In the present technical article, we describe a method for generating a new dichoptic motion stimulus, the monocular components of which are dynamic random noise without constant figural cues for feature-tracking-based motion. Our dichoptic motion stimulus adds a new line of evidence, which supports the original conclusion of M. Shadlen and T. Carney (1986) that motion detection can be solely derived from early binocular motion processing. Further, we describe novel motion displays in which monocular motion and binocular motion are in opposite directions with variable intensity ratios. Our dichoptic stimuli will serve as a useful tool to investigate the interaction between low-level binocular motion detectors and monocular motion detectors without requiring feature extraction before motion detection.

*L*(

*x,*

*t*) and

*R*(

*x,*

*t*) are the luminance profiles of the left and right eye's inputs at position

*x*and time

*t*.

*ω*

_{ x},

*ω*

_{ t},

*C,*and

*m*are spatial frequency, temporal frequency, mean luminance, and amplitude/contrast, respectively.

*I*(

*x,*

*t*) is the luminance profile of an arbitrary spatiotemporal random-dot pattern.

*H*

_{ x/ t}denotes Hilbert transformation in the dimension of

*x*or

*t*. The right side of the equation is the Fourier series expansion of the left side, where

*ω*

_{ xi}= 2

*πi*/

*N*is the spatial frequency,

*N*is the number of pixels,

*ω*

_{ tj}= 2

*πj*/

*T*is the temporal frequency,

*T*is the number of frames, and

*m*

_{ ijmn}is the amplitude of the (

*i,*

*j,*

*m,*

*n*)th component, respectively. The phase,

*ϕ*

_{0/1}is 0 or

*π*/2. As can be seen in Equation 2, the Hilbert transformation of dynamic random noise both in space and time domains remains dynamic random noise, whereas the sum of the left and right dynamic noise has motion energy in one direction (at different velocities

*ω*

_{ tj}/

*ω*

_{ xi}). We can extend 1D space dynamic random noise to 2D space without breaking the quadrature relationship in one orientation and time. Movie 1 is an example of the dichoptic motion stimuli generated by the method described. The Hilbert transformation was applied to the vertical direction to produce upward motion when fusing a stereo–movie pair. (The observations made on this movie and on the following movies were confirmed by seven observes who had normal binocular vision.) Movie 2 demonstrates dichoptic clockwise rotation motion made by applying the Hilbert transformation to the angular direction in the polar coordinate. Here, movements of the pattern of dots in a unique direction under dichoptical presentation are perceived, although the image presented to each eye is dynamic random noise with neither directional information nor trackable features.

*a*(>1) is a parameter manipulating the ratio of the amplitudes of monocular motion and binocular motion. In Equation 3, each monocular input contains moving waves in the negative direction (the first term inside the large pair of brackets), whereas the summation of the two is a moving wave in the positive direction. Therefore, binocular motion is perceived in the direction opposite to that of monocular motion when the stimulus is dichoptically observed. Movies 4 and 5 are examples of motion stimuli generated by this method. Monocular motion and binocular motion cause motion rivalry where observers usually see only one of two directions at one time. This means binocular motion perception can exist independently of monocular motion perception and provides strong evidence that early binocular motion detectors represent mechanisms separable from monocular motion detectors (Anstis & Duncan, 1983). We can define the intensity of monocular motion MI as the ratio of amplitudes of standing waves (noise) and traveling wave (motion signal), which is a function of parameter

*a*.

*a,*whereas the intensity of binocular motion is an increasing function of parameter

*a*in Equation 3. Pure binocular motion stimulus defined by Equation 2 is the limit of Equation 3 when parameter

*a*is infinite.

*I*(

*x,*

*y,*

*t*) is the luminance profile of an arbitrary dynamic random noise at 2D space (

*x,*

*y*) and time

*t*. As can be seen in Equation 7, each monocular input is moving in the

*x*direction, whereas the summation of the two eyes' inputs has motion energy in the diagonal direction, on average. In Movie 6, random-dot patterns for each eye move toward the left, whereas dichoptic motion is in a left–down direction. Again, motion rivalry occurs between monocular and binocular motion.

*a*= 1, 1.25, 1.5, 2, 3, and 4, respectively. The motion stimuli were then presented with a duration of 250 ms in pseudorandom order (6 stimuli × 2 direction × 30 trials). Left-eye images were output from PC through green signal (8 bits), whereas right-eye images were output through blue signal. Stimuli were rear projected from a CRT projector whose blue gun was replaced by a green gun with a horizontally polarizing filter while the original green gun was covered with a vertically polarizing filter. Images were then segregated by eyeglasses that covered the left eye with a vertically polarizing filter and vice versa. Observers viewed the image screen (81° × 81°, 512 × 640 pixel resolution, 60 Hz refresh rate) from a distance of 50 cm. Seven healthy observers (of whom six were naive to the purpose of the experiment) whose visual acuity and stereoscopic depth detection performance are normal (or corrected to a normal level) participated in the experiments. All seven observers verbally reported that both monocular and binocular motions were visible but qualitatively different from each other. Binocular motion tends to be perceived stronger at the fixation depth around the central visual area, whereas monocular motion tends to be perceived stronger around the peripheral area at the beginning of stimulus presentation. To direct observer's attention to binocular motion, we instructed the observers to report the direction of dominant motion (up or down by mouse button pressing, 2AFC) around the central fixation depth at the end of stimulus presentation. We then plotted the response rate, selecting the direction of binocular motion as dominant against motion intensity (binocular motion intensity − monocular motion intensity).

^{1}and depth from motion parallax. This view is supported by the fact that binocular disparity (interocular spatial shift) and an interocular time delay are both theoretically (Qian & Andersen, 1997) and experimentally (Anzai et al., 2001; Carney, Paradiso, & Freeman, 1989) indistinguishable. It is worth noting that the stimulus configuration we used for generating dichoptic motion is similar to that of stereograms and Pulfrich-type effects in the sense that all of these binocular stimuli include spatial and/or temporal shifts between the two eyes; dichoptic motion requires a 90° phase shift in both space and time, whereas the Pulfrich-type effect requires an interocular time delay/temporal phase shift and stereoscopic depth requires binocular disparity (space shift; see Table 1). Given that our dichoptic motion stimulus derives from motion energy detection after simple summation of the left and right eyes' inputs, we can consider that dichoptic motion is also processed by the same neural population, and thus, the underlying neural mechanism of dichoptic motion could be as early as binocular V1 simple and complex cells.

Operation | |
---|---|

Dynamic random-dot stereogram | Left: I( x, y, t) |

Right: I( x + Δ x, y, t) | |

Pulfrich effect | Left: I( x, y, t) |

Right: I( x, y, t + Δ t) | |

Morgan and Fahle's ( 2000) display | Left: I( x, y)cos( ω _{ t} t) |

Right: I( x, y)cos( ω _{ t} t + ϕ) | |

Carney and Shadlen's ( 1993) random texture motion display | Left: I( x, y)cos( ω _{ t} t) |

Right: H _{ x}( I( x, y))sin( ω _{ t} t) | |

Our dichoptic motion | Left: I( x, y, t) |

Right: H _{ x}( H _{ t}( I( x, y, t))) |

^{1}The Pulfrich-type effect is seen when dynamic visual noise is viewed with a dark filter over one eye (or interocular delay (Ross, 1974), or interocular temporal phase shift (Morgan & Fahle, 2000). The noise is usually perceived as dots moving in an ellipse around the vertical axis of the stimulus display (the dots in front of the fixation plane appear to move in the direction of the filtered eye, and dots behind the fixation plane appear to move in the opposite direction).