Article

i-Perception

May-June 2017, 1–16

The Author(s) 2017

The ‘‘Spinner’’ Illusion:

More Dots, More Speed?

!

DOI: 10.1177/2041669517707972

journals.sagepub.com/home/ipe

Hiroshi Ashida

Kyoto University, Kyoto, Japan

Alan Ho

Ambrose University, Alberta, Canada

Akiyoshi Kitaoka

Ritsumeikan University, Kyoto, Japan

Stuart Anstis

University of California, San Diego, CA, USA

Abstract

The perceived speed of a ring of equally spaced dots moving around a circular path appears faster

as the number of dots increases (Ho & Anstis, 2013, Best Illusion of the Year contest). We

measured this ‘‘spinner’’ effect with radial sinusoidal gratings, using a 2AFC procedure where

participants selected the faster one between two briefly presented gratings of different spatial

frequencies (SFs) rotating at various angular speeds. Compared with the reference stimulus with

4

c/rev (0.64 c/rad), participants consistently overestimated the angular speed for test stimuli of

higher radial SFs but underestimated that for a test stimulus of lower radial SFs. The spinner effect

increased in magnitude but saturated rapidly as the test radial SF increased. Similar effects were

observed with translating linear sinusoidal gratings of different SFs. Our results support the idea

that human speed perception is biased by temporal frequency, which physically goes up as SF

increases when the speed is held constant. Hence, the more dots or lines, the greater the

perceived speed when they are moving coherently in a defined area.

Keywords

psychophysics, speed perception, visual illusion, visual motion

Introduction

Visual motion provides us with vital information about the environment necessary for our

daily survival. The ability to perceive the speed and direction of external moving objects

enables us to act on the objects or to navigate through the environment safely without being

harmed. While detection of motion and identiﬁcation of direction have been studied

Corresponding author:

Hiroshi Ashida, Graduate School of Letters, Kyoto University Sakyo, Kyoto 6068501, Japan.

Email: ashida@psy.bun.kyoto-u.ac.jp

Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License

(http://www.creativecommons.org/licenses/by/3.0/) which permits any use, reproduction and distribution of the work without

further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sage-

pub.com/en-us/nam/open-access-at-sage).

2

i-Perception

extensively by psychophysicists, physiologists, and computational neuroscientists, our

knowledge of speed perception is rather limited in terms of its phenomenology and

underlying mechanisms (e.g., see a review by Nishida, 2011). One possible factor limiting

our understanding of speed perception and vision in general is the inverse projection problem

(

Palmer, 1999). This problem arises because an inﬁnite number of distal environmental

objects with diﬀerent shapes and sizes seen in the three-dimensional (3D) world can cast

the same two-dimensional (2D) optical image onto the retina, introducing ambiguities

diﬃcult to solve. A moving distal environmental object further extends the inverse

projection problem into the time domain and possibly introduces more uncertainty and

inaccuracy for the visual system in processing visual motion information. Since the claims

that the human visual system analyses complex visual images by their spatial frequency (SF)

content like a Fourier analyzer (Campbell & Robson, 1968; Sachs, Nachmias, & Robson,

1

971), researchers have been using sinusoidal gratings extensively to study human vision. The

speed of a moving stimulus used in researches is consequently expressed in terms of its spatial

and temporal frequencies, and is susceptible to biases from other stimulus properties such as

its luminance contrast (Thompson, Brooks, & Hammett, 2006; Thompson, 1982) and colour

(

Cavanagh, Tyler, & Favreau, 1984).

A counterintuitive bias in speed perception was recently demonstrated by Ho and Anstis

2013) in the 2013 Best Illusion of the Year contest. They later redesigned it as ‘‘the spinner

(

illusion’’ using simpler disk elements, as shown in Figure 1 (see also Appendix Movie 1). The

four yellow dots on the left and the eight yellow dots on the right were both set to revolve at

the same rate, yet all observers consistently reported seeing the dots on the right as rotating

faster than those on the left. In the demonstration video, the number of dots on the right

increases from 4 to 8 and then 12, with the rotation seeming faster with each increase.

The spinner illusion is interesting because there is no obvious reason in physics why

increasing the number of dots should increase their apparent speed, assuming that all the

dots are clearly visible. Ho and Anstis (2013) originally suggested that the greater retinal blur

caused by more dots might make them look faster. While it is known that motion streaks can

enhance motion perception (Apthorp et al., 2013; Geisler, 1999), their inﬂuence on speed

Figure 1. The spinner illusion. The four and eight yellow dots revolve around the blue disks at the same

physical speed (top), but the perceived speed appears to be faster with eight dots than with four dots

(bottom). Arrow lengths symbolize speeds. The blue disks were not included in the original illusion work, but

are shown here for illustration purposes.

Ashida et al.

3

perception has not been established. We therefore measured the spinner eﬀect with sine wave

grating stimuli that are smooth and less susceptible to smearing.

An alternative account would treat this illusion as a partial failure to compute speed from

the temporal frequency (TF) and SF of the stimulus. While local speed is obtained by local

TF divided by SF in theory, this computation might be performed only in an approximate

way. It has been reported that perceived speed of translating one-dimensional (1D) sinusoidal

gratings depends on their SF. Campbell and Maﬀei (1981) studied rotating 1D gratings and

found that their perceived speed followed an inverted-U function of spatial frequency.

Diener, Wist, Dichgans, and Brandt (1976) reported increased perceived speed at higher

SFs measured by magnitude estimation, a ﬁnding that was later echoed by Chen, Bedell,

and Frishman (1998) using a 2AFC procedure. Smith and Edger (1990) showed opposite

results that both perceived speed and TF decreased as the SF increased, but they pointed out

that the results may depend on the range of SFs used.

In the spinner illusion (Figure 1), SF along the circular path of motion increases as the

number, and thus density, of dots increases. Possibly this illusion directly reﬂects the

spatiotemporal characteristics of the visual system as described earlier. If so, one extreme

possibility would be that speed judgments of rotating stimuli are made on the basis of local

TF, ignoring the SF. Or they might be made as a compromise between the speed and TF of a

rotating stimulus. The results in the literature are not conclusive. One problem is that it is not

straightforward to apply results from the linear gratings to the conﬁguration of a rotating

spinner illusion. We ﬁrst need to conﬁrm that simple sinusoidal patterns give similar illusions,

and then to examine the spatiotemporal characteristics of the illusion parametrically.

We therefore investigated the eﬀect of SF on the spinner illusion in radial gratings

Figure 2). First, we conﬁrmed that the spinner illusion occurs with simple radial

(

sinusoidal gratings for naıve participants (Experiment 1). Sinusoidal modulation is also

¨

eﬀective in minimizing the eﬀect of blur, as image blur does not yield motion streaks but

only reduces the eﬀective contrast. Second, we examined whether the illusion depends more

on speed itself or TF, by taking more detailed measurements from trained participants

(

Experiment 2). Finally, we conﬁrmed that a similar illusion occurs for translational

motion of one-dimensional gratings (Experiment 3). We will then discuss the cause of this

illusion in terms of general spatiotemporal integration.

Experiment 1

The point of subjective equality (PSE) in perceived speed for two simultaneously presented

rotating radial sinusoidal gratings of diﬀerent radial spatial frequencies (RSFs) was assessed

psychophysically using a method of constant stimuli. Speciﬁcally, the rotating speed of the

1

matching stimulus (RSF of 4 c/rev: cycle per revolution ) was varied randomly between trials

and was compared with that of the test stimulus (RSF of either 8, 10, or 12 c/rev; used

uniquely in separate experimental blocks) that was kept constant at 0.33 rev/s, in order to

obtain psychometric functions for the estimation of their PSEs. We expected the resulting

PSE to be higher than the veridical speed of the test stimuli (0.33 rev/s) if the spinner eﬀect

occurred.

Methods

Participants. Eight psychology undergraduate students (6 females and 2 males, aged 19–22)

¨

in Kyoto University participated to fulﬁll partial requirement of a course. They were naıve

4

i-Perception

Figure 2. The basic stimulus configuration. Left: matching stimulus of 4 c/rev, Right: test stimulus of 12 c/rev

as an example. Both stimuli rotated in the same direction. The test and matching sides as well as their yoked

ꢁ

direction of rotation were randomized and balanced across trials. In Experiment 1: a ¼ 2.2 , b ¼ 8.8 , and

ꢁ

c ¼ 5.5 . In Experiments 2 and 3: a ¼ 2.75 , b ¼ 11.0 , and c ¼ 6.9 .

as to the speciﬁc purpose of the experiment, although they had seen a demonstration

of the spinner illusion prior to the experiment. All had normal or corrected-to-normal vision.

Apparatus and stimuli. Stimuli were generated and presented by using PsychToolBox 3

Brainard, 1997; Pelli, 1997) on MATLAB (The Mathworks, Inc., Natick, MA, USA).

(

They were presented on one of the three monitors: two 24-inch (BenQ XL2411) and

a 23-inch (Mitsubishi RDT233WX) LCD with 1920 ꢀ 1080 resolution and 60 Hz refresh

rate, driven by PCs running Microsoft Windows 7. Participants rested their heads

comfortably on a chin rest during experiment with a viewing distance at 50 cm. The

2

mean luminance was 40 cd/m for one BenQ and 100 cd/m for the others. The

luminance proﬁle of each screen was measured and was linearized using a photometer

(

Minolta LM1).

The basic stimulus conﬁguration is shown in Figure 2 (see also Appendix Movie 2). Two

ꢁ

radial gratings, each presented inside a ring-shaped window subtending a visual angle of 8.8 ,

ꢁ

were centered 5.5 laterally on each side of the central red ﬁxation mark. The width of the

ꢁ

rings was 2.2 . The two yoked stimuli always appeared and disappeared on the screen

simultaneously. They had a sluggish temporal envelope: Their luminance contrast was

increased linearly from 0% to 50% in 0.25 s and stayed at 50% for 0.5 s, and then

decreased linearly back to 0% in 0.25 s. The two stimuli rotated in the same direction in

each trial, and both directions were tested within each block of trials.

The RSF for the matching stimulus was 4 c/rev (0.64 c/rad), while the RSF of the test

stimulus was picked from three preset values of 8, 12, or 16 c/rev (1.27, 1.91, and 2.55 c/rad)

and stayed constant within each block of trials.

Ashida et al.

5

(

a)

(b)

1.0

1

00

8

6

4

2

0

.5

8

c/rev

main

1

2 c/rev

6 c/rev

mirrored

0

0.1

0.2

0.4

0.6 0.8

5

10

15

Matching Speed (rev/s)

Radial Spatial Frequency (c/rev)

Figure 3. The results of experiment 1: (a) pooled psychometric functions from all the participants. The

speed of the 4 c/rev matching stimuli needed to be increased from 0.33 rev/s to match the speed of 8 to

1

6 c/rev test stimuli (arrow). (b) The averaged PSE values (matched speeds) across participants, plotted as a

function of RSF with 95% confidence intervals. The dashed straight line in each panel shows the actual speed

of the test stimuli. (b) The filled symbols represent the main results, while the open symbols represent the

auxiliary results with the speed of the higher SF stimuli manipulated; they are above and below the actual

speed line in about the same distances in the log scale, so the two results agree quantitatively as to the

amount of speed overestimation. The shifts of the psychometric functions (a) and thus the shifts of the

matching speed (b) are all consistent with speed overestimation for higher RSFs.

The speed for the test stimulus was ﬁxed at 0.33 rev/s (2.09 rad/s) and the speed for the

matching stimulus was picked randomly from seven preset values between 0.17 and 0.67 rev/s

(

1.05–4.19 rad/s).

Procedure

The method of constant stimuli was used to present a yoked test-matching stimulus pair on

each trial. The participants judged whether the radial grating inside the left or the right

annulus window appeared faster in a 2AFC procedure and responded by pressing one of

two designated computer keys.

Trials were organized in blocks by the three test RSFs. One block consisted of 28 trials

(

7 manipulated speeds ꢀ 2 sides ꢀ 2 rotation directions), and each block was repeated four

times in a pseudorandom order, resulting in 16 measurements per manipulated matching

speed. The computer programme randomized the manipulated speed variations, direction of

stimulus-pair rotation, and the presentation sides of test-matching stimuli.

Results and Discussion

Probit analysis (Finney, 1971; with the scripts by Johnson, Dahlgren, Siegfried, & Ellis, 2013)

was used to estimate each participant’s PSE in perceived speed for each test RSF. The results

were collapsed across presentation sides of stimuli and their rotation directions. Figure 3(a)

shows the averaged psychometric functions from all participants, and Figure 3(b) shows

estimated PSE values for all test-matching paired stimuli. It is evident from the data that

6

i-Perception

the speed of the matching stimulus needed to be turned up beyond the test speed of 0.33 rev/s

to match the perceived speeds of the test stimuli. In other words, the speed of a higher RSF

test stimulus was consistently overestimated by the participants, which agreed with the

original spinner illusion observation.

Speciﬁcally, the participants required the 4 c/rev matching stimulus to rotate 32% to 36%

faster than the actual speed of the high-RSF test stimuli in order to match the perceived

speeds. There was no signiﬁcant diﬀerence in the matched speeds among the test stimuli of 8,

1

2, and 16 c/rev, F(2,14) ¼ 0.334, p ¼ 0.721 by repeated-measure ANOVA.

The speed overestimation of the test stimuli (>30%) here is similar to the report of 33%

for 8 versus 16 dot condition of the original spinner illusion (Anstis & Ho, 2014). It is,

however, not consistent that our data from Experiment 1 did not reveal diﬀerences among

the three high-RSF tests. A possible factor might be compression of perceived speed in a

higher RSF range; tiny diﬀerences for higher RSFs may be buried in noise under the ceiling

eﬀect.

We therefore ran an auxiliary experiment with a diﬀerent speed manipulation in a mirrored

fashion where the speeds of the higher RSF stimuli (8, 12, 16 c/rev) were manipulated

to match the apparent speed of the 4 c/rev reference stimulus. The reference speed used

here was the same as the test speed in the main experiment (0.33 rev/s ¼ 2.09 rad/s).

We used the same set of apparatus, but used PsychoPy (Peirce, 2007) for

stimulus generation and experimental control. The manipulated speed for the test

stimulus was picked randomly from seven preset values between 0.17 and 0.47 rev/s

(

¨

1.05–2.96 rad/s). Nine diﬀerent naıve participants (2 females and 7 male psychology

students, aged 19–22) participated to fulﬁll partial requirement of a course. Their results

are shown in Figure 3(b) by open symbols. Similar to the ﬁndings from the main

experiment, no signiﬁcant diﬀerence in the estimated PSE values was observed among the 8,

1

2, and 16 c/rev test stimuli, F(2,16) ¼ 1.063, p ¼ .369 by repeated-measure ANOVA.

Participants required the speed of higher RSF test stimuli to be decreased to 72% to 76%

of the actual 4 c/rev reference stimulus speed to perceptually match the perceived rotational

speed of the yoked stimulus pair. By taking the reciprocals of these PSE values, the

result corresponded to a speed overestimation of higher RSF stimuli by 31% to 39%, an

observed spinner eﬀect which is quantitatively consistent with the main results of 33% to

3

6% obtained in the main experiment. Thus, the results here mirrored those of the main

experiment, indicating that the ﬂat results among the test RSFs is not an artefact of the

ceiling eﬀect.

We then reasoned that the insigniﬁcant diﬀerences observed could possibly be due to a

¨

high level of internal noise from our naıve participants, lack of regression precision due to

rough sampling of test speeds, or possible dependence of the eﬀects upon the test speed. In

Experiment 2, we therefore further assessed the spinner eﬀect more extensively using trained

participants with a staircase method while adopting a wider range of test RSFs in

combination with multiple test speeds as manipulated variables.

Experiment 2

Participants

One of the authors and two psychophysically trained participants were tested (one female and

¨

two males, aged 22–47). The two participants other than the author were naıve as to the

speciﬁc purpose of this experiment, and were paid for their time at the university standard

rate. All participants had normal or corrected-to-normal vision.

Ashida et al.

7

Apparatus and Stimuli

The stimuli were generated by using PsychoPy 1.82 (Peirce, 2007), running on an Apple

MacBook Pro 15, and were presented on a 19-inch CRT (EIZO T761) with 1024 ꢀ 768

resolution and 75 Hz refresh rate. The screen was viewed from the distance of 45 cm with

the aid of a chin rest. Luminance proﬁle of the screen was measured and linearized with a

photometer (Photo Research PR-655).

The basic stimulus conﬁguration was the same as in Experiment 1 but 25% larger in size;

ꢁ

the ring-shaped windows subtended 11 , with the annulus subtending 2.75 in width

ꢁ

(

Figure 2). These two stimulus windows were centered laterally at an eccentricity of 6.9

on both sides of the central ﬁxation mark. The time course of stimulus presentation was

the same, too: linear increase for 0.25 s, staying at 50% for 0.5 s, and linear decrease to zero

for 0.25 s.

The RSF of the matching stimulus used here was again 4 c/rev (0.64 c/rad) as used in

Experiment 1. Five test SFs were used: 2, 8, 12, 16, and 20 c/rev (0.32, 1.27, 1.91, 2.55,

3

.18 c/rad) in combination with three test speeds: 0.17, 0.33, and 0.50 rev/s (1.05, 2.09, and

.14 rad/s).

Procedure

Participants were given the same 2AFC discrimination task as described in Experiment 1,

judging the faster stimulus. All participants were tested with 15 diﬀerent test stimulus

conditions (i.e., the ﬁve test RSFs ꢀ three test speeds as stated earlier) to complete this

experiment. A staircase method (1-up and 1-down) with smaller preset step sizes was used

for capturing more precise changes in participants’ responses around the PSE for each test

stimulus.

Each condition was tested in separate blocks of randomly interleaved double staircases

one staircase for one direction of motion). Each staircase was terminated after 28 trials

i.e., 56 trials per run with double staircases). Each block was repeated three times,

(

bringing a grand total of 168 trials per stimulus condition.

Results

Responses were pooled for each test stimulus condition within individual participant. The

perceived matched speed (PSE) for each test stimulus condition was estimated with 95%

conﬁdence intervals using probit analysis (Finney, 1971; Johnson et al., 2013).

Figure 4 shows the results for all three participants. Matched speeds (PSEs) of the

matching stimulus to the test stimuli are plotted as a function of RSF for each participant

in separate panels. Since the 4 c/rev stimulus was used as the matching stimulus, we assumed

the veridical speed to be its perceived speed for each test speed level (marked by larger

symbols in Figure 4). The results look very similar across all three participants. Most of

the test stimuli of 8 c/rev RSF or greater required the matching speed to be set above the

corresponding actual test speed, demonstrating overestimated perceived speed of higher RSF

test stimuli as found in Experiment 1. On the other hand, the matching speeds for the 2 c/rev

test stimulus all fell below their veridical speed lines, revealing an underestimation of

perceived speed for the lower RSF stimulus.

All the PSE curves fell within an area between the constant-TF and veridical test speed

lines, and tended toward horizontal as the RSF of the test stimuli increased. These data reveal

8

i-Perception

1

0

.5

.0

.5

.0

S1

S2

S3

const. const.

speed TF

results

0

.50 rev/s

.33 rev/s

.17 rev/s

0

5

10

15

20

0

5

10

15

20

0

5

10

15

20

Radial Spatial Frequency (c/rev)

Figure 4. Results of Experiment 2 for all three participants in linear scales. PSE speeds are plotted as

a function of the test RSF for each test speed. Error bars show 95% confidence intervals. The larger data

symbols at 4 c/rev denote the matching stimulus itself where its own PSEs were not measured. Pale solid

horizontal lines depict the physical speeds of the three test stimuli, and the pale dashed lines depict the

physical speeds that give constant TFs (i.e., hypothetical lines of matched speeds if the perceived speeds

of test stimuli were determined solely by the local TF characteristics.).

that the participants made a compromise between the actual speed and the TF of the moving

stimuli in making their speed judgments on the revolving stimuli. The response functions are

also very similar in trend across the three tested speed levels for all tested RSFs, with PSE

values increasing as the RSF and the test speed increase. To compare the results across test

speeds, each participant’s PSE data are normalized with the test speeds (i.e., divided by

corresponding test speed) and replotted in a log-log scale as presented in Figure 5(a). Note

that this normalized plot shows quadratic trends for all three test speeds; log-quadratic

2

functions were ﬁtted well to the averaged data across participants (r > .99). The three

curves nearly superimposed on each other except for the one obtained at the lowest test

speed (0.17 rev/s), where PSEs for the lowest and highest RSFs were much lower than

those for the faster test speeds. It is also noticed from the other two ﬁtted curves that

participants’ overestimation on perceived speeds for the higher RSF test stimuli started to

level oﬀ at 8 c/rev. There are only subtle diﬀerences in speed overestimation among the

stimuli of 8 to 16 c/rev, conﬁrming our earlier ﬁnding in Experiment 1. We also noticed

that the results from the three participants were quantitatively consistent except for data

points at either end of RSFs examined.

Furthermore, from Figure 5(a), we see that perceived speed on the 2 c/rev stimulus lies

much closer to the oblique TF line than the horizontal line, a characteristic that is opposite

for the higher RSF stimuli. This means that speed perception is more heavily weighted by TF

at low RSFs but more by the actual stimulus speed at high RSFs. To quantify such changes in

weighing on speed perception by the TF characteristics of a revolving stimulus, we evaluated

the contribution of TF by the following equation that can account for the matched speed as a

weighted sum of the constant-TF speed and the stimulus’ actual angular speed:

m ¼ b ꢂ STF þ ð1 ꢃ bÞS

Ashida et al.

9

(

a)

(b)

1

.8

.6

.4

.2

0

2

.0

0.17 rev/s

y=-0.42 log(x)+1.24

1

0.33 rev/s

y=-0.31 log(x)+0.99

0.50 rev/s

const. TF

y=-0.24 log(x)+0.79

const. speed

0.50 rps

S1

S2

S3

0.33 rps

0.17 rps

0

.2

0

1

10

1

10

Radial Spatial Frequency (c/rev)

Figure 5. (a) The results of Experiment 2 normalized with the corresponding test speed in a log-log scale,

with different symbols representing results of each participant (adapted from Figure 4). The large black square

denotes the matching speed, which corresponds to the larger symbols in Figure 4. Solid curves show fitted

2

double-log quadratic functions to the averaged data across participants for each test speed (r > 0.99 for all).

The 4 c/rev stimulus was used as the matching stimulus, and therefore no PSE estimate was made. The gray

lines show equal speeds (solid) and equal-TFs (dashed). (b) Estimated TF bias for each test speed. Colored

2

lines show fitted linear functions (r > 0.98 for all) for TF weighting (b). Dotted lines represent the weights on

actual speed (1 ꢃ b).

where m is the matched speed for a revolving stimulus, b is the TF-bias weighing factor, S_T_Fis

the constant-TF speed at each spatial frequency, and S is the veridical stimulus speed. TF

would have no eﬀect with b ¼ 0 and the strongest eﬀect with b ¼ 1. Figure 5(b) shows b (solid

lines) and 1 ꢃ b (dotted lines) as a function of the RSF, which were obtained by solving this

equation for the averaged results in Figure 5(a) as m for each test speed. This plot reveals that

the TF weighting on speed perception falls almost linearly in a log scale as the RSF of a

stimulus increases. Even though the speed overestimation eﬀect increases for stimuli of higher

RSFs, the eﬀect of TF on speed perception is actually stronger for stimuli of lower RSFs.

This plot also indicates that the eﬀect of TF is larger for a slower speed at the lowest RSF

tested; the reason is not clear, but it could be an artefact of showing very thick stripes in

narrow rings.

The curves may be subject to change by the choice of the matching stimulus. An auxiliary

experiment performed by S1, however, suggested that such a nonlinear eﬀect, if any, might

not be substantial at least for our stimulus set; the speed of the 8 c/rev stimulus was matched

to that of the 16 c/rev stimulus by the same procedure, and the speed of 16 c/rev stimulus was

overestimated by 9.2% with the 95% conﬁdence interval from 5.9% to 12.5%. The data from

S1 in Figure 4 increased by 11.5% from 8 c/rev to 16 c/rev, which falls within this conﬁdence

interval.

In short, the spinner eﬀect is observed with radial sinusoidal stimuli. Perceived speed

of a test stimulus does increase with the RSF of the stimulus, weighted concomitantly

by an increasing TF. But the magnitude of the spinner eﬀect reaches a plateau relatively

quickly at higher RSFs, indicating that the bias toward TF is actually smaller for

higher RSFs. Therefore, possible diﬀerence among 8 to 16 c/rev stimuli could be

1

0

i-Perception

easily buried in noise in Experiment 1 with naı

¨

speeds.

ve participants and with coarser grain of test

Experiment 3

If the spinner illusion reﬂects a genuine SF dependent speed overestimation, it may not be

speciﬁc to rotational motion. We can actually experience an analogous speed illusion in the

demonstration movie with translating linear gratings (Appendix Movie 3), as also predicted

from previous reports (Chen et al., 1998; Diener et al., 1976). In Experiment 3, we therefore

assessed if analogous characteristics of the spinner illusion would be found in drifting vertical

sine wave gratings. The SFs of the 1D gratings used here were roughly matched to the SF of

the radial stimuli in Experiment 2.

Methods

Participants. The same three participants as in Experiment 2 were tested.

Apparatus and stimuli. The apparatus was the same as in Experiment 2, also controlled with

PsychoPy 1.82 (Peirce, 2007). The layout of the paired matching-test stimulus was similar to

that used in Experiment 2. Here, two 1D vertical sinusoidal grating of diﬀerent SFs, always

ꢁ

drifting in the same direction, were presented inside two separate, 11 diameter circular

windows on both sides of the central ﬁxation point. Their maximum luminance contrast

was 50%, presented to participants using the same trapezoidal time envelope as before.

The SFs were approximately matched to those of the radial gratings as follows;

luminances were modulated horizontally in the frequencies of 2, 4, 8, 12, and 16 cycles per

the circumference of the middle point of the ring in Experiment 2 (i.e., along the circle of

ꢁ

8

.25 diameter), resulting in 0.08, 0.15, 0.31, 0.46, and 0.62 c/deg, respectively. The SF of the

matching stimulus was 0.15 c/deg, and that of the test stimulus was one of the other four SFs.

A single standard speed of 8.64 deg/s (corresponding to 0.33 rev/s ¼ 2.09 rad/s of the radial

grating at the middle radius of the ring) was tested.

Procedure. The task and the design was the same as in Experiment 2; each test SF was tested

separately in a double-random-staircase run of 28 trials for each direction, and each run was

repeated three times in a random order.

Results

Probit analysis (Finney, 1971; Johnson et al., 2013) was used to estimate the matched speed at

9

5% conﬁdence intervals. Figure 6(a) shows the matched speed as a function of the test SF.

Again, the PSE values fell between the area bounded by speed with constant TF and the

veridical base speed of the test stimuli as shown in Figure 5(a), indicating overestimations and

underestimations of perceived speed in higher and lower test SFs, respectively, when

compared with the 0.15 c/deg matching stimulus.

Corresponding data from Experiment 2 were converted in the way as described in the

Apparatus and Stimuli section and were plotted together in Figure 6(a). The pattern of results

2

is very similar to that of the radial stimuli, as the ﬁtted log-quadratic function (r > .99) is

comparable to the adapted curve from Figure 5(a). While the overestimation was somewhat

larger for the linear gratings, this diﬀerence is surprisingly small, given many possible

confounds such as imperfect matching of SFs, diﬀerent stimulus windows, or larger SF

Ashida et al.

11

(

a)

(b)

1

.8

.6

.4

.2

0

2

1

0

linear

y=-0.25 log(x)+0.086

radial

y=-0.33 log(x)-0.468

S1

S2

S3

const. TF

const. speed

average linear

average radial

2

0

.05

0.1

0.2

0.4

0.05

0.1

0.2

0.4

Spatial Frequency (c/deg)

Figure 6. Results of Experiment 3. (a) Matched speed of the 0.15 c/deg stimulus is plotted as a function of

the test spatial frequency. Symbols show individual results with 95% confidence intervals. The larger square

shows the point of matching SF (not measured). The thick black curve denotes the fitted log-quadratic

function to the averaged data. The fitted curve for the 4 c/rev condition in Figure 5(a) was adapted and

superimposed as a dotted curve. (b) Estimated TF weighting, plotted as a function of spatial frequency.

2

A linear function was fitted to the data (r > .99). Corresponding data for the radial stimuli in Experiment 2

(

standard speed of 0.33 rev/s) were adapted from Figure 5(b) and superimposed (gray squares and gray lines).

The dashed lines represent bias for speed (1 ꢃ b).

artefacts at the stimulus edges of linear gratings, which are inevitable for the diﬀerent kinds of

stimuli. This result suggests that the spinner illusion is a consequence of general speed

computation from spatiotemporal frequencies, rather than manifestation of some

idiosyncratic rotation-speciﬁc eﬀects.

Figure 6(b) depicts the TF weighting on perceived speeds of drifting gratings in the same

way as in Figure 5(b) but as a function of linear SF. The data for the corresponding condition

in Experiment 2 with radial gratings (standard speed of 0.33 rev/s) are adapted from

Figure 5(b) and are plotted along in this ﬁgure. The decline of TF weighting is very

similar for the two types of stimuli. The small diﬀerence in the slopes may be due to

several factors as noted earlier.

We should also note that the shape of the curve is similar to that of speed matching by

Jogan and Stocker (2015; their Figure 5(b), test stimuli of A–D), although they did not

discuss this ‘‘single-channel’’ response in detail, because their focus was on integration of

such responses in compound SF stimuli.

General Discussion

The spinner illusion demonstrates that perceived speed is aﬀected by the number of dots even

when they move at a constant speed. We have conﬁrmed that this eﬀect generalizes to radial

and linear forms of sinusoidal gratings. The spinner illusion therefore is considered to reﬂect

a general speed overestimation for high SFs that has been reported in the literature. The eﬀect

of motion blur, if any, is not a necessary condition.

1

2

i-Perception

The spinner illusion as a TF bias in spatiotemporal integration

As the spinner illusion occurs in a very similar way for radial and linear gratings, the eﬀect is

consistent with a number of studies that showed higher perceived speed for higher SFs with

linear gratings (Brooks, Morris, & Thompson, 2011; Campbell & Maﬀei, 1981; Chen et al.,

1

998; Diener et al., 1976; McKee & Silverman, 1986). The asymptotic curve in our Figure 6(a)

parallels with Figure 6 in McKee & Silverman (1986) and Figure 3 of Brooks et al. (2011).

Smith and Edgar showed opposite results of speed underestimation for high SFs, but as

they discussed (1990, p. 1473), their results are not necessarily in conﬂict because they used

higher range of SFs (0.5–2 c/deg) than ours (0.08–0.68 c/deg) and Diener et al.’s (0.01–

0.07 c/deg); the overall SF tuning might be inverted U-shaped as observed in Campbell

and Maﬀei (1981).

Taken together, these results support a bias toward TF in the spinner illusion, as Anstis

and Ho (2014) proposed. TF should increase along with increasing SF in order to keep the

speed constant, and this higher TF could bias speed coding. Although we can make speed and

¨

TF judgments independently (Smith & Edgar, 1990, p. 1469), naıve judgments may be

erroneously contaminated by the TF. This, however, does not seem to explain our

compelling perception of speed diﬀerence in the spinner illusion demonstrations. Also, the

¨

results were consistent across naıve and trained participants in our experiments. The TF bias

therefore could be an innate property in speed perception.

It is conceived that the visual system initially takes separate measures in space and time

(

i.e., SF and TF), and then integrates these measures into the metric of speed at the level

of V1 complex cells to the area MT/V5 both in macaques (Priebe, Cassanello, &

Lisberger, 2003; Priebe, Lisberger, & Movshon, 2006) and also in humans (Lingnau,

Ashida, Wall, & Smith, 2009). Integration across space and time is then required for

perceiving global pattern of linear or circular motion (e.g., Morrone, Burr, & Vaina,

1

995). While the TF bias may arise at any of these stages, the results of similar spinner

eﬀects on circular and translating motions might suggest that it occurs before the stage of

global integration.

The exact mechanism of the TF bias in speed perception is yet to be investigated, but our

results of stronger TF bias for lower SFs might be explained by hypothetical receptive ﬁelds

that are not large enough for the low-SF stimuli. The nominal SF of our stimuli extends

down to 0.08 c/deg, that is, 12.5 deg/c. This is larger than the human population receptive

ﬁeld sizes, measured by using fMRI, in most visual areas including putative human MT and

ꢁ

MST up to the eccentricity of 10 in the periphery (Amano, Wandell, & Dumoulin, 2009).

Appendix Movie 4 shows a hypothetical receptive ﬁeld that covers less than one cycle of a

low-SF drifting grating, which is therefore seen as mostly ﬂickering with very little motion

signal. On the other hand, the same receptive ﬁeld can register several moving bars of a high-

SF grating, so the direction of motion is now unambiguous—and also looks fast. This simple

model explains both the basic spinner eﬀect, that ﬁne bars appear to move faster than coarse

bars, and also the fact that speed judgments of coarse moving bars are more strongly

weighted by TF than by actual velocity.

Note that the illusion could be understood in accordance with the gradient-based models

of motion detection (e.g., Anstis, 1967, 1990; Johnston, McOwan, & Buxton, 1992; Marr &

Ullman, 1981). In the case of sinusoidal modulation, because d/dt[sin(ft)] ¼ fcos(ft),

maximum temporal gradient is proportional to TF. Speed perception could be understood

as biased toward temporal gradient instead of TF.

Ashida et al.

13

Ecological Interpretations

For periodic grating patterns, SF (or RSF) is a reciprocal of the size of each bar. The spinner

eﬀect therefore parallels the classic report of Brown (1931) that ‘‘other things being equal

larger ﬁgures are phenomenally slower’’ (p. 222). It is, however, not fully understood why

speed perception depends on size. A possible account could refer to speed constancy across

distances; as an object comes closer, the retinal size and speed increase when the physical

speed is constant. While Brown (1931) argued that constancy of velocity (i.e., speed) is not

fully deducible from size constancy, Rock, Hill, and Fineman (1968) concluded that size

constancy and speed constancy are indeed related, from the results of experiments without

visible frames of references.

The rotating spinner illusion is not readily explained by speed constancy because

RSF does not change across distances. On the other hand, the two-dimensional SF

components along the x-y coordinates do change with distance for both linear or radial

gratings, while TF remains constant. TF is therefore a more invariant measure than SF

across distances, which may be one reason for more dependence on TF in speed

computations.

Other possible explanations might refer to the statistical tendency that lower SFs are likely

more stable than higher SFs in the scene. This is related to the hypothesis of Bayesian prior

for slow motion (Jogan & Stocker, 2015; Vintch & Gardner, 2014; Weiss, Simoncelli, &

Adelson, 2002), reﬂecting the fact that the world is mostly stable while smaller objects can

move around, although this might not always hold (Hammett, Champion, Thompson,

Morland, 2007).

Limitations

There remains a question: Why does the speed appear to get faster steadily whenever the

number of discs increase in the original spinner illusion, while the perceived speed saturated

rapidly in our experiments? A potential cause for the discrepancy might be the high-SF

harmonic components in the dot stimuli, as Brooks et al. (2011) showed that a complex

grating of 1f þ 2f SF components yielded less asymptotic curves of speed overestimation

for higher SFs than a simple grating. Smith and Edgar (1991) also revealed nonlinear ways

of combining element speeds in various complex gratings, but how this is related to the

spinner illusion remains open for further investigation. Another factor could be the retinal

blur due to sharp edges that might add to the eﬀect, as Ho and Anstis (2013) originally

postulated.

The physical contrast was always held constant at 50% in our experiments, and there

could have been a confound of perceived contrast across SFs, since perceived speed depends

on contrast (Thompson, 1982). We do not, however, consider that this eﬀect is crucial in our

case, because the eﬀect of contrast is less clear for high-contrast stimuli. While Stone

and Thompson (1992) showed that the eﬀect does not saturate up to 70% contrast, Smith

and Edgar (1990) informally noted that the perceived speed was independent of contrast

above 10%.

Another remaining question is the generality of the spinner eﬀect for second-order stimuli

that cannot be computed from spatial and temporal frequencies, which is currently under

investigation by one of the authors (A. H.).

1

4

i-Perception

Author Note

Preliminary results were presented at ECVP 2014 by H. A. and A. K.

Declaration of Conflicting Interests

The author(s) declared no potential conﬂicts of interest with respect to the research, authorship, and/or

publication of this article.

Funding

The author(s) disclosed receipt of the following ﬁnancial support for the research, authorship, and/or

publication of this article: This study was supported by JSPS Grant-in-Aid for Scientiﬁc Research

(

KAKENHI) #15H01984 for AK and HA, and #26285165 for HA. SA was supported by a grant

from the UCSD Department of Psychology. AH was supported by a professional development grant

from the Ambrose University.

Supplemental Material

The online appendix movies are available at http://journals.sagepub.com/doi/suppl/10.1177/

2

041669517707972.

Note

1

. We use the unit of c/rev for RSF because it is more intuitive and directly comparable to the number

of dots in the original spinner illusion. We also use the unit of rev/s for speed, for consistency.

Corresponding values in SI units (c/rad and rad/s, respectively) are presented in parentheses in the

methods sections.

References

Amano, K., Wandell, B. A., & Dumoulin, S. O. (2009). Visual ﬁeld maps, population receptive ﬁeld

sizes, and visual ﬁeld coverage in the human MTþ complex. Journal of Neurophysiology, 102,

2704–2718. doi:10.1152/jn.00102.2009

Anstis, S. (1990). Motion aftereﬀects from a motionless stimulus. Perception, 19, 301–306.

Anstis, S. (1967). Visual adaptation to gradual change of intensity. Science, 155, 710–712.

Anstis, S., & Ho, A. (2014). Apparent speed of a rotating disk varies with texture density. Journal of

Vision, 14, 1333. doi:10.1167/14.10.1333

Apthorp, D., Schwarzkopf, D. S., Kaul, C., Bahrami, B., Alais, D., & Rees, G. (2013). Direct evidence

for encoding of motion streaks in human visual cortex. Proceedings of the Royal Society of London.

B: Biological Sciences, 280, 20122339. doi:10.1098/rspb.2012.2339

Brainard, D. H. (1997). The Psychophysics Toolbox. Spatial Vision, 10, 433–436.

Brooks, K. R., Morris, T., & Thompson, P. (2011). Contrast and stimulus complexity moderate the

relationship between spatial frequency and perceived speed: Implications for MT models of speed

perception. Journal of Vision, 11, 19. doi:10.1167/11.14.19

Brown, J. F. (1931). The visual perception of velocity. Psychologische Forschung, 14, 199–232.

doi:10.1007/BF00403873

Campbell, F. W., & Maﬀei, L. (1981). The inﬂuence of spatial frequency and contrast on the perception

of moving patterns. Vision Research, 21, 713–721.

Campbell, F. W., & Robson, J. G. (1968). Application of Fourier analysis to the visibility of gratings.

The Journal of Physiology, 197, 551–566.

Cavanagh, P., Tyler, C. W., & Favreau, O. E. (1984). Perceived velocity of moving chromatic gratings.

Journal of the Optical Society of America A, 1, 893–899.

Ashida et al.

15

Chen, Y., Bedell, H. E., & Frishman, L. J. (1998). The precision of velocity discrimination across spatial

frequency. Percept Psychophys, 60, 1329–1336.

Diener, H. C., Wist, E. R., Dichgans, J., & Brandt, T. (1976). The spatial frequency eﬀect on perceived

velocity. Vision Research, 16, 169–176.

Finney, D. J. (1971). Probit analysis 3rd ed. Cambridge, England: Cambridge University Press.

Geisler, W. S. (1999). Motion streaks provide a spatial code for motion direction. Nature, 400, 65–69.

doi:10.1038/21886

Hammett, S. T., Champion, R. A., Thompson, P. G., & Morland, A. B. (2007). Perceptual distortions

of speed at low luminance: Evidence inconsistent with a Bayesian account of speed encoding. Vision

Research, 47, 564–568. doi:10.1016/j.visres.2006.08.013

Ho, A., & Anstis, S. (2013). The Coyote Illusion: Motion blur increases apparent speed . Paper presented

at the Best illusion of the year contest 2013. Retrieved from http://illusionoftheyear.com/2013/05/

the-coyote-illusion-motion-blur-increases-apparent-speed/

Jogan, M., & Stocker, A. A. (2015). Signal integration in human visual speed perception. Journal of

Neuroscience, 35, 9381–9390. doi:10.1523/JNEUROSCI.4801-14.2015

Johnson, R. M., Dahlgren, L., Siegfried, B. D., & Ellis, M. D. (2013). Acaricide, fungicide and drug

interactions in honey bees (Apis mellifera). PLoS One, 8, e54092. doi:10.1371/journal.pone.0054092

Johnston, A., McOwan, P. W., & Buxton, H. (1992). A computational model of the analysis of some

ﬁrst-order and second-order motion patterns by simple and complex cells. Proceedings of the Royal

Society of London. B: Biological Sciences, 250, 297–306. doi:10.1098/rspb.1992.0162

Lingnau, A., Ashida, H., Wall, M. B., & Smith, A. T. (2009). Speed encoding in human visual cortex

revealed by fMRI adaptation. Journal of Vision, 9, 3.1–3.14. doi:10.1167/9.13.3

Marr, D., & Ullman, S. (1981). Directional selectivity and its use in early visual processing. Proceedings

of the Royal Society of London. B: Biological Sciences, 211, 151–180.

McKee, S. P., Silverman, G. H., & Nakayama, K. (1986). Precise velocity discrimination despite

random variations in temporal frequency and contrast. Vision Research, 26, 609–619.

Morrone, M. C., Burr, D. C., & Vaina, L. M. (1995). Two stages of visual processing for radial and

circular motion. Nature, 376, 507–509. doi:10.1038/376507a0

Nishida, S. (2011). Advancement of motion psychophysics: Review 2001–2010. Journal of Vision, 11,

11. doi:10.1167/11.5.11

Palmer, S. (1999). Vision Science: From Photons to Phenomenology. Cambridge, MA: MIT Press.

Peirce, J. W. (2007). PsychoPy—Psychophysics software in Python. Journal of Neuroscience Methods,

162, 8–13. doi:10.1016/j.jneumeth.2006.11.017

Pelli, D. G. (1997). The VideoToolbox software for visual psychophysics: transforming numbers into

movies. Spatial Vision, 10, 437–442.

Priebe, N. J., Cassanello, C. R., & Lisberger, S. G. (2003). The neural representation of speed in

macaque area MT/V5. Journal of Neuroscience, 23, 5650–5661.

Priebe, N. J., Lisberger, S. G., & Movshon, J. A. (2006). Tuning for spatiotemporal frequency and

speed in directionally selective neurons of macaque striate cortex. Journal of Neuroscience, 26,

2

941–2950. doi:10.1523/JNEUROSCI.3936-05.2006

Rock, I., Hill, A. L., & Fineman, M. (1968). Speed constancy as a function of size constancy. Perception

Psychophysics, 4, 37–40.

&

Sachs, M. B., Nachmias, J., & Robson, J. G. (1971). Spatial-frequency channels in human vision.

Journal of the Optical Society of America, 61, 1176–1186.

Smith, A. T., & Edgar, G. K. (1990). The inﬂuence of spatial frequency on perceived temporal

frequency and perceived speed. Vision Research, 30, 1467–1474.

Smith, A. T., & Edgar, G. K. (1991). Perceived speed and direction of complex gratings and plaids.

Journal of the Optical Society of America A, 8, 1161–1171.

Stone, L. S., & Thompson, P. (1992). Human speed perception is contrast dependent. Vision Research,

32, 1535–1549.

Thompson, P., Brooks, K., & Hammett, S. T. (2006). Speed can go up as well as down at low contrast:

implications for models of motion perception. Vision Research, 46, 782–786. doi:10.1016/

j.visres.2005.08.005

1

6

i-Perception

Thompson, P. G. (1982). Perceived rate of movement depends on contrast. Vision Research, 22,

77–380.

3

Vintch, B., & Gardner, J. L. (2014). Cortical correlates of human motion perception biases. Journal of

Neuroscience, 34, 2592–2604. doi:10.1523/JNEUROSCI.2809-13.2014

Weiss, Y., Simoncelli, E. P., & Adelson, E. H. (2002). Motion illusions as optimal percepts. Nature

Neuroscience, 5, 598–604. doi:10.1038/nn858

Author Biographies

Hiroshi Ashida received his PhD in psychology from the Kyoto

University, Japan. He has been working at Kyoto University

since 2001 and became a professor in 2015. His main research

interest is in visual processing of motion and visual illusion in

general, studied with psychophysics and MRI.

Alan Ho was born in Hong Kong. He did his postdoctoral work

with Stuart Anstis at UCSD after obtaining his PhD in

psychology from the Florida State University. His primary

research interest is in visual motion perception. The ‘‘Coyote

Illusion’’ that Alan and Stuart reported in 2013 was selected to

be a Top 10 Illusion of the Year. He is currently an associate

professor of psychology at the Ambrose University, Calgary,

Canada.

Akiyoshi Kitaoka is a professor of psychology in Ritsumeikan

University, Kyoto/Osaka, Japan. He studies visual illusions and

produces a variety of illusion works and exhibits them in his

webpages or SNSs.

Stuart Anstis was born in England and was a scholar at

Winchester and Cambridge. Since his PhD at Cambridge with

Richard Gregory, he has taught at the Universities of Bristol

(

UK), York (Toronto), and California, San Diego (UCSD). He

has published about 170 peer-reviewed papers. He is a visiting

fellow at Pembroke College, Oxford, and a Humboldt fellow

and received the Kurt-Koﬀka Medal for outstanding

contributions to Vision Science in 2013.