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Nonlinear circuits for naturalistic visual motion estimation.

Fitzgerald JE, Clark DA - Elife (2015)

Bottom Line: Furthermore, a diversity of inputs to motion detecting neurons can provide access to more complex higher-order correlations.Collectively, these results illustrate how non-canonical computations improve motion estimation with naturalistic inputs.This argues that the complexity of the fly's motion computations, implemented in its elaborate circuits, represents a valuable feature of its visual motion estimator.

View Article: PubMed Central - PubMed

Affiliation: Center for Brain Science, Harvard University, Cambridge, United States.

ABSTRACT
Many animals use visual signals to estimate motion. Canonical models suppose that animals estimate motion by cross-correlating pairs of spatiotemporally separated visual signals, but recent experiments indicate that humans and flies perceive motion from higher-order correlations that signify motion in natural environments. Here we show how biologically plausible processing motifs in neural circuits could be tuned to extract this information. We emphasize how known aspects of Drosophila's visual circuitry could embody this tuning and predict fly behavior. We find that segregating motion signals into ON/OFF channels can enhance estimation accuracy by accounting for natural light/dark asymmetries. Furthermore, a diversity of inputs to motion detecting neurons can provide access to more complex higher-order correlations. Collectively, these results illustrate how non-canonical computations improve motion estimation with naturalistic inputs. This argues that the complexity of the fly's motion computations, implemented in its elaborate circuits, represents a valuable feature of its visual motion estimator.

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Correlations in binarized natural images.(A) We transformed each image in the van Hateren natural image database (van Hateren and van der Schaaf, 1998) with several binarizing nonlinearities. To implement the simplest binarizing nonlinearity, we set all pixels to +1 or −1 depending on whether that pixel exceeded or fell below the median intensity in the image. For the nonlinearity with two steps, the thresholds were at the 25th and 75th intensity percentiles. For the nonlinearity with three steps, the thresholds were at the 25th, 50th, and 75th intensity percentiles. When a pixel intensity exactly equaled a threshold, we considered its value below threshold. Binary nonlinearities with a larger number of steps produced grainier images that indicate a spatial decorrelation of the transformed image. (B) We computed second-order spatial correlation functions across the nonlinearly transformed natural image ensemble. This confirmed that each step in the binarizing nonlinearity further decorrelated the image ensemble. (C) In addition to decreasing the spatial extent of correlations, a larger number of transitions also degraded the performance of the front-end nonlinearity model.DOI:http://dx.doi.org/10.7554/eLife.09123.016
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fig7: Correlations in binarized natural images.(A) We transformed each image in the van Hateren natural image database (van Hateren and van der Schaaf, 1998) with several binarizing nonlinearities. To implement the simplest binarizing nonlinearity, we set all pixels to +1 or −1 depending on whether that pixel exceeded or fell below the median intensity in the image. For the nonlinearity with two steps, the thresholds were at the 25th and 75th intensity percentiles. For the nonlinearity with three steps, the thresholds were at the 25th, 50th, and 75th intensity percentiles. When a pixel intensity exactly equaled a threshold, we considered its value below threshold. Binary nonlinearities with a larger number of steps produced grainier images that indicate a spatial decorrelation of the transformed image. (B) We computed second-order spatial correlation functions across the nonlinearly transformed natural image ensemble. This confirmed that each step in the binarizing nonlinearity further decorrelated the image ensemble. (C) In addition to decreasing the spatial extent of correlations, a larger number of transitions also degraded the performance of the front-end nonlinearity model.DOI:http://dx.doi.org/10.7554/eLife.09123.016

Mentions: A comparison between the estimation performance of binarizing and equalizing front-end nonlinearities was complicated by the fact that the models produced outputs that differed in both their point statistics and their correlation structures. To gain more direct insight into how spatial correlations affect motion estimation performance, it would be helpful to compare front-end nonlinearity models that differ only through their output correlation structures. We implemented this comparison using a family of binarizing front-end nonlinearities that undergo multiple steps between +1 and −1 (Appendix figure 2A). Although these nonlinearities are not physiologically realistic, they are conceptually useful because they each produced a stimulus ensemble that minimized the kurtosis yet achieved distinct correlation structures (Appendix figure 2B). These nonlinearities thus allow us to assess directly whether spatial decorrelation of inputs degrades the motion estimation performance of the HRC. We found that each binarizing front-end nonlinearity model outperformed the original HRC (Appendix figure 2C). However, we found that the magnitude of the improvement decreased with the number of steps (Appendix figure 2C). Since spatial cross-correlations also decreased as a function of the number of steps (Appendix figure 2B), these results support our hypothesis that the correlations present in natural visual inputs aid the functionality of the standard HRC.10.7554/eLife.09123.016Appendix figure 2.Correlations in binarized natural images.


Nonlinear circuits for naturalistic visual motion estimation.

Fitzgerald JE, Clark DA - Elife (2015)

Correlations in binarized natural images.(A) We transformed each image in the van Hateren natural image database (van Hateren and van der Schaaf, 1998) with several binarizing nonlinearities. To implement the simplest binarizing nonlinearity, we set all pixels to +1 or −1 depending on whether that pixel exceeded or fell below the median intensity in the image. For the nonlinearity with two steps, the thresholds were at the 25th and 75th intensity percentiles. For the nonlinearity with three steps, the thresholds were at the 25th, 50th, and 75th intensity percentiles. When a pixel intensity exactly equaled a threshold, we considered its value below threshold. Binary nonlinearities with a larger number of steps produced grainier images that indicate a spatial decorrelation of the transformed image. (B) We computed second-order spatial correlation functions across the nonlinearly transformed natural image ensemble. This confirmed that each step in the binarizing nonlinearity further decorrelated the image ensemble. (C) In addition to decreasing the spatial extent of correlations, a larger number of transitions also degraded the performance of the front-end nonlinearity model.DOI:http://dx.doi.org/10.7554/eLife.09123.016
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4663970&req=5

fig7: Correlations in binarized natural images.(A) We transformed each image in the van Hateren natural image database (van Hateren and van der Schaaf, 1998) with several binarizing nonlinearities. To implement the simplest binarizing nonlinearity, we set all pixels to +1 or −1 depending on whether that pixel exceeded or fell below the median intensity in the image. For the nonlinearity with two steps, the thresholds were at the 25th and 75th intensity percentiles. For the nonlinearity with three steps, the thresholds were at the 25th, 50th, and 75th intensity percentiles. When a pixel intensity exactly equaled a threshold, we considered its value below threshold. Binary nonlinearities with a larger number of steps produced grainier images that indicate a spatial decorrelation of the transformed image. (B) We computed second-order spatial correlation functions across the nonlinearly transformed natural image ensemble. This confirmed that each step in the binarizing nonlinearity further decorrelated the image ensemble. (C) In addition to decreasing the spatial extent of correlations, a larger number of transitions also degraded the performance of the front-end nonlinearity model.DOI:http://dx.doi.org/10.7554/eLife.09123.016
Mentions: A comparison between the estimation performance of binarizing and equalizing front-end nonlinearities was complicated by the fact that the models produced outputs that differed in both their point statistics and their correlation structures. To gain more direct insight into how spatial correlations affect motion estimation performance, it would be helpful to compare front-end nonlinearity models that differ only through their output correlation structures. We implemented this comparison using a family of binarizing front-end nonlinearities that undergo multiple steps between +1 and −1 (Appendix figure 2A). Although these nonlinearities are not physiologically realistic, they are conceptually useful because they each produced a stimulus ensemble that minimized the kurtosis yet achieved distinct correlation structures (Appendix figure 2B). These nonlinearities thus allow us to assess directly whether spatial decorrelation of inputs degrades the motion estimation performance of the HRC. We found that each binarizing front-end nonlinearity model outperformed the original HRC (Appendix figure 2C). However, we found that the magnitude of the improvement decreased with the number of steps (Appendix figure 2C). Since spatial cross-correlations also decreased as a function of the number of steps (Appendix figure 2B), these results support our hypothesis that the correlations present in natural visual inputs aid the functionality of the standard HRC.10.7554/eLife.09123.016Appendix figure 2.Correlations in binarized natural images.

Bottom Line: Furthermore, a diversity of inputs to motion detecting neurons can provide access to more complex higher-order correlations.Collectively, these results illustrate how non-canonical computations improve motion estimation with naturalistic inputs.This argues that the complexity of the fly's motion computations, implemented in its elaborate circuits, represents a valuable feature of its visual motion estimator.

View Article: PubMed Central - PubMed

Affiliation: Center for Brain Science, Harvard University, Cambridge, United States.

ABSTRACT
Many animals use visual signals to estimate motion. Canonical models suppose that animals estimate motion by cross-correlating pairs of spatiotemporally separated visual signals, but recent experiments indicate that humans and flies perceive motion from higher-order correlations that signify motion in natural environments. Here we show how biologically plausible processing motifs in neural circuits could be tuned to extract this information. We emphasize how known aspects of Drosophila's visual circuitry could embody this tuning and predict fly behavior. We find that segregating motion signals into ON/OFF channels can enhance estimation accuracy by accounting for natural light/dark asymmetries. Furthermore, a diversity of inputs to motion detecting neurons can provide access to more complex higher-order correlations. Collectively, these results illustrate how non-canonical computations improve motion estimation with naturalistic inputs. This argues that the complexity of the fly's motion computations, implemented in its elaborate circuits, represents a valuable feature of its visual motion estimator.

Show MeSH
Related in: MedlinePlus