Sighted animals extract motion information from visual scenes by processing spatiotemporal patterns of light falling on the retina. The dominant models for motion estimation exploit intensity correlations only between pairs of points in space and time. Moving natural scenes, however, contain more complex correlations. We found that fly and human visual systems encode the combined direction and contrast polarity of moving edges using triple correlations that enhance motion estimation in natural environments. Both species extracted triple correlations with neural substrates tuned for light or dark edges, and sensitivity to specific triple correlations was retained even as light and dark edge motion signals were combined. Thus, both species separately process light and dark image contrasts to capture motion signatures that can improve estimation accuracy. This convergence argues that statistical structures in natural scenes have greatly affected visual processing, driving a common computational strategy over 500 million years of evolution.
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- Supplementary Figure 1: Models of motion estimation. (331 KB)
(a) The classical Hassenstein-Reichardt Correlator (HRC). In this paper, h1(x) and h2(x) were modeled as Gaussian spatial acceptance filters (centered on different points in visual space), f(t) was a low-pass filter, and g(t) was a high-pass filter. In essence, the HRC multiplies delayed values of the contrast with current contrast values across two spatial points. The subtraction stage results in mirror symmetry, thereby enabling responses to both rightward and leftward motion. (b) The classical motion energy (ME) model applies several oriented spatiotemporal filters to the visual input. These filtered signals are subsequently squared and linearly combined to compute the 'motion energy.' (c) To compute the 2- and 3-point correlation images, we computed the product with the rightward orientation (left) and then subtracted the mirror symmetric product with a leftward orientation (center). This results in the images on the right, which are also displayed in Figure 1b. (d) HRC-like diagrams for the diverging and converging 3-point correlators used in Figure 1d.
- Supplementary Figure 2: Triple correlations only signify motion when the stimulus is light-dark asymmetric. (193 KB)
Each row presents a comparison between correlational motion signatures. Columns present: (i) context for each comparison; (ii) properties of pairwise motion estimators; (iii) properties of diverging 3-point estimators; and (iv) properties of converging 3-point estimators. (ai) Motion is approximated by the rigid translation of images. (aii-aiv) Cartoon of the correlation structure that each estimator detects. (bi) Example sinusoidal grating. (bii) Pair correlations signified motion across the image. (biii-biv) Triple correlations depended on the local phase of the sinusoidal grating and spatially averaged to zero. (ci) Example asymmetric grating. The luminance at each point in space was the luminance of the example sinusoidal grating raised to the tenth power. (cii) Pair correlations varied across the image. (ciii-iciv) Triple correlations still depended on the local phase of the grating, but their spatial average was nonzero. (di) Cartoon of an ensemble of sinusoidal gratings that vary in period and phase. (dii-div) The accuracy with which correlations convey motion was examined across this ensemble. The performance of each estimator was quantified through the Pearson's correlation between the estimator output and the simulated velocity. We linearly combined estimators to quantify the improvements afforded by multiple correlational signals. Neither spatial averaging nor triple correlations improved the motion estimate. (e) Same as (d), but for asymmetric gratings. In this case, both spatial averaging and triple correlations improved the accuracy of motion estimation. The numbers above each bar denote the fractional increase with respect to the 2-point estimate. Error bars are standard deviations over cross-validating trials (see Online Methods).
- Supplementary Figure 3: Correlational motion estimation with spatially varying contrast gain. (181 KB)
Rows a-c present a comparison between correlational motion signatures, when (a) the contrast gain is set locally by considering the average luminance over one degree squares of pixels, (b) the contrast gain is set locally by considering the average luminance over five degree squares of pixels, (c) the contrast gain is set globally by considering the average luminance over the full image. Columns apply to rows a-c and present: (i) example local luminance average, which sets the contrast gain; (ii) accuracy of pairwise motion estimators; (iii) accuracy of diverging 3-point estimators; and (iv) accuracy of converging 3-point estimators. Columns (ii)-(iv) are of the same format as in Figs. 1 and S2, and Figs. S3cii-civ are identical to Figs. 1cii-iv. Error bars are standard deviations over cross-validating trials (see Online Methods). (d) Contrast histograms when the contrast gain was determined by averaging over one degree squares of pixels (left), five degree squares of pixels (center), or the full visual field (right). The mean (i.e. c̄ = c), variance (i.e. (c−c̄)2), and third central moment (i.e. (c−c̄)3) are shown alongside each histogram.
- Supplementary Figure 4: Glider construction and model responses. (359 KB)
(a) Diagrams of the update rules that generate glider stimuli (see also Online Methods). Given a seed row and a seed column of pixel contrasts (upper left), the glider update rules fill in all remaining pixels, one row at a time, to generate an instantiation of the glider. The red points in the diagrams exemplify the update rule for each glider. The illustrative choices are not special, as any such pixel combinations will obey the update rule by construction. (b) Within a 2-point glider, all 3-point correlations average to 0. Similarly, within a 3-point glider, 2-point correlations (and the other 3-point correlations) average to 0. (c) Example space-time plots of the glider stimuli. (d) The ON/OFF model proposed in Eichner et al.27 correctly predicted the signs of the 2-point glider responses but did not predict the observed 3-point glider responses. Error bars are SEM, as in Fig. 3.
- Supplementary Figure 5: Drosophila respond to several triple correlations involving two points in space and three points in time. (135 KB)
The correlation structures for each glider and sample space-time intensity plots are shown at top, and the behavioral responses (relative to the positive 2-pt glider response) are shown below. We found that flies respond less strongly to these gliders than to the diverging and converging gliders (compare to Fig. 3d). We measured statistically significant responses in only 2 of 6 cases (two-tailed t-test, '*' corresponds to p=2.0×10-2 (t15=2.6) and '**' corresponds to p=3.7×10-3 (t15=3.4)). Error bars are SEM and N=16.
- Supplementary Figure 6: We computed the abundance of each correlational element in each edge type. (105 KB)
We first counted the number of times that each correlational element appeared in right and left-moving edges of the same polarity. The difference between the rightward and leftward counts provided an edge-specific directional signal (denoted “Net” in the figure). As expected, these directional signals depended on edge type for 3-point correlational elements but not for 2-point correlational elements. In particular, the sign of each 3-point directional signal inverted when the edge polarity inverted. In Figure 5, we used these directional signals as linear weighting coefficients to predict Drosophila behavioral responses to moving edges from measured glider responses.
- Supplementary Figure 7: EEG experimental details. (239 KB)
(a) Space-time plots of the two mirror-symmetric opposing edge adapters. The light and dark edges moved in opposite directions and are highlighted by the green and purple lines, respectively. Each presentation of the adapters had a random spatial phase. See also movie M1 for examples of the adapters. The probe temporally alternated between adapter A and adapter B. The spatial period of the adapting stimuli was doubled in the probe stimulus, but the speed of the edges remained the same. Green and purple lines highlight moving edges and show that the directions of the light and dark edges invert during the two halves of the probe. The probe was always presented with the same spatial phase. See also movie M2 for an example of the probe. (b) Evoked response waveforms for the probe stimuli under unadapted and adapted conditions. Data were only from the time interval shown in Figure 6a (and in panel c below). The data show that responses to identical stimuli were differentially affected by the identity of the adapter. (c) Strength of the first harmonic response as a function of time after the end of the adapting period. Both adapted responses were above baseline for approximately 5 seconds. Error patches on lines represent 1 SEM. (d) Phase-amplitude plots for the adapted EEG responses shown in Figure 6c. Ellipses represent 1 SEM.
- Supplementary Figure 8: Human psychophysics experimental details. (440 KB)
(a-b) Space-time intensity plots of the adapters and gliders. (a) Subjects' visual systems were adapted with a static adapter, with opposing edge motion, with light edge motion, and with dark edge motion. Each presentation of the adapters had a random spatial phase. See also movie M1 for an example opposing edge stimulus. (b) Space-time plots corresponding to a single row of each glider stimulus (shown after adaptation). All centroids move to the right in the top row and to the left in the bottom row. See also movie M3 for example glider stimuli. (c) Individual subject responses to the glider stimuli following adaptation to the static adapter. Individual subjects' responses are coded by color. The underlying bar plot shows subject means and SEMs for each glider. (d) Two out of nine subjects perceived an overwhelming motion after-effect after adaptation to light or dark edge motion. Shown here is one of these subject's glider responses to the gliders after adaptation to rightward-moving light edges. All responses were to the left, a result that we interpreted as a motion after-effect resulting from net motion in the adapter. The opposing edge adapter avoided this problem.
- Video 2: Probe edges. (1 MB, Download)
- This stimulus consisted of two alternating versions of the opposing edge stimuli. Light edges moved to the right for half of the probe and to the left for the other half. Dark and light edges always moved in opposite directions. See Fig. S7 for a space-time diagram of this stimulus.
- Video 3: Glider stimuli. (12.16 MB, Download)
- Here each 3-pt glider stimulus is presented sequentially: positive diverging, negative diverging, positive converging, and negative converging. All glider centroids moved to the right. Most subjects perceived leftward motion in the second glider and rightward motion in the first, third, and fourth gliders (see Figure 7 and S8).
- Supplementary Text and Figures (13,783 KB)
Supplementary Figures 1–8, Supplementary Table 1, Supplementary Modeling, Supplementary Movies 1–3