Experiment

E xperim ent 1 used radially sym m etric d ifference o f G ausssian (D oG ) dots becau se th ey o ffe r a stim u lu s o f re stric te d sp a tia l fre q u e n c y co n ten t. M anipulating their size m anipulated the spectral content o f the stim uli. In that experim ent it was found that sensitivity to radial patterns o f global m otion was highest when the dots were constrained to rem ain o f fixed size (and hence spatial frequency), contrary to the naturally occurring increase in retinal size o f a genuine object approaching in depth. Previous w ork (Regan & H am stra, 1993; Regan & V incent, 1995; V incent & Regan, 1997; Beverley & Regan, 1983), has shown that veridical elem ent grow th is not necessary to su p p o rt accurate estim ates o f tim e to contact, and when available play a m inor role except where they are in gross conflict w ith other m otion-in-depth cues (Harris & G iachritsis, 2000). Early studies have characterised the effect o f elem ent grow th as a m atter o f size, rather than o f changing spatial frequency content.

The results o f E xperim ent 1 do not reveal w hether the increased sensitivity found in the zero growth rate condition was due to shared elem ent size, or shared spatial frequency content. A t first sight the issue m ay seem unim portant, as these two characteristics norm ally co-vary. How ever, for this experim ent a stim ulus has been designed which allow s the m anipulation o f dot size w hile m aintaining spatial frequency content constant (see M ethods section). W ith this new stim ulus Experim ent 2 m easured sensitivity to detect radial optic flow across a range o f speeds and elem ent sizes, as before, using the m otion coherence m ethod to establish the sensitivity o f subjects.

Lum inance plots in two spatial dimensions (x and y) showing the effect o f tlltering a binary dot. R e fe r to Panel A. C o n v o l v in g a dot (left) with a high fre q u en c y filte r (centre) results in an is om etric dot o f defined spatial fre quency content. T his will be referred to as a ‘circular g r a ti n g ’. Panels B and C sh ow how the same filter applied to different dots results in spectrally similar dots, differing in size.

4.4.1 Methods

A s fo r E x p e rim e n t 1, w ith th e d e sig n o f e a c h d o t b e in g th e o n ly d iffe re n c e . T o p r o d u c e d iffe rin g d o t s iz e s w ith c o n s ta n t s p a tia l c o n te n t a tw o -d im e n s io n a l b a n d p a s s filte r (o f G a u ssia n p ro file in th e sp atial fre q u e n c y d o m a in ) w as a p p lie d to a c o n v e n tio n a l c irc u la r d o t, i.e. o n e w h o se lu m in a n c e p ro file c o n ta in s o n ly

two grey levels representing black and white (see figure 4.5, panel A, left). The effect o f applying a filter (figure 4.5, panel A, centre) was to create a circularly sym m etric circular grating o f defined spatial content (figure 4.5, panel A, right). (NB consequently the spectral content o f these dots was different to those used in the first experim ent). By choosing different sizes o f p re-filtered dot the diam eter o f the resulting circular grating was m anipulated, independently o f spatial frequency. The G aussian-shaped filter (in frequency space) is defined by the follow ing form ula:

1

y = ^ =

—

2k ^ g

where,

a = one standard deviation o f the filter 0.084 degrees (at 57cm ) r= distance from the centre o f the circular filter

fpk= the peak frequency o f the filter, 0.29 degrees (at 57cm)

A pplying this filter to each o f a range o f dots resulted in isom etric bandpass circular gratings o f average centre frequency 1.44 cycles per degree (at the view ing distance o f 57cm ) and average bandw idth o f 1.8 octaves. Figure 4.6 show s the pow er spectrum o f a sam ple o f dot sizes after filtering. It can be seen that the spectra are not identical for all filtered dots, how ever the ‘fo rm a n ts’ (peaks and troughs) are a consequence o f the discrete Fourier transform w hich can only retu rn frequencies o f in teg er m ultiples. T hese do not reflec t the resp o n ses o f frequency selective cells found in m am m alian vision that are know n to integrate over com parable ranges o f frequencies (e.g. 1-2.5 octaves,

G e o rg e s o n , 1980; W ils o n , M c F a rla n e , & P h ilip s , 1983), a n d w h ic h w o u ld c o n se q u e n tly re sp o n d sim ila rly to e a c h o f the a m p litu d e p ro file s sh o w n in fig u re 4 .6 . C e n tre fre q u e n c y an d b a n d w id th w e re e s tim a te d fo r e a c h d o t siz e a n d th e fig u re s q u o te d ab o v e re p re se n t th e a v e ra g e fo r th e set. T h e ran g e o f siz e s o f d o ts (p re -filte rin g ) w as: 0 .0 8 4 -0 .2 9 d e g re e s.

DoG frequ en cy spectrum

2 5 2 0 0) ■D 3 a E 0 2 4 6 8 1 0 --- 0.08 degrees ---0.12 degrees ---0.16 degrees --- 0.20 degrees --- 0.29 degrees fre q u e n c y (c y c le s / d e g re e )

Fig ure 4.6 F requency spectra o f a sam ple o f the filtered dots o f E xperim e nt 2. Dots o f d iffe ren t sizes were co n v o l v e d with the sam e filter, resu ltin g in isotropic e lem e n ts diffe ring in size, yet sharin g a co m m o n spatial freq u en cy com position. Sizes o f dots prior to filtering are listed in the insert.

4.4.2 Results

F ig u re 4 .7 s h o w s m o tio n c o h e re n c e th re s h o ld as a fu n c tio n o f e le m e n t g ro w th ra te in m u ltip le s o f th e v e rid ic a l rate. T h re e c u rv e s a re sh o w n , o n e fo r e a c h sp e e d c o n d itio n . A s b e fo re , b lu e d ia m o n d s re p re se n t a m ean sp eed o f 1 d e g re e /s, p in k sq u a re s re p re se n t 2 d e g re e s /s , and red tria n g le s re p re se n t 4 d e g re e s/s. E a c h d a ta p o in t is th e m ean th re s h o ld o f th re e o b s e rv e rs , an d th e e rro r b a rs are o n e

standard error o f the m ean. The graph clearly show s an effect o f speed, with m otion coherence thresholds elevated in the 4 degrees/s condition. This was confirm ed to be a significant m ain effect o f speed w ith a two w ay, repeated m easures A N O V A (F(2 4)=12.36, p<0.05). The analysis o f variance revealed no reliab le e ffe c t o f elem en t grow th (F(3 5)=1.78, p > 0.05), and no sig n ifican t interaction betw een the two factors (F (6 j2)^0.354, p>0.05). A Bonferroni/D unn post hoc test show ed that the difference was betw een the slow (1 degree/s) and fast (4 degrees/s) conditions (p<0.01).

There are tw o points to note from these results. Firstly, the sensitivity advantage p rev io u sly obtained in the zero grow th rate condition has been abolished. H ow ever, this is not to say that sensitivity in this condition has declined, rather that thresholds rem ain low under other conditions. This is m ost pronounced in the slow speed (1 degree/sec) curve, w here thresholds o f around 17% are c o m parable w ith optim um thresholds found in E x p erim ent 1, zero grow th condition. T he second point to stress is the p ronounced effect o f speed on thresholds. A clear drop in sensitivity accom panies increasing speeds. T he rela tiv e a b sen ce o f this e ffe c t in the prev io u s e x p e rim e n t in d icates th at controlling spatial content has produced this phenom enon. This point will be elaborated in the Discussion.

0 .5 0 ;ü o 0 . 0 5 0 . 0 0 0 . 4 5 0 . 4 0 0 . 3 5 y 0 . 3 0 i t 0 . 2 5 " 0 . 2 0 " 0 . 1 5 0 . 1 0 1 2 e l e m e n t g r o w t h 3 4 v e r i d i c a l r a t e ) 1 d e g/s 2 d e g/s 4 d e g/s

Figure 4.7 Coherence thresholds for detecting radial motion. Three curves are shown, one for each speed condition explored. Thresholds on the y-axis are plotted as a function of the elem ent growth rate, on the x-axis. Each data point represents the mean threshold of three observers. Error bars are one standard error of the mean.

4.5 D iscussion

E x p e rim e n t 1 e x a m in e d th e e ffe c t o f e le m e n t g ro w th on th e a b ility to d e te c t o p tic flo w . T h e rate o f c h a n g e o f the siz e o f d o ts in a ra d ia lly e x p a n d in g R D K p a tte rn w a s m a n ip u la te d , in d e p e n d e n tly o f th e ra te at w h ic h d o ts d iv e rg e d . S e n s itiv ity w a s fo u n d to b e g r e a te s t w h e n c o n s e c u tiv e s a m p le s o f d o t s ’ tra je c to rie s w e re id e n tic a l in siz e . H o w e v e r, as s iz e a n d sp e c tra l c o n te n t c o ­ v a rie d it w a s n o t p o s s ib le to tell w h e th e r size o r sp a tia l fre q u e n c y c o n te n t w as re s p o n s ib le fo r the e n h a n c e d p e rfo rm a n c e . If sp atial fre q u e n c y w as th e c a u se o f th e e ffe c t, this co u ld be a ttrib u te d to th e c h a ra c te ris tic s o f lo w -le v e l local m o tio n d e te c to rs . If size w ere the cru c ia l fa c to r th is w o u ld lo c a te the c a u se o f the e ffe c t at a h ig h e r le v e l, p e rh a p s a m e c h a n ism a d d re s s in g th e c o rre s p o n d e n c e p ro b le m , g lo b a lly . T o te a s e siz e a n d sp e c tra l c o n te n t a p a rt. E x p e rim e n t 2 p re s e n te d a s im ila r ra d ia lly e x p a n d in g fie ld o f d o ts w ith the c ru c ia l d iffe re n c e th a t d o t size c o u ld be m a n ip u la te d w ith o u t d ra s tic a lly a lte rin g its sp atial fre q u e n c y s ig n a tu re .

Sensitivity to detect expansion was found not to vary with the rate o f size change o f dot elem ents, im plying that the credit for enhanced detection in Experim ent 1 belongs to the presence o f com m on spatial frequencies, rather than com m on siz e . M uch p re v io u s w ork on the p e rc e p tio n o f m o tio n -in -d e p th has characterised the stim uli used in term s o f size, and size change, rather than in term s o f spectral content. This has been true in recent studies using random dot stim uli (H arris & G iachritsis, 2000), or earlier w ork using geom etric figures such as textured squares (e.g. Regan & H am stra, 1993; Regan & V incent, 1995; V incent & Regan, 1997). The use o f the term ‘size’ may have obscured the role played by early m otion system s in the perform ance o f the tasks set. Size is, after all an ‘object lev e l’ property, and dependence on its change for the perception o f m otion-in-depth w ould require a parsing o f the scene into its discrete entities prior to analysis o f the type o f m otion present. R eferring to the ‘size’ o f stim uli conceals at least tw o other m eans by w hich an approaching object m ay be perceived as such. A loom ing square w ith a uniform surface contains relative m otion betw een its edges, analogous to the divergence am ong random dots seen in a radially expanding RD K . Indeed Freem an & H arris (1992) suggested a nam e for the psychological m echanism responsible for perceiving loom ing: the R elative M otion System . A nother candidate for registering loom ing, recently reported by Schraeter, Knill & Sim oncelli (2000) is that scale change alone can signal m otion-in-depth. These authors found that a loom ing percept could be induced w ithout any net m otion signals (in the conventional sense) being present in their display. T heir anim ation com prised several fram es o f independently generated w hite noise, each o f w hich w as passed through a low er frequency filter than the last. This resulted in a sequence o f fram es that w ere uncorrelated, b u t w hen show n sequentially presented a sm ooth transition along the spatial frequency spectrum from high frequencies to low, i.e. a progressive reduction in spatial scale. O bservers w ere able to m atch this sequence to an optic flow anim ation com prising radially expanding dots (of fixed size) im plying that the perception o f loom ing may in part be m ediated by a progressive reduction in the spatial scale o f the image. O bservers also experienced m otion after-effects to the

changing scale sequences, suggesting that they do indeed stim ulate m otion m echanism s. Schrater, K nill & Sim oncelli (2000) ensured that conventional local m otion detection m echanism s w ere not responsible for the perception o f e x p a n sio n by u sin g u n c o rre la ted fram es o f no ise. S till, th e ir resu lt is controversial follow ing a recent failure to replicate (Rogers & A nstis, 2002). In view o f this the results obtained in the experim ents reported here have been interpreted to reflect processing lim itations at the local level. This is in line with the conventional view that the properties o f local m otion detectors place a constraint on the capabilities o f global m otion detectors (e.g. Ledgew ay, 1996), and supports the h ierarch ical m otion p ro cessin g arch itectu re p ro posed by M aunsell & van Essen (1983) and Van Essen & M aunsell (1983).