours, contours without gradients, and quasi-perceptive margins [Bradley and Dumais, 1975]). An illusory contour is seen when a stimulus configuration produces the perception of an edge in an area where there is no physical change in intensity, wavelength, or depth [Meyer and Ming, 1988] [Von Grunau 1979]. To investigate the factors which produce the illusory contours in LED displays, in this case, it is necessary to discuss the LED activation method employed by these devices. This method is referred to as one-seventh multiplexing.

3 2 One-seventh multiplexing The term one-seventh multiplexing derives from the fact that standard LED arrays consist of an array of 96 columns by 7 rows. When text is to be displayed, each row is fed in turn with the light pattern which it must display. Each row displays this pattern in rapid succession. Only one row of LEDs are activated at any one time but, due to the persistence of human vision and the rapidity of display sequence, it appears all the rows are on at the same time. It is usually the case that the bottom row displays its information for a short period of time, then the next row up is displayed, and so on, until the top row is reached. As we have noted, it will appear as if all the rows are on together creating what shall henceforth be called one frame of text. Many frames displayed in rapid succession will produce the appearance of motion (the scrolling-effect) if the pattern of activated LEDs is displaced by, say, one column of LEDs, between each frame. Now consider the simple example of one single vertical line (a column) scrolling from right to left. In order to scroll this line (right to left), we simply require that the line be displayed for a short period of time in a particular column, then the display is blanked for a very short period of time, and the line is then displayed in the column directly to the left of the previous column. Repetition of this cycle will produce apparent motion or Phi Movement [Gordon, 1989] resulting in the appearance of a scrolling (or horizontally moving) line. We will refer to the delay between frames as the inter-frame delay. As we noted above, each frame is sub-divided into its seven separate rows. When displaying our scrolling vertical line, the LED on the bottom row of the column will be activated, then deactivated as the LED next from the bottom is activated, and so on until the top LED in the column is reached. The delay between deactivating one row and activating the next row is referred to as the inter-row delay. Because of the way these devices are constructed, and because of the human persistence of vision, all seven LEDs will appear to be on at the same time and will form a conceptual column in a manner consistent with established Gestalt figural grouping principles. In summary, to display a scrolling vertical line pattern, the LEDs in one column are activated and deactivated in succession, and then the LEDs in the column to the left of this one are activated and deactivated, and then the ones to the left of this, and so on. With this appreciation of the operation of LED displays, it is now possible to describe a theory to explain the apparent tilt during scrolling.

4 Figure 2. The labelling order of LEDs 3 The theory The question which must be answered is: What is the relationship between the right-toleft displacement of the LED activation pattern and the persistence which causes the group to be seen as a single column (albeit that the individual LEDs are activated at different times)? Still considering the example of the single scrolling line, the theory regarding the apparent tilt during motion centres around the fact there are two grouping principles at work. The first is the normal spatial figural grouping principle based on co-linearity, spatial proximity, and similarity. This causes the vertical line of activated LEDs to be grouped as a percept. The second principle is a temporal grouping principle predicated on the constant velocity of a stimulus (i.e. the Phi phenomenon). To understand the perception of the apparent tilt, we first note that, although only one LED on a column is active at any one time, the rapid successive activation of rows up the display causes a linear figural grouping because of persistence of human vision. Let the inter-row delay time be δt. At the same time, an LED scrolling to the right will have an apparent motion with a given velocity. The value of this velocity will be equal to the inter-column spacing, divided by the total time taken between frames. If we let the inter-column space be written d, then the velocity, v, will simply be given by v = d /7δt. The apparent position of an individual LED will naturally be its initial position plus its apparent velocity times the time elapsed ( t): x=x 0 + v * t Let us label the LEDs in one column L 1 to L 7, as we move upwards, and the LEDs in a column to its left L 8 to L 14 (see figure 2). Let the initial position (in the horizontal

5 Figure 3. An illusory contour formed direction) be set arbitrarily to zero (i.e. x 0 = 0), then the position of L 1 at time t = 0 is simply 0 + v * 0, i.e. zero. At time t = δt, the position of L 1 is 0 + v * δt, which is in fact d / 7, since v = d / 7δt At time t = 2δt, the position of L 1 is 2d / 7 and the position of L 2 is d / 7. In the same way, at time t = 3δt, the position of L 1 is 3d / 7, the position of L 2 is 2d / 7, and the position of L 3 is d / 7. By the time t = 6δt, i.e. a full frame has been displayed and L 7 has been activated, L 1 will appear to be at position 6d/7, L 7 will be at position 0, and L 2 to L 6 will all have appear to have moved proportionately and the spatial figural grouping will give rise to a co-linear sequence of simultaneously activated LEDs where the bottom LED, i.e. L 1 leads the top LED L 7 by a distance of 6d/7. That is, there will now be a perception of an illusory contour of LEDs where the position does not correspond to the position or orientation of the physical stimulii (i.e. the actual LEDs) - see Figure 3. Remember, though, that this illusory contour is the result of two grouping, phenomena: one is a spatial grouping based on the proximity and consistency of form (pragnanz) whilst the other is a temporal grouping based on the constant velocity of the stimulus giving rise to a Phi phenomenon. Consequently, at time t = 7δt, when L 8 is activated in the next physical column of LEDs, the apparent position of the LED which 'started off at L 1, and which will have occupied (perceptually) the space between L 1 and L 8 as it appears to translate across the display, will have now have shifted to L 8 and the entire cycle starts all over again. Thus, the entire pattern will appear to translate horizontally with a smooth phi motion and with the lower LEDs leading, the upper LEDs by a fixed amount resulting in an apparent tilt of the pattern.

6 We are now in a position to answer the question we posed at the outset of this section: What is the relationship between the right-to-left displacement of the LED activation pattern and the persistence which causes the group to be seen as a single column (albeit that the individual LEDs are activated at different times)? It is this. The single column can be seen in one of two ways: it can be perceived as an upright vertical column or as a tilted column with the lower LEDs leading the upper ones. An upright column is clearly a grouping, of a real set of LEDs, i.e., it forms a real contour. On the other hand, a tilted column is clearly an illusory contour. Each case evokes a different persistence, with the persistence associated with an illusory contour being greater than that of a real contour. If the right to left displacement is effected at a velocity such that the temporal grouping becomes a factor (in addition to the spatial grouping,) then a uniformly translating illusory contour will result; otherwise one will perceive a sequence of upright columns displacing at regular intervals. Significantly, the critical velocity at which the illusory contour is perceived, i.e. at which temporal grouping takes effect, is a function of the persistence of vision itself, a phenomenon which in turn depends on the duration of the presentation of the physical stimulus. Thus, the point at which the illusion breaks down indicates a limiting instance of the persistence of an illusory contour, i.e. illusory persistence, and, equally, the limiting duration of the presented physical stimulus which is necessary to cause the illusory persistence. 4 Implications of the theory We are now in position both to validate this hypothesis and to learn something about the variation of illusory persistence with the duration of the presentation of a physical stimulus. Specifically, if we can measure the illusory persistence as a function of the duration of the presentation of the physical stimulus (i.e. the activation time of a single LED) and if these results are consistent with established values then clearly we can have confidence in the above hypothesis. In addition, if we make these measurements for a range of stimulus duration, we will have determined new empirical results for illusory persistence. Here we must note that the duration of the illusory persistence is simply the duration of a complete frame, i.e., the time period between L 1 and L 8 and being activated, just prior to the illusion breaking down. This is so since this is the maximal delay (between the presentation of each individual physical stimulus) for which temporal grouping and phi motion is perceived. 5 Results A series of tests were performed in which the duration of the presentation of the physical stimulus (t s ) was varied between 0 and 25 ms1 and a delay introduced between the activation of the top row LED and the activation of the bottom row LED of the next column (i.e. a delay which extends the overall frame time without affect the activation 1 It is important to note that this range of stimulus durations is different to that investigated by Meyer and Ming.

7 t s t f Table 1. Results of test series time of each LED). We will refer to this delay as the inter-frame delay (t i ). This delay was increased until the illusion broke down. The overall limiting frame time (t f ) at which the illusion breaks down provides us with an estimate of the illusory persistence for a given duration of stimulus activation (t s ). Table 1 summarises the measured values of t f at this limiting point as a function of t s. It should be noted that the illusion of motion breaks down in any case for values of stimulus duration greater than 25ms, and it is, therefore, impossible to determine values for the persistence of illusory contours whose stimulus duration is greater than 25ms using this method. All results are mean values of five separate trials. 6 Discussion Meyer and Ming, 1988, determined values for (stationary) illusory contours for stimulus durations in the range ms and values of ms persistence. In the graphs in figures 4 and 5, we show our results together with those of Meyer and Ming. From inspection it can be seen that both sets are consistent and, indeed, a linear regression of our results provides an estimate of the persistence of vision in the range investigated by Meyer and Ming. This analysis reveals that, for example, the persistence of vision for stimulus duration of 50ms (which we did not measure but which we estimate by regression) is 283ms. This compares well with the value measured by Meyer and Ming of approximately 276ms. The results which have been presented do indeed confirm that apparent tilt of a pattern in a scrolling LED display using one-seventh multiplexing is caused by illusory contours and, more importantly, their measurement represent new empirical data regarding, the persistence of illusory contour s for stimuli for a duration of between 0ms and 25ms.

8 Combined Results Persistence (msecs) Stimulus Duration (msecs) Figure 4. Graph of results. Data points in the range 0-25ms (with persistences in the range 0-140ms) are as a result of the work presented in this paper; data points in the range ms (with persistences in the range ms) are due to work done by Meyer and Ming. Combined Results (Closer View) Persistence (msecs) Stimulus Duration (msecs) Figure 5. As above, with a closer view of the gap (in the range 25-50ms) between the results presented here and those of Meyer and Ming.

9 REFERENCES Bradley D R, Dumais S T, 1975, "Ambiguous cognitive contours" Nature (London) Gordon I E, 1989, Theories of Visual Perception, John Wiley & Sons Halpern D F, 1981, "The determinants of illusory-contour perception" Perception Meyer G E, Ming C, 1988, "The visible persistence of illusory contours" Canadian Journal of Psychology Schumann F, 1904, "Einige Beobachtungen uber die Zusammenfassung von Gesichtseindrucken zu Einheiten" Psychologische Studien Smith A, Over R, 1975, "Tilt after-effects with subjective contours" Nature (London) Von Grunau M W, 1979, "The involvement of illusory contours in stroboscopic motion" Perception & Psychophysics