Sistema de gestión y de control 1. Riesgo(s) definido(s)

Psychophysical studies have identified the conditions under which humans perceive occlusion in kinetic random dot displays. Kaplan first studied whether di↵erences in the movement patterns of two surfaces alone yield percepts of relative depth and kinetic occlusion (Kaplan, 1969). He tested the hypothesis that accretion/deletion of texture elements optically specify “the direction of depth” or figure-ground relations about a kinetic edge. Subjects viewed moving ink blots that occupied one of two regions separated by a vertical kinetic edge on an overhead projector and underwent horizontal motion. Kaplan manipulated the relative velocities of the ink blots in either region and the initial placement of the kinetic edge. The ink blots were sufficiently fine so that the display appeared as a continuous texture when the blots were stationary. When texture in either region moved to the left or right, but the kinetic edge remained fixed over the ⇠4 sec trial, subjects responded that the stationary surface occluded the moving surface (stationary condition, Figure 5.1.1a). Subjects reported that the stationary surface was “covering” the moving surface, whose texture elements were deleted at the stationary kinetic edge. When dots in the two regions moved at

Figure 5·2: Kinetic random dot displays tested by the model, each rep- resents an important test for neural models of kinetic border-ownership. The dashed green lines show the location of the kinetic edges that sep- arate di↵erent regions of the display. Only dense random dots actually are in the displays. (a) Stationary condition. A display similar to those used in Kaplan (1969) whereby dots in ‘A’ move to the right, dots in ‘B’ remain stationary, and the kinetic edge between them re- mains stationary and therefore is correlated with the dots in ‘B’. Hu- mans perceive surface ‘B’ (figure) as occluding surface ‘A’ (ground). (b) Encroach condition. A display similar to those used in Kaplan (1969) whereby dots in ‘B’ move to the left and encroach on those in ‘A’. When dots in ‘B’ are displaced leftward toward ‘A’, dots in ‘A’ are deleted. The kinetic edge is thereby correlated with dot motion in ‘B’. Humans perceive surface ‘B’ (figure) as occluding and sliding over surface ‘A’ (ground). (c) Gap condition. Similar to (b), except a white gap moves leftward with the dots in ‘B’ such that no texture accretion/deletion occurs (Yonas et al. 1987). Human subjects report seeing ‘B’ as occluding ‘A’, but with decreasing probability as the gap width increases. (d) Shear condition. Dots in ‘A’ move parallel to the kinetic edge such that no texture accretion/deletion occurs and dots in ‘B’ remain stationary (Royden et al. 1988). Humans report seeing surface ‘A’ as figure and ‘B’ as ground. (e) Strip condition. Dots in the center region ‘B’ remain stationary and surrounding dots in ‘A’ move orthogonally to the vertical kinetic edges. Human responses indicate that subjects see ‘B’ in front of ‘A’ (van Doorn & Koenderink 1982). (f ) Object and Window conditions. A square region is defined by dot motion and luminance contrast di↵erences from the sur- rounding annular region (von der Heydt et al. 2003). The square region either appears as an ‘object’ (bottom left panel) or ‘window’ (bottom right panel). Top panel taken with permission from von der Heydt et al. (2003).

di↵erent speeds and potentially di↵erent directions or when the texture to one side moved while the other remained stationary, but the kinetic edge moved with one of the surfaces, the surface that was correlated with the edge was seen as in front of the other (encroach condition, Figure 5.1.1b). Both conditions are examples of the Gestalt principle of common-fate — the surface that moves together with the kinetic edge is seen as the figure and the other surface is the ground. The kinetic edge is perceived as owned by the occluding surface. Border-ownership reports in humans are consistent with analyses performed by Gibson and his students, which indicate that the covering and revealing of a surface under certain conditions may be optically specified by texture accretion/deletion (Gibson et al., 1969). Subjects in Kaplan’s study did not always perceive figure-ground relationships, as was the case when the horizontal dot velocities in ‘A’ and ‘B’ were equal in magnitude, di↵ered in direction, the kinetic edge remained fixed, and moving dots in ‘A’ and ‘B’ were deleted upon arriving at the kinetic edge (degenerate condition). Instead of perceiving figure and ground surfaces, subjects perceived a thin kinetic edge that did not belong to either region. Models of figure-ground segregation should di↵erentiate between the cases wherein humans do and do not perceive strong depth orderings around a kinetic edge.

Gap Condition

In Kaplan’s study, texture elements in the figure surface always were correlated with the kinetic edge direction of motion, texture accretion/deletion always occurred at the kinetic edge, and texture elements in both surfaces moved relative to one another. From the experiments of Kaplan, it is not clear whether the visual system relies on accretion/deletion or relative motion information to determine the figure-ground relationships of the two surfaces. Yonas tested whether texture accretion/deletion be- tween two kinetic random dot surfaces is necessary to obtain figure-ground percepts

by introducing a white, variably-sized “gap” between the independently controlled left and right regions of the display (gap condition, Figure 5.1.1c) (Yonas et al., 1987). The percentage of trials in which subjects responded that there was a depth ordering in the displays was highest when there was texture accretion/deletion (zero gap). Depth ordering percepts dropped o↵ monotonically as the size of the gap between the two regions grew. The results are compatible with the idea that neurons in the visual system with limited receptive field sizes are involved in the determination of kinetic border-ownership and figure-ground segregation. By virtue of their preva- lence in early primate visual areas, B cells have small receptive field sizes — both compared to many other visual cortical areas and the figures to which they respond. For example, von der Heydt and colleagues report that median B cell receptive field sizes at foveal eccentricities are 0.5 , 0.7 , and 3.6 in monkey visual areas V1, V2, and V4, respectively (Zhou et al., 2000). The rich percept of border-ownership at the kinetic edge and the dependence on narrow gap sizes for robust depth ordering percepts to occur suggest that B cells may be involved in the same cortical network that determines figure-ground relations in kinetic random dot displays.

Shear Condition

The displays used in the experiments of Kaplan and Yonas required horizontal dot motion, perpendicular to a vertical kinetic edge. Royden studied kinetic random dot displays that involved a motion-defined rectangle surrounded on all sides by another region of stationary dots (Royden et al., 1988). Dots moved either horizontally or vertically within the rectangle, and the aspect ratio of the rectangle was manipulated. Kinetic edges were defined either by texture accretion/deletion, as was the case in the displays of Kaplan and Yonas, or shearing motion whereby the dot motion was parallel to the kinetic edge (shear condition, Figure 5.1.1d). When the rectangle aspect ratio made the kinetic edges where accretion/deletion occurred much longer

than those where shearing motion was present, subjects responded that the rectan- gle appeared to be occluded by the surrounding stationary dots, similar to human reports in the stationary condition (Figure 5.1.1a). Conversely, when the rectan- gle aspect ratio made the kinetic edges where shearing motion occurred longer than those where accretion/deletion occurred, subject responses indicated that the rectan- gle appeared in front of the surrounding region. Moreover, the data indicate that the figure-ground percept is more powerful when the rectangle was defined predominately by accretion/deletion than shearing motion. Any model that makes mechanistic pre- dictions about how the visual system performs kinetic figure-ground segregation must address the di↵erence in percepts that occur when a kinetic edge is defined by texture accretion/deletion or shearing motion.

Strip Condition

Rather than dividing the kinetic random dot display into two adjacent regions, van Doorn studied the e↵ects that tiling parallel kinetic edges across the display had on figure-ground perception (van Doorn and Koenderink, 1982). The displays of van Doorn consist of rectangular regions of dots whereby dot velocities alternate in adjacent regions (strip condition). When the strips were thick, subjects indicated that they perceived adjacent strips as separate surfaces. Figure 5.1.1e shows an example of a strip condition display with vertically-oriented kinetic edges. Because the kinetic edges remain stationary, deletion of the left peripheral texture occurs at the left kinetic edge, and accretion of the right peripheral texture occurs at the right kinetic edge, the central strip appears in front of the surrounding two strips. When the strips were very narrow, responses indicated that the subject saw dots occupying two superimposed transparent planes. Subjects saw alternating motion- defined surfaces when the thickness was as narrow as 200_{, which demonstrates the high}

kinetic figure-ground relations. Thicknesses in between resulted in incoherent, white noise “snow” percepts. Models of figure-ground segregation in kinetic random dot displays should assign border-ownership of the kinetic edges inward toward the strip centers when humans perceive the strips as figures. The presence of multiple strips adds to the complexity of the displays because the visual system determines that certain pairs of adjacent kinetic edges belong to the same strip, and models must perform the same border-ownership assignment.

Object & WIndow Conditions

Von der Heydt and colleagues tested whether kinetic random dot displays elicit border-ownership responses in primate visual areas V2, where there are cells known to exist that produce border-ownership signals to static displays (von der Heydt et al., 2003). von der Heydt and colleagues presented monkeys visual displays that consisted of two regions that di↵ered due to dot motion di↵erences and luminance contrast (Figure 5.1.1f). The square region has a di↵erent mean grayscale luminance value than the surrounding region and either region contained sparse moving or sta- tionary dots. The kinetic edges that border the square region were either correlated with the dots in the square (object condition) or with the surround region (window condition). In the object condition, the square appeared as the figure surface. The dots within the square region were constrained to move with the same velocity as the kinetic edges (the kinetic edges remained fixed if the dots in the square had zero velocity). In the window condition, the square region appeared as a hole or aper- ture and the surrounding region served as the figure surface. The texture in the square region was accreted/deleted and the surrounding texture moved with the ki- netic edges. In both conditions, there were cases in which either the kinetic edges had a zero (“stationary edge” condition) or non-zero (“moving edge” condition) ve- locity. von der Heydt and colleagues also reversed the luminance contrast polarity

on separate trials. For example, there were window stationary edge conditions in which the mean square luminance was either lighter or darker than the surroundings. Border-ownership neurons whose receptive fields were centered on the kinetic edges of the square elicited ceteris paribus di↵erential responses in the object and window conditions, which suggests B cells incorporate texture accretion/deletion information in border-ownership signals. Interestingly, more neurons in the sample preferentially signaled border-ownership when the square was consistent with the object interpre- tation than the window interpretation. The results indicate that there are B cells in V2 that produce border-ownership signals near kinetic edges.

Kinetic random dot displays represent important tests for any model that at- tempts to describe the underlying neural dynamics of kinetic border-ownership be- cause reliable luminance contrast information is absent. In particular, the model should yield border-ownership signals consistent with human figure-ground percep- tion in the displays of Kaplan (Figure 5.1.1). The model should show that texture accretion/deletion is sufficient, but not necessary, to elicit kinetic border-ownership signals (Yonas et al., 1987), and it should be able to di↵erentiate between accre- tion/deletion (Figure 5.1.1a) and shearing motion (Figure 5.1.1d). When there are multiple kinetic edges, under appropriate conditions the model border-ownership sig- nals should indicate the presence of di↵erent strip surfaces (van Doorn and Koen- derink, 1982). Finally, when random dots within a shaped region (e.g. square) move di↵erently than in the surrounding region, model border-ownership signals should di↵er when the square region is interpreted as an object or a window (von der Heydt et al., 2003). We present a simple neural model that performs border-ownership as- signment consistent with human perception in these kinetic random dot displays, us- ing grouping and competition between units that respond to di↵erent spatio-temporal correlations. Our model is consistent with known neurophysiology and the results

explain how cells in primate V2 may produce border-ownership signals of kinetic edges (Zhou et al., 2000; von der Heydt et al., 2003). The model specifically predicts that known anatomical connectivity between areas V2, V4, and MT at least in part subserves motion-induced border-ownership signal generation.

5.2

Methods

Visual Input Tonic Cells LGN Transcient Cells V1 Complex Cells Motion Static B Cells B Cells V2 MT Additive Cells + + + + + + + + Grouping Cells V4 LEGEND Connections Excitatory Inhibitory

Conduction Delays Correlation/velocity cell

Strong response Left Right Static

Weak response Left Right Static

Border-ownership Left Motion Selective Right Motion Selective Static Selective Strong Weak

Left Border-ownership Selective

Correlation Directions Stationary Magnocellular Pathway Parvocellular Pathway f s f s Fast Slow Border-ownership Strength =Modulatory+ = =

In this section, we introduce the core model circuits, visual displays that are simulated in the model, and mathematical equations.

5.2.1 Magnocellular and parvocellular pathways

Figure 5_{·3 summarizes the model architecture. The model contains stages that corre-} spond to populations of cells within the primate retina (not shown), lateral geniculate nucleus (LGN), primary visual cortex (V1), V2, V4, and medial temporal area (MT).

Figure 5_{·3: Model diagram. The model consists of stages corre-} sponding to primate visual areas LGN, V1, V2, V4, and MT. The top (bottom) set of panels define model magnocellular (parvocellular) pathways. Magnocellular model units detect non-zero (moving) spatio- temporal correlations and determine border-ownership of regions with motion, while parvoceullar units detect stationary correlations and de- termine border-ownership of static regions. The model uses two sub- populations of LGN cells: transient and tonic. The former decays faster than the latter. V1 units detect spatio-temporal correlations by receiv- ing feedforward input from several spatially displaced LGN cells with di↵erent conduction delays. V1 units with di↵erent spatio-temporal correlations compete in a contrast-enhancing network. Each type of V1 unit that is tuned to a di↵erent spatio-temporal correlation projects separately to B cells in V2. Magnocellular B cells project to MT and parvocellular B cells project to V4. MT cells send feedback to both in- hibit magnocellular and parvocellular B cells in V2 in locations where MT receives excitatory feedforward input. V4 units also feedback to V2, but only target parvocellular units and units with spatio-temporal correlation sensitivities in directions that are orthogonal with respect to the V4 cell circular receptive field shape (see Figure 6 and Table 1 for more details).

Because the visual displays used to investigate the perception of figure-ground segre- gation and border-ownership in humans involve dots that either remain stationary or move, our model contains parallel subsystems that correspond to the magnocellular (Figure 5_{·3, top pathway) and parvocellular (Figure 5·3, bottom pathway) pathways} of the primate visual system. Cells within the primate parvocellular pathway have higher spatial, but lower temporal resolution compared to those in the magnocellular pathway (Livingstone and Hubel, 1988). Therefore, model cells in the parvocellular and magnocellular pathways are more sensitive to static surfaces and moving dot patterns in moving surfaces, respectively.

Model V1 cells are tuned to di↵erent spatio-temporal correlations due to the con- vergence of inputs from LGN cells with spatially displaced receptive field centers and conduction delays. Each type of correlation cell in V1 projects to correspond- ing B cells in V2, which are sensitive therefore to the same range of spatio-temporal correlations. Possible mechanisms by which B cells acquire their side-of-figure selec- tivities in static displays with shapes defined by luminance contrast have been stud- ied (Craft et al., 2007; Layton and Browning, 2012). The mechanisms underlying motion-induced border-ownership sensitivity have not been extensively investigated. Border-ownership units in our model develop side-of-figure selectivites via feedback from units with larger receptive fields within areas V4 and MT. After model area V2, the parvocellular and magnocellular pathways bifurcate — the former independently projects to model V4 and the later to model MT. When the pathways diverge, both projections to V4 and MT include both feedforward and feedback connections.

Although there is evidence for separate magnocellular and parvocellular pathways in the primate visual system, recent data suggest that there are substantial interac- tions between the pathways (Sincich and Horton, 2005). Our model includes consider- able competitive/cooperative interactions between the parvocellular and magnocellu-

lar systems. Units in V1 compete across correlations to perform contrast-enhancement on spatio-temporal correlation signals. MT units feedback to inhibit B cells with dif- ferent spatio-temporal correlation selectivities than the B cell that supplied the MT unit input. B cells tuned to moving correlations modulate V4 cells that are driven by B cells tuned to stationary correlations by enhancing the V4 unit’s activity when accretion/deletion is detected within the V4 unit’s receptive field.

Transient cells in model LGN respond to changes in luminance, irrespective of the dot motion direction. Magnocellular and parvocellular LGN cells both elicit a transient response, except parvocellular cells decay much faster (Figure 5·3, tonic and transient LGN cell panels). The response of model LGN cells is consistent with the neurophysiological data of Maunsell (Maunsell et al., 1999). In the study, macaque monkeys were presented spots of light and single-cell recording was performed on neurons in LGN. Magnocellular response latencies preceded the fastest parvocellular response latencies by approximately 10 msec. In one monkey, magnocellular minimum and median response latencies were 16 msec and 21 msec, respectively, and parvocel- lular minimum and median response latencies were 24 msec and 31 msec, respectively. M retinal ganglion cells and magnocellular LGN cells have a higher ratio of early to late average firing than P retinal ganglion cells and parvocellular LGN cells, which suggests that magnocellular neurons in the early visual system exhibit a higher degree of transience and decay faster than parvocellular neurons (Schiller and Malpeli, 1977; Schiller and Malpeli, 1978). Indeed, evidence suggests that magncellular LGN neu- rons conduct impulses faster than parvocellular LGN neurons (Dreher et al., 1976). Although it has been estimated that cells in the magnocellular pathway transmit impulses to LGN and V1 ⇠3 msec and ⇠5 msec quicker, respectively, than cells in the parvocellular pathway, LGN neurons in both pathways have highly overlapping response latency distributions (Nowak and Bullier, 1997). In macaque V1 neurons,

lesioning parvocellular LGN neurons increased the transience of V1 cell responses, but lesioning magnocellular LGN cells had no e↵ect (Maunsell and Gibson, 1992). This suggests that the responses of V1 cells obtain their transience at least in part by feedforward projections from magnocellular LGN neurons, but not parvocellular LGN neurons.

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