Conclusions

In these experim ents it has been shown that a radially expanding pattern o f dots continues to be perceived to m ove faster than a rotating pattern, despite the p resen ce o f disparity and size-change depth cues indicating th at the dots occupied a fixed or receding depth plane. I f the relative m otion p resent in expanding patterns is interpreted as m otion-in-depth, then the additional depth cues introduced here h ave been show n to be ineffective in influencing that perception, im plying that relative m otion is a prim e source o f depth inform ation. A lternatively, the source o f the speed illusion is not related to a m otion-in-depth interpretation, and rem ains to be explained. G eesam an & Qian (1996) suggested that the illusion m ight be a function o f the larger quantity o f radially-sensitive cells found in M T com pared to rotationally-sensitive cells. If anything, m ore cells w ould simply allow an increase in resolution/accuracy along the dim ension m easured by such cells, rather than some distortion o f reality. A lthough Clifford (1999) argued on theoretical grounds in favour o f m otion-in-depth, em pirically the inconclusive results reported here ensure the basis o f the speed illusion rem ains unresolved. R egarding the second explanation (the m otion-in-depth hypothesis is incorrect), all that can be claim ed at this stage is that no evidence has been found in favour o f the m otion-in-depth hypothesis. H ow ever, absence o f evidence is not evidence o f absence, and it rem ains possible that there exist com binations o f depth cues that w ould override RM and dim inish the speed illusion.

T hese results have im plications for m odellers o f cue com bination. A them e o f these m odels is the m ethod by which depth cues are integrated when available in

d ifferent 'currencies'. B y different currencies it is m eant that som e cues, for exam ple disparity, signal relative depth w hile occlusion signals ordinal depth (i.e. w hich one is closer). A fter B ulthoff & M allot's (1988) characterisation o f fo u r ty p es o f cue in te ra c tio n : a c c u m u la tio n , veto, d isa m b ig u a tio n and cooperation, M aloney, Landy and colleagues (e.g L andy et. al., 1995) have developed a m odified w eak fusion theory o f cue interaction. Their m odel seeks to strike a balance betw een m odular approaches to cue integration on one hand, and highly interactive approaches on the other. M odular schem es have depth estim ates com puted independently, then com bined in an averaging process. Non- m o d u la r ap p ro a c h e s allow full in teractio n betw een cues in sim u ltan eo u s satisfaction o f m ultiple constraints e.g. N akayam a & Shim ojo (1992). T hese findings can be taken as further evidence that disparity is a cue with low w eight w here m otion is along the observer's line o f sight.

Chapter 6

Discrimination of Speed in Radial, Rotation and Translation Motion Mechanisms

6.1 Abstract

K now ing the speed at w hich you and other people or objects are m oving is a critical skill for all hum ans in their interaction w ith the environm ent. T he patterns o f optic flow generated by such m otions are projected on to the retina in a w ay that m ust be analysed at a global level. It is the analysis o f the speed o f large-scale m ovem ent that is the subject under investigation here. M echanism s resp o n siv e to w ide-field p atterns o f m otion com p risin g m any speeds and directions are thought to be a distinct class to local m otion sensors. As such they m ay possess distinct tuning characteristics. P revious attem pts to m easure the speed tuning o f such m echanism s have not distinguished betw een local and global m echanism s. H ere three experim ents are rep o rted that address the problem o f excluding local speed m echanism s from the m easurem ent o f global speed discrim ination thresholds. Tw o techniques are em ployed, one to render local cues unreliable, the other to render them com pletely uninform ative. The first technique provided estim ates o f speed discrim ination thresholds for radial, rotation and translation (20% -70% ) that w ere higher than m any previous studies have reported. H ow ever the technique m ay be inappropriate for this type o f w ork. The second technique, used with rotation only, provided low er estim ates o f 5% -30% that are m ore in keeping with the existing literature.

6.2 Introduction

T he perception o f sim ple form s o f m ovem ent such as translation in the fronto- parallel plane has been explored m any tim es. F or exam ple studies o f speed discrim ination (De Bruyn & Orban, 1988; M cK ee, 1981; M estre et. al., 2001) in hum ans has shown them to be capable o f determ ining differences o f around 4% to 20% (expressed as W eber fractions), depending on the underlying speed o f the reference. H ow ever, retinal stim ulation produced by ego m otion contains signals over large areas o f the visual field, com prising a diverse range o f speeds and directions. It has been postulated that special m echanism s exist in prim ate v isio n (T an ak a & S aito , 1989; D uffy & W u rtz, 1991) to p ro cess such h e te ro g en e o u s signals, and p rev io u s exp erim en tal w ork has attem p ted to docum ent the com petence o f such ‘globally’ tuned m echanism s in the detection and discrim ination o f speed.

G lobal Speed Discrimination: Translation, Rotation and Radial Motion

In one o f several related experim ents. Sm ith, Snow den & M ilne (1994) found that a field o f translating dots (all o f the same speed) needed a velocity increase o f som e 10-12% to be d istinguished from a referen ce pattern m oving at 4 degrees/s. Extending earlier work on the speed discrim ination o f sim ple singular translational m otions, V erghese & Stone (1995) asked observers to discrim inate on the basis o f speed betw een two anim ations, each com prising m ultiple G abor p atch es. T hey found th at speed discrim in atio n th resh o ld s decreased w ith in creasin g num ber o f patches (1 p atch= circa 19%; 6 patches = circa 11%, interpreted from their figure 3), a finding they attributed to the parsing o f visual space into discrete entities. W hen the area o f a single patch was increased in line w ith th a t sh ared a c ro ss m u ltip le p a tc h e s th re sh o ld s w ere c o n sta n t, at approxim ately 20% (interpreted from their figure 5a).

A particular em phasis has been placed on the ability o f observers to exploit the radial pattern o f optic flow produced by forw ard m otion along the actor’s line o f sight. The param eters o f m echanism s responsive to such radial flow have also

been thoroughly investigated. F or exam ple, m uch w ork has focussed on how accurately an observer can ju d g e the tim e it will take for a sim ulated object to reach them , know n as its ‘tim e-to -co n tact’ (TTC). V incent & Regan (1997) dem onstrated TTC discrim ination thresholds to be around 8%. Sim ilarly, Regan & H am stra (1993) reported TTC d iscrim ination thresholds fo r a sim ulated approaching object to be in the range 7-13% .

M ore d irect attem pts to m easure speed discrim in atio n thresholds in radial patterns, rath er than TTC discrim ination thresholds, have been m ade. Sekuler (1992) com pared discrim ination perform ance in rotation and ‘loom ing’ (radial expansion) patterns using random dot kinem atogram (RDK) stim uli. Thresholds for both patterns were sim ilar, ranging betw een 5% and 16%, depending on observer.

C lifford, B eardsley & V aina (1999) m easured speed discrim ination thresholds for a relatively high reference speed (21.3 degrees/s.) in R D K ’s, establishing low W eber fractions o f betw een 3% and 4% for both rotation and radial patterns. A t m uch low er reference speeds (1, 0.5 & 0.33 degrees/s) Bex, M etha & M akous (1998) found discrim ination thresholds for gratings to vary with speed, recording fractions no greater than 15%, and m ore typically betw een 5% and 10%.

K aiser (1990) exam ined the ability o f observers to discrim inate the angular velocities o f tw o sim ulated objects that rotated about axes orthogonal to the su b je c t’s line o f sight. If the three spatial dim ensions are term ed x-axis for horizontal, y-axis for vertical and z-axis for depth, (where the observer’s line o f sight is the z-axis) the stim uli w ere rotated about the x and y-axes. Som etim es com parisons w ere m ade betw een rotations on identical axes (i.e. both objects rotating about the x-axis, or both rotating about the y-axis), som etim es betw een opposing axes (i.e. one rotating about the x-axis, the other rotating about the y- axis). V arying the size and shape o f objects, their phase relationships and directions o f rotation, the authors reported that angular velocity discrim ination com petence o f around 12% was achieved. M atching angular velocity betw een objects o f differing sizes show ed that small objects needed to have, on average, 9% g rea ter rotatio n al speed to be p e rc e iv e d as e q u iv a len t to th eir larg e r

asso ciates. T hese results, how ever, do not inform o f the type o f rotation- se n sitiv e m echanism s th at address detection o f rotation about the z-axis. N onetheless the figures reported are sim ilar to those found by the follow ing workers w ho did investigate rotation about the z-axis.

A study by K aiser & C alderone (1991) exam ined angular velocity m atching and discrim ination in rotation about the z-axis. Using a dense field o f rotating single­ pixel dots they reported discrim ination thresholds o f betw een 4% and 6% when test and reference kinem atogram s w ere o f equal diam eter, and sim ilar values (3% -6% ) w hen diam eters differed by a factor o f two. E xam ining the points o f subjective equality revealed no bias w hen kinem atogram s w ere o f the sam e diam eter, but a significant bias (17% ) w hen diam eters differed. This indicates th at local velocities w ere influencing speed ju d g em en ts, though they w ere clearly not com pletely relied upon as the size difference betw een rotating patterns m eant that local dot speeds differed by a factor o f two, im plying a bias o f 100% if m atches were being m ediated by linear m otions.

W ork on rotational speed tuning (speed m atching and speed discrim ination) centred on the z-axis has also been reported in three papers by W erkhoven & K oenderink (1990, 1991, 1993) using random dot stim uli. T heir first study exam ined speed discrim ination betw een rotating annuli, show ing that low est d ifference thresholds o f 8-10% w ere achievable, w ithin the range for local judgem ents (De Bruyn & Orban, 1988; and M cKee, 1981). In their second paper (W erkhoven & K oenderink, 1991), a series o f four experim ents exam ined the dependency o f speed discrim ination on several factors: tem poral factors o f fram e duration and trial duration; textural factors, i.e. num ber o f dots and dot density; spatial scale, w here bo th com parison stim uli w ere p resented at a range o f view ing distances to m anipulate their retinal sizes (test and reference always the sam e size); and finally, the dependence o f discrim ination threshold on speed was explored to ascertain w hether W eber’s law held for rotational m otion in the way it does fo r lin e a r m o tio n . T he authors found th at speed d isc rim in a tio n perform ance in all experim ents was sim ilar to that previously found for linear m otion. They concluded that observers w ere not able to m ake use o f angular

velocity to judge difference thresholds, and were therefore basing their decisions on the local retinal velocities, averaging these w here m ultiple speeds w ere present in the stimulus.

In their later study, W erkhoven & K oenderink (1993) further explored the effect o f spatial scale by assessing how perceptual m atches and speed discrim ination thresholds w ere influenced by differences in the radii o f test and reference patterns. This was done for a range o f speeds, using rotating random dot stim uli. D iscrim ination thresholds w ere found to vary w ith the degree o f m ism atch betw een the radii o f com parison stimuli. M inim um threshold was obtained when sizes w ere equal (7%), increasing to m ore than 20% w hen radii differed by a factor o f two. Again, the authors concluded that fundam entally the local linear speed o f dots was being used in preference to the angular speed o f rotation.

T argeting global m echanism s in an attem pt to m easure speed discrim ination thresholds encounters a m ajor problem im plied by the ‘m ultiple stage’ theory o f m otion sensing currently in favour (A delson & M ovshon, 1982; W elch, 1989). T his m odel addresses the problem o f how an initially piecem eal analysis o f the visual scene can be used to appreciate events in the w orld w hose consequences span w ide fields o f view. O ne sim ple form ulation o f the idea has a battery o f spatially localised m otion detectors at the first stage, with small receptive fields tuned for specific directions o f m otion, feeding into a second stage m echanism that integrates across the inputs from the first stage. If the directional properties o f first stage m otion detectors w ere carefully arranged spatially to m atch the distribution o f speeds and directions of, say, a rotation pattern, then the second stage m echanism w ould inherit a large receptive field tuned for ju s t such a stereotypical rotation event. Such m odels are described as tem plates, since they sim ply respond when there is a m atch betw een them and the external stim ulus (e.g. Perrone & Stone, 1998). How ever, as first stage m echanism s have m otion- sensing com petence o f their ow n, it is difficu lt to be sure that attem pted m easurem ents o f second stage global detectors are not in fact tapping the first stage. S ekuler (1992) concluded that speed sensitivity to com plex form s o f

m otion w as indeed m ediated by sim ple pooling over local m echanism s, as illustrated in a quantitative m odelling exercise they carried out. W erkhoven & K oenderink (1993) cam e to sim ilar conclusions, that fundam entally local linear speeds o f dots were being used in preference to the angular speed o f rotation of the patterns. The speed discrim ination results (3% -4% ) o f Clifford, B eardsley & V aina (1999) and K aiser & C alderone (1991) (3% -6% ) are perhaps the m ost sim ilar to previous local m otion discrim ination figures (e.g. 5%, M cK ee, 1981). It was decided to address the problem o f precluding the use o f local m otion d etecto rs in the assessm ent o f speed d iscrim ination p erform ance in global patterns o f motion. Two m ethods have been em ployed. In Experim ent 1 a signal- in-noise paradigm is used, in com bination with ‘speed balancing’ to discourage reliance on local m otion signals. A signal-in-noise task involves recording the p erfo rm an ce o f an ob serv er as a fu nction o f the ratio o f signal to noise inform ation contained in the stim ulus. The ratio o f signal in the patterns used here was 50% , considerably above norm al m otion coherence threshold o f circa 5% (Scase, B raddick & R aym ond, 1996). In E xperim ents 2 and 3 the usual connection betw een local and global speeds is broken to achieve the sam e objective. These techniques are described in the relevant experim ental sections. E xperim ent 1 explores discrim ination thresholds in global patterns o f translation, rotation and radial m otion, w hereas E xperim ents 2 and 3 are lim ited to the investigation o f rotation.

6.3 Experiment 1. Speed Discrimination Thresholds for Global Motion: