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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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The Hassenstein-Reichardt correlator (HRC) model is an incomplete description of Drosophila's motion estimator.(A) Diagram of the HRC model. (B) We assessed motion estimation performance across an ensemble of naturalistic motions, each of which consisted of a natural image (van Hateren and van der Schaaf, 1998) and a velocity chosen from a normal distribution. (C) We quantified model accuracy by comparing the model response to the true velocity using the mean squared error. (D) We summarized the error with the correlation coefficient between the model output and the true velocity. (E) In previous work (Clark et al., 2014), we used a panoramic display and spherical treadmill to measure the rotational responses of Drosophila to visual stimuli. (F) We presented flies with binary stimuli called gliders (Hu and Victor, 2010), which imposed specific 2-point and 3-point correlations (Clark et al., 2014). (G) Flies turned in response to 3-point glider stimuli, but these responses cannot be predicted by the standard HRC. (H) Diagram of the converging 3-point correlator, which is designed to detect higher-order motion signals like those found in 3-point glider stimuli. (I) Adding the converging 3-point correlator to the HRC improved motion estimation performance with naturalistic inputs. We optimized weighting coefficients to minimize the mean squared error over the ensemble of naturalistic motions and used cross-validation to protect against over-fitting. (J) This model predicted that Drosophila would weakly turn in response to 3-point glider stimuli.DOI:http://dx.doi.org/10.7554/eLife.09123.004
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fig1: The Hassenstein-Reichardt correlator (HRC) model is an incomplete description of Drosophila's motion estimator.(A) Diagram of the HRC model. (B) We assessed motion estimation performance across an ensemble of naturalistic motions, each of which consisted of a natural image (van Hateren and van der Schaaf, 1998) and a velocity chosen from a normal distribution. (C) We quantified model accuracy by comparing the model response to the true velocity using the mean squared error. (D) We summarized the error with the correlation coefficient between the model output and the true velocity. (E) In previous work (Clark et al., 2014), we used a panoramic display and spherical treadmill to measure the rotational responses of Drosophila to visual stimuli. (F) We presented flies with binary stimuli called gliders (Hu and Victor, 2010), which imposed specific 2-point and 3-point correlations (Clark et al., 2014). (G) Flies turned in response to 3-point glider stimuli, but these responses cannot be predicted by the standard HRC. (H) Diagram of the converging 3-point correlator, which is designed to detect higher-order motion signals like those found in 3-point glider stimuli. (I) Adding the converging 3-point correlator to the HRC improved motion estimation performance with naturalistic inputs. We optimized weighting coefficients to minimize the mean squared error over the ensemble of naturalistic motions and used cross-validation to protect against over-fitting. (J) This model predicted that Drosophila would weakly turn in response to 3-point glider stimuli.DOI:http://dx.doi.org/10.7554/eLife.09123.004

Mentions: The HRC is the dominant model of motion computation in flies and other insects. In this paper we describe several generalizations of the HRC, but it is helpful to first review this canonical model. The HRC comprises three stages of processing. First, two different temporal filters (here, a low-pass filter and a high-pass filter ) are applied to each of two spatially filtered visual input streams (Figure 1A, ‘Materials and methods’). These four filtered signals are then paired and multiplied (Figure 1A). Finally, the HRC takes the difference between the two multiplied signals to obtain a mirror anti-symmetric motion estimator (Figure 1A). Because the HRC combines its two input channels via a multiplication operation, the average output of the HRC depends only on 2-point correlations in the visual stimulus. We thus refer to the HRC as a 2-point correlator, and we will return to this mathematical characterization of the HRC repeatedly throughout this work.10.7554/eLife.09123.004Figure 1.The Hassenstein-Reichardt correlator (HRC) model is an incomplete description of Drosophila's motion estimator.


Nonlinear circuits for naturalistic visual motion estimation.

Fitzgerald JE, Clark DA - Elife (2015)

The Hassenstein-Reichardt correlator (HRC) model is an incomplete description of Drosophila's motion estimator.(A) Diagram of the HRC model. (B) We assessed motion estimation performance across an ensemble of naturalistic motions, each of which consisted of a natural image (van Hateren and van der Schaaf, 1998) and a velocity chosen from a normal distribution. (C) We quantified model accuracy by comparing the model response to the true velocity using the mean squared error. (D) We summarized the error with the correlation coefficient between the model output and the true velocity. (E) In previous work (Clark et al., 2014), we used a panoramic display and spherical treadmill to measure the rotational responses of Drosophila to visual stimuli. (F) We presented flies with binary stimuli called gliders (Hu and Victor, 2010), which imposed specific 2-point and 3-point correlations (Clark et al., 2014). (G) Flies turned in response to 3-point glider stimuli, but these responses cannot be predicted by the standard HRC. (H) Diagram of the converging 3-point correlator, which is designed to detect higher-order motion signals like those found in 3-point glider stimuli. (I) Adding the converging 3-point correlator to the HRC improved motion estimation performance with naturalistic inputs. We optimized weighting coefficients to minimize the mean squared error over the ensemble of naturalistic motions and used cross-validation to protect against over-fitting. (J) This model predicted that Drosophila would weakly turn in response to 3-point glider stimuli.DOI:http://dx.doi.org/10.7554/eLife.09123.004
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getmorefigures.php?uid=PMC4663970&req=5

fig1: The Hassenstein-Reichardt correlator (HRC) model is an incomplete description of Drosophila's motion estimator.(A) Diagram of the HRC model. (B) We assessed motion estimation performance across an ensemble of naturalistic motions, each of which consisted of a natural image (van Hateren and van der Schaaf, 1998) and a velocity chosen from a normal distribution. (C) We quantified model accuracy by comparing the model response to the true velocity using the mean squared error. (D) We summarized the error with the correlation coefficient between the model output and the true velocity. (E) In previous work (Clark et al., 2014), we used a panoramic display and spherical treadmill to measure the rotational responses of Drosophila to visual stimuli. (F) We presented flies with binary stimuli called gliders (Hu and Victor, 2010), which imposed specific 2-point and 3-point correlations (Clark et al., 2014). (G) Flies turned in response to 3-point glider stimuli, but these responses cannot be predicted by the standard HRC. (H) Diagram of the converging 3-point correlator, which is designed to detect higher-order motion signals like those found in 3-point glider stimuli. (I) Adding the converging 3-point correlator to the HRC improved motion estimation performance with naturalistic inputs. We optimized weighting coefficients to minimize the mean squared error over the ensemble of naturalistic motions and used cross-validation to protect against over-fitting. (J) This model predicted that Drosophila would weakly turn in response to 3-point glider stimuli.DOI:http://dx.doi.org/10.7554/eLife.09123.004
Mentions: The HRC is the dominant model of motion computation in flies and other insects. In this paper we describe several generalizations of the HRC, but it is helpful to first review this canonical model. The HRC comprises three stages of processing. First, two different temporal filters (here, a low-pass filter and a high-pass filter ) are applied to each of two spatially filtered visual input streams (Figure 1A, ‘Materials and methods’). These four filtered signals are then paired and multiplied (Figure 1A). Finally, the HRC takes the difference between the two multiplied signals to obtain a mirror anti-symmetric motion estimator (Figure 1A). Because the HRC combines its two input channels via a multiplication operation, the average output of the HRC depends only on 2-point correlations in the visual stimulus. We thus refer to the HRC as a 2-point correlator, and we will return to this mathematical characterization of the HRC repeatedly throughout this work.10.7554/eLife.09123.004Figure 1.The Hassenstein-Reichardt correlator (HRC) model is an incomplete description of Drosophila's motion estimator.

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