General Discussion

M echanism s w hose ability to detect m otion is spatially restricted (i.e. 'local') w ere show n in Experim ent 1 to have bandw idths som ew hat narrow er than has previously been estim ated. E xperim ent 2 sought to estim ate bandw idths o f m echanism s integrating over larger regions o f space (i.e. 'globally') to confirm that the findings o f E xperim ent 1 did not inadvertently reflect the action o f global m echanism s. W hy doubt that the stim uli in the first experim ent excited only local m echanism s? The first and m ost obvious observation is that those stim uli (see figure 3.1) extended over large regions o f space, and so w ould certainly be candidates to be integrated into a global percept. In answ er to this criticism it is som etim es assum ed that this global integration does not take place at the very low levels o f contrast used. To detect the presence o f a stim ulus at

contrast threshold is presum ed to require, m inim ally, only one o f the m any dots available. Still, there are reasons to question this interpretation. Firstly, there is no way o f confirm ing or ensuring that one dot is being used to m ediate the task. Secondly, the point o f contrast threshold is an interpolated point betw een seeing all o f the stim ulus, and seeing none o f it. It m ay not be possible to interpret it as equivalent to seeing a single dot. For these reasons the possibility that stim uli at low contrast levels excite global m otion m echanism s m ust be en tertained. Perhaps the only way to avoid integration over m any local m otions is to use only one dot in the stim ulus. N evertheless, since the latte r ex p erim en t yielded substantially n arrow er bandw idths than the form er, tw o d ifferen t levels o f processing appear to have been tapped.

A ccepting that global m echanism bandw idths m ay be as narrow as 16 degrees (Experim ent 3), these results bear on the ‘basis se t’ theory o f com plex m otion processing. Som e authors (e.g. M orrone et al, 1999; Burr, B adcock and Ross, 2001) have cited evidence for ‘cardinal detecto rs’, that is those tuned for the orthogonal directional patterns o f rotation and radial m otion. If these and only these detectors exist it w ould be possible to code for interm ediate spiral m otions via a com bination o f this basis set, provided that basis com ponents w ere broad in their tuning. This concept is therefore incom patible w ith these results as such n arro w ly tu n ed m ec h a n ism s w ould n o t p ro v id e s u ffic ie n t c o v e ra g e o f interm ediate d irections to be sim ultaneously stim u lated by a spiral fallin g m idw ay betw een. C onsequently this w ork represents further support for those favouring the existence o f sensors coding interm ediate directions directly (e.g. Snowden & M ilne, 1996; M eese & Anderson, 2002), a position supported by the known physiology (e.g. Duffy & W urtz, 1991; G raziano, A ndersen & Snow den, 1994), and reflected in the em ergent properties o f M ST sim ulation (Beardsley & Vaina, 1998).

It has to be acknow ledged that the m odel used to calculate bandw idths is critical to the values suggested. W hile the fram ew ork em ployed has the b en efit o f

sim plicity, other, m ore realistic m odels exist. For exam ple B eardsley & V aina (2001) recently sim ulated a b io lo g ically inspired architecture th at could be responsible for m ediating discrim ination perform ance betw een perturbed optic flow patterns sim ilar to those presented here. The key objective o f their study w as to investigate how lateral interconnections w ithin an M ST-like layer m ight be involved in achieving the discrim ination perform ance o f hum an observers. They found that lateral inhibition betw een m echanism s tuned to a range o f optic flow patterns (radial through spiral to rotation) w as required to obtain the m ost a c cu ra te sim u latio n s. S uch in te ra c tio n s are a b sen t from the c o n cep tu al fram ew ork used to interpret these data, and their inclusion m ight change the estim ated bandw idths significantly.

V iew ing distance m anipulation.

In the foregoing experim ents the spatial frequency o f the D oG elem ents was m anipulated by altering the view ing distance. In addition to changing the spatial frequency this strategy had the effect o f varying both the size o f the stim ulus, and the retinal speed o f the DoG elem ents. As these changes w ere confounded w ith the spatial frequency m anipulation it is not possible to say w hether they exaggerated or m itigated the inconsistent bandw idth figures recorded in these ex p erim en ts. C hanges in size have b een found to affect p erceiv ed speed (Snow den, 1999), how ever it is not know n w hether changes in either o f these attributes affects the ability to discrim inate the direction o f com plex m otion. F ield size has been show n to in flu en ce d isc rim in a tio n b etw een opposite directions o f unidirectional motion (Burr, M orrone & Vaina, 1998). It is possible that too small a stim ulus, i.e. one that is not m atched to the receptive field size o f the detecting neurones w ould lead to less accurate estim ates o f direction, introducing noise to the data.

B a se d on the a b ility o f o b se rv e rs to d isc rim in a te b e tw e en o p p o sin g unidirectional global m otion, Edw ards, Badcock & Sm ith (1998) proposed that two global m otion system s existed, each differently tuned for speed (see also De Bruyn & Orban, 1988). If this finding w ere to generalise to com plex optic flow

patterns then it is conceivable that altering the retinal size and hence speed o f our patterns could have stim ulated different system s. H ow ever the consequences o f this for direction discrim ination in com plex m otion p atterns are as yet unknown and rem ain to be explored.

Chapter 4

The Dependency of Sensitivity on Spatial Frequency in Radial Flow

4.1 Abstract

R elative m otion b etw een an ob serv er and an ap p roaching tex tu red object produces a radially expanding pattern o f optic flow on the retina. N ot only does the retinal projection o f the object grow in size, its local features grow and diverge from each other over tim e, providing cues to the presence o f m otion-in- depth. Previous studies exam ining the relative im portance o f size change and divergence rate have concluded that size change plays only a m inor role in 3d m otion perception com pared to divergence. H ow ever recent evidence (Schraeter, K nill & Sim oncelli, 2000) suggests that spatial scale has an im portant role to play in the perception o f m otion-in-depth. To explore further the influence o f sp atial frequency on the p e rcep tio n o f 3d m o tio n tw o exp erim en ts w ere perform ed. M otion coherence thresholds to detect radial expansion in a random dot stim ulus w ere m easu red across a range o f speeds. T he rate at w hich individual filtered dots grew w as m anipulated w hile dot divergence rem ained constant.

4.2 Introduction

W hen an observer watches an approaching object, such as a football, the im age projected on the retina grows larger, and any m arkings on the ball will, in retinal term s, becom e m ore w idely separated and will sim ultaneously increase in size. All o f these cues m ay be useful in interpreting the retinal signals as being produced by an object m oving in depth. Previous research has confirm ed the effectiveness o f these attributes in stim ulating a sense o f m otion-in-depth.

O bject size change: Regan & H am stra (1993) established that rate o f change o f size could be used effectively by subjects in discrim inating the tim e to contact (TTC) o f a uniform square used to sim ulate an object approaching along the line o f sight. This ability to discrim inate TTC according to rate o f size change was also found to hold for a peripherally presented square by R egan & V incent (1995) using sim ilar stim uli and m ethodology. T odd (1981) presented tw o expanding squares, each defined by individual dots (the dots rem ained o f fixed size as the squares grew larger). Subjects w ere required to discrim inate w hich square would reach them first, a task that they were readily able to do with high accuracy, suggesting that they could use rate o f size change to discrim inate the relative TTC o f the sim ulated objects.

O bject size and texture: Beverley & Regan (1983) presented a textured square stim ulus. The texture could expand or contract, w hile the overall size o f the square could change in size congruently, change in size in the opposite direction, or could rem ain fixed. T heir m ethod w as to adapt subjects to these various com binations o f object and texture size changes, and m easure the am ount o f m otion required to null the m otion after-effect (M AE) induced. The test pattern was an un-textured square whose direction o f size change m atched that o f the adapting stim ulus, and therefore was opposite to the after-effect. They found that after-effects w ere m axim al when texture and square size changed in tandem ; that texture size change alone (i.e. no overall object size change) was less effective at inducing a m otion after-effect, and that conflicting size and texture changes

could result in abolition o f the motion after-effect. This clearly dem onstrates the interaction o f both sources o f inform ation on a m etric (the M A E) that is widely assum ed to indicate the selective response o f the m otion system . V incent & Regan (1997) docum ented the perform ance o f subjects estim ating TTC when presented w ith a sim ulation o f an approaching textured square w hose size and texture grow th rates w ere m anipulated independently. They found that TTC discrim ination thresholds were little affected by m ism atching the tw o attributes, but that errors in estim ating TTC w ere low w hen square grow th and texture grow th w ere congruent, but increased w ith the degree o f m ism atch in their growth rates.

Size, separation and texture: Gray & Regan (1999) investigated the effect o f dot size on the accuracy o f TTC estim ates. W hile object size and texture divergence increased in tandem , dots could either grow veridically, or rem ain o f fixed size. T heir stim ulus w as a square figure m ade up o f evenly spaced dots w ith a G aussian lum inance profile. Estim ates o f TTC w ere found to be m ost accurate when all three attributes w ere m ade congruent. W hen texture elem ents (circular dots) were small, fixing their size had little effect on errors in TTC estim ation, but this was not true o f large dots, w hich produced large over-estim ations in TTC.

Texture and separation: By presenting a random dot kinem atogram (RDK) w ithin a constant diam eter w indow H arris & G iachritsis (2000) w ere able to rem ove the overall stim ulus size as a cue to m otion-in-depth, leaving only dot (or texture elem ent) grow th and dot divergence rates as relevant variables. Again T T C w as used to assess the relativ e co n trib u tio n o f dot grow th and dot divergence. Except w hen growth and divergence signalled opposite directions o f m otion-in-depth, they found that perform ance was little affected when elem ent grow th rate was m anipulated, and concluded that the size change o f their RD K dots had only a small part to play in determ ining the perception o f retinal flow com pared to the relative m otion among dots.

The consensus from the foregoing studies is that elem ent size change has a lim ited influence on the perception o f stim uli sim ulating loom ing, with overall size change and elem ent divergence rates rem aining as the m ost significant cues to m otion-in-depth. H ence local directional signals seem m ore prom inent than size change in determ ining quantitative perform ance in m otion-in-depth tasks.

C urrent m odels o f local m otion detection postulate spatially and directionally restricted m echanism s, capable only o f sensing m otion within a small region o f visual space and within a lim ited range o f directions (e.g. A lbright, 1984). In order to detect w ide field optic flow created by events such as forw ard m otion it has been suggested that these local m otion signals are integrated in a second stage o f processing that allow s interaction betw een local signals. In this way global m otion detectors are constructed from sim ple elem ents (e.g. Perrone & Stone 1998). H ow ever, a further feature o f m odels o f lo ca l detectors is their lim ited spatial frequency bandw idth (A delson & B ergen, 1985; H arris, 1986; Van Santen & Sperling, 1984; W atson & Ahum ada, 1985). Given this specificity o f response at the local level, it follow s from the hierarchy described above that glo b al m otion m echanism s m ig h t be re stric te d by the sp atial freq u en cy specificity o f their local precursors. S upport for this idea w as provided by L edgew ay (1996) who presented w ide field translation in two fram e R D K ’s. O bservers were asked to discrim inate the global direction o f m otion. Each fram e o f the anim ation was convolved w ith its own filter, discrim ination only being possible when filters were separated by less than an octave in frequency space. This result was taken to show that local m echanism s restricted in their frequency tuning constrained the global perception o f the direction o f motion.

U sing random dots, Y ang & B lake (1994) provided evidence that the spatial frequency tuning o f global m echanism s is quite broad, m easuring a bandw idth o f around 2.4 octaves at half-height. In their detection task, w here a translation signal im m ersed in dynam ic noise was discrim inated from random m otion in dynam ic noise, dynam ic noise dots were convolved with a different filter to that used on all other dots. Y et even w hen filter centre frequencies w ere w idely

spaced discrim ination perform ance was reduced by the noise-m ask, im plying that a wide range o f spatial frequencies was being integrated in global translation detection.

T he preceding tasks used translating stim uli to investigate the consequence of using narrow band stim uli on the perception o f global m otion. The effect on com plex form s o f global m otion, such as radial flow has not received m uch attention. To test w hether spatial scale plays a p art in the detection o f radial m otion tw o ex p erim en ts w ere perform ed. In both experim ents the spatial structure o f elem ents m aking up a random dot field sim ulating radial optic flow was m anipulated. In the first experim ent a radially expanding or contracting R D K was presented w hose elem ents w ere circularly sym m etric difference o f G aussian dots (DoG's). The spatial frequency bandw idth o f these dots is lim ited, and changes in tandem with their retinal size, therefore altering elem ent growth rate affects spatial scale change. Four rates o f elem ent grow th were presented: the zero grow th condition involved no size or spatial frequency change betw een successive sam ples o f a dot's trajectory. The veridical grow th condition saw the dots grow at a rate com m ensurate with the rate o f dot divergence (com m ensurate in the case o f the approach o f a fronto-parallel plane). The third level o f growth was double the veridical rate, and the last was four tim es the veridical rate. The speed o f the optic flow pattern was varied to see if any effect o f spatial scale differed with this param eter. Three conditions o f velocity were explored.

In the first experim ent the spatial scale o f the optic flow pattern was m anipulated by changing the size o f a spatially lim ited dot, the difference o f G aussian. The