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Sparse coding predicts optic flow specificities of zebrafish pretectal neurons

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Abstract

Zebrafish pretectal neurons exhibit specificities for large-field optic flow patterns associated with rotatory or translatory body motion. We investigate the hypothesis that these specificities reflect the input statistics of natural optic flow. Realistic motion sequences were generated using computer graphics simulating self-motion in an underwater scene. Local retinal motion was estimated with a motion detector and encoded in four populations of directionally tuned retinal ganglion cells, represented as two signed input variables. This activity was then used as input into one of three learning networks: a sparse coding network (competitive learning), PCA whitening with subsequent sparse coding, and a backpropagation network (supervised learning). All simulations developed specificities for optic flow which are comparable to those found in a neurophysiological study (Kubo et al. in Neuron 81(6):1344–1359, 2016. https://doi.org/10.1016/j.neuron.2014.02.043), but relative frequencies of the various neuronal responses were best modeled by the sparse coding approach without whitening. We conclude that the optic flow neurons in the zebrafish pretectum do reflect the optic flow statistics. The predicted vectorial receptive fields show not only typical optic flow fields but also “Gabor” and dipole-shaped patterns that likely reflect difference fields needed for reconstruction by linear superposition.

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References

  1. Antinucci P et al (2016) Neural mechanisms generating orientation selectivity in the retina. Curr Biol 26(14):1802–1815. https://doi.org/10.1016/j.cub.2016.05.035

    Google Scholar 

  2. Bak-Coleman J, Smith D, Coombs S (2015) Going with, then against the flow: evidence against the optomotor hypothesis of fish rheotaxis. Anim Behav 107:7–17. https://doi.org/10.1016/j.anbehav.2015.06.007

    Google Scholar 

  3. Barlow HB (1972) Single units and sensation: A neuron doctrine for perceptual psychology? Perception 1(4):371–394. https://doi.org/10.1068/p010371

    Google Scholar 

  4. Dosovitskiy A et al (2015) FlowNet: learning optical flow with convolutional networks. In: 2015 IEEE international conference on computer vision (ICCV). IEEE, pp 2758–2766. https://doi.org/10.1109/iccv.2015.316

  5. Franz MO, Chahl JS, Krapp HG (2004) Insect-inspired estimation of egomotion. Neural Comput 16(11):2245–2260. https://doi.org/10.1162/0899766041941899

    MATH  Google Scholar 

  6. Honegger KS, Campbell RAA, Turner GC (2011) Cellular-resolution population imaging reveals robust sparse coding in the drosophila mushroom body. J Neurosci 31(33):11772–11785. https://doi.org/10.1523/JNEUROSCI.1099-11.2011

    Google Scholar 

  7. Hyvärinen A, Hurri J, Hoyer PO (2009) Natural image statistics. Springer, London. https://doi.org/10.1007/978-1-84882-491-1

    MATH  Google Scholar 

  8. Hyvärinen A, Oja E (2000) Independent component analysis: algorithms and applications. Neural Netw 13(4):411–430

    Google Scholar 

  9. Ilg E et al (2017) FlowNet 2.0: evolution of optical flow estimation with deep networks. In: 2017 IEEE conference on computer vision and pattern recognition (CVPR). IEEE. https://doi.org/10.1109/cvpr.2017.179

  10. Kubo F et al (2014) Functional architecture of an optic flow-responsive area that drives horizontal eye movements in zebrafish. Neuron 81(6):1344–1359. https://doi.org/10.1016/j.neuron.2014.02.043

    Google Scholar 

  11. Marr D (1982) Vision: a computational investigation into the human representation and processing of visual information. W.H. Freeman, New York

    Google Scholar 

  12. Nikolaou N et al (2012) Parametric functional maps of visual inputs to the tectum. Neuron 76(2):317–324. https://doi.org/10.1016/j.neuron.2012.08.040

    Google Scholar 

  13. Olshausen BA, Field DJ (1996) Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381(6583):607–609. https://doi.org/10.1038/381607a0

    Google Scholar 

  14. Olshausen BA, Field DJ (2005) How close are we to understanding V1? Neural Comput 17(8):1665–1699. https://doi.org/10.1162/0899766054026639

    MATH  Google Scholar 

  15. Olshausen BA, Field DJ (1997) Sparse coding with an overcomplete basis set: a strategy employed by V1? Vis Res 37(23):3311–3325. https://doi.org/10.1016/s0042-6989(97)00169-7

    Google Scholar 

  16. Orban GA (2008) Higher order visual processing in macaque extrastriate cortex. Physiol Rev 88(1):59–89. https://doi.org/10.1152/physrev.00008.2007

    Google Scholar 

  17. Papadopoulou M et al (2011) Normalization for sparse encoding of odors by a wide-field interneuron. Science 332(6030):721–725. https://doi.org/10.1126/science.1201835

    Google Scholar 

  18. Perrone JA (1992) Model for the computation of self-motion in biological systems. J Opt Soc Am A 9(2):177. https://doi.org/10.1364/josaa.9.000177

    MathSciNet  Google Scholar 

  19. Raudies F, Neumann H (2012) A review and evaluation of methods estimating ego-motion. Comput Vis Image Underst 116(5):606–633. https://doi.org/10.1016/j.cviu.2011.04.004

    Google Scholar 

  20. Rozell CJ et al (2008) Sparse coding via thresholding and local competition in neural circuits. Neural Comput 20(10):2526–2563. https://doi.org/10.1162/neco.2008.03-07-486

    MathSciNet  Google Scholar 

  21. Schultz PF et al (2014) Replicating kernels with a short stride allows sparse reconstructions with fewer independent kernels. arXiv preprint arXiv:1406.4205

  22. Spence R et al (2007) The behaviour and ecology of the zebrafish, Danio rerio. Biol Rev 83(1):13–34. https://doi.org/10.1111/j.1469-185X.2007.00030.x

    Google Scholar 

  23. Timofte R, Van Gool L (2015) Sparse flow: sparse matching for small to large displacement optical flow. In: 2015 IEEE winter conference on applications of computer vision. IEEE, pp 1100–1106. https://doi.org/10.1109/wacv.2015.151

  24. Verri A, Girosi F, Torre V (1989) Mathematical properties of the two-dimensional motion field: from singular points to motion parameters. JOSA A 6(5):698–712

    MathSciNet  Google Scholar 

  25. Vijayanarasimhan S et al (2017) Sfm-net: learning of structure and motion from video. arXiv preprint arXiv:1704.07804

  26. Wulff J, Black MJ (2015) Efficient sparse-to-dense optical flow estimation using a learned basis and layers. In: 2015 IEEE conference on computer vision and pattern recognition (CVPR). IEEE, pp 120–130. https://doi.org/10.1109/cvpr.2015.7298607

  27. Zhou T et al (2017) Unsupervised learning of depth and ego-motion from video. In: 2017 IEEE conference on computer vision and pattern recognition (CVPR). IEEE. https://doi.org/10.1109/cvpr.2017.700

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Acknowledgements

This work was carried out at the Department of Biology of the Eberhard-Karls-University, Tübingen, Germany. Additional support was obtained for TW from the Deutsche Forschungsgemeinschaft within the Werner Reichardt Center for Integrative Neuroscience (CIN), Tübingen.

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Correspondence to Gerrit A. Ecke.

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Ecke, G.A., Bruijns, S.A., Hölscher, J. et al. Sparse coding predicts optic flow specificities of zebrafish pretectal neurons. Neural Comput & Applic 32, 6745–6754 (2020). https://doi.org/10.1007/s00521-019-04500-6

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