{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T16:49:38Z","timestamp":1791996578098,"version":"4.4.0"},"reference-count":50,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,9,21]],"date-time":"2023-09-21T00:00:00Z","timestamp":1695254400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2019s Horizon H2020-EIC-FETPROACT-2019","award":["951910"],"award-info":[{"award-number":["951910"]}]},{"name":"European Union\u2019s Horizon H2020-EIC-FETPROACT-2019","award":["945539"],"award-info":[{"award-number":["945539"]}]},{"name":"European Union\u2019s Horizon H2020-EIC-FETPROACT-2019","award":["952215"],"award-info":[{"award-number":["952215"]}]},{"name":"European Union\u2019s Horizon H2020-EIC-FETPROACT-2019","award":["820213"],"award-info":[{"award-number":["820213"]}]},{"name":"European Union\u2019s Horizon H2020-EIC-FETPROACT-2019","award":["2017KZNZLN"],"award-info":[{"award-number":["2017KZNZLN"]}]},{"name":"European Union\u2019s Horizon H2020-EIC-FETPROACT-2019","award":["PE0000013-FAIR"],"award-info":[{"award-number":["PE0000013-FAIR"]}]},{"name":"European Union\u2019s Horizon H2020-EIC-FETPROACT-2019","award":["IR0000011\u2013EBRAINS-Italy"],"award-info":[{"award-number":["IR0000011\u2013EBRAINS-Italy"]}]},{"name":"Human Brain Project SGA3","award":["951910"],"award-info":[{"award-number":["951910"]}]},{"name":"Human Brain Project SGA3","award":["945539"],"award-info":[{"award-number":["945539"]}]},{"name":"Human Brain Project SGA3","award":["952215"],"award-info":[{"award-number":["952215"]}]},{"name":"Human Brain Project SGA3","award":["820213"],"award-info":[{"award-number":["820213"]}]},{"name":"Human Brain Project SGA3","award":["2017KZNZLN"],"award-info":[{"award-number":["2017KZNZLN"]}]},{"name":"Human Brain Project SGA3","award":["PE0000013-FAIR"],"award-info":[{"award-number":["PE0000013-FAIR"]}]},{"name":"Human Brain Project SGA3","award":["IR0000011\u2013EBRAINS-Italy"],"award-info":[{"award-number":["IR0000011\u2013EBRAINS-Italy"]}]},{"name":"TAILOR","award":["951910"],"award-info":[{"award-number":["951910"]}]},{"name":"TAILOR","award":["945539"],"award-info":[{"award-number":["945539"]}]},{"name":"TAILOR","award":["952215"],"award-info":[{"award-number":["952215"]}]},{"name":"TAILOR","award":["820213"],"award-info":[{"award-number":["820213"]}]},{"name":"TAILOR","award":["2017KZNZLN"],"award-info":[{"award-number":["2017KZNZLN"]}]},{"name":"TAILOR","award":["PE0000013-FAIR"],"award-info":[{"award-number":["PE0000013-FAIR"]}]},{"name":"TAILOR","award":["IR0000011\u2013EBRAINS-Italy"],"award-info":[{"award-number":["IR0000011\u2013EBRAINS-Italy"]}]},{"name":"European Research Council","award":["951910"],"award-info":[{"award-number":["951910"]}]},{"name":"European Research Council","award":["945539"],"award-info":[{"award-number":["945539"]}]},{"name":"European Research Council","award":["952215"],"award-info":[{"award-number":["952215"]}]},{"name":"European Research Council","award":["820213"],"award-info":[{"award-number":["820213"]}]},{"name":"European Research Council","award":["2017KZNZLN"],"award-info":[{"award-number":["2017KZNZLN"]}]},{"name":"European Research Council","award":["PE0000013-FAIR"],"award-info":[{"award-number":["PE0000013-FAIR"]}]},{"name":"European Research Council","award":["IR0000011\u2013EBRAINS-Italy"],"award-info":[{"award-number":["IR0000011\u2013EBRAINS-Italy"]}]},{"name":"Italian Ministry for Research MIUR","award":["951910"],"award-info":[{"award-number":["951910"]}]},{"name":"Italian Ministry for Research MIUR","award":["945539"],"award-info":[{"award-number":["945539"]}]},{"name":"Italian Ministry for Research MIUR","award":["952215"],"award-info":[{"award-number":["952215"]}]},{"name":"Italian Ministry for Research MIUR","award":["820213"],"award-info":[{"award-number":["820213"]}]},{"name":"Italian Ministry for Research MIUR","award":["2017KZNZLN"],"award-info":[{"award-number":["2017KZNZLN"]}]},{"name":"Italian Ministry for Research MIUR","award":["PE0000013-FAIR"],"award-info":[{"award-number":["PE0000013-FAIR"]}]},{"name":"Italian Ministry for Research MIUR","award":["IR0000011\u2013EBRAINS-Italy"],"award-info":[{"award-number":["IR0000011\u2013EBRAINS-Italy"]}]},{"name":"PNRR MUR","award":["951910"],"award-info":[{"award-number":["951910"]}]},{"name":"PNRR MUR","award":["945539"],"award-info":[{"award-number":["945539"]}]},{"name":"PNRR MUR","award":["952215"],"award-info":[{"award-number":["952215"]}]},{"name":"PNRR MUR","award":["820213"],"award-info":[{"award-number":["820213"]}]},{"name":"PNRR MUR","award":["2017KZNZLN"],"award-info":[{"award-number":["2017KZNZLN"]}]},{"name":"PNRR MUR","award":["PE0000013-FAIR"],"award-info":[{"award-number":["PE0000013-FAIR"]}]},{"name":"PNRR MUR","award":["IR0000011\u2013EBRAINS-Italy"],"award-info":[{"award-number":["IR0000011\u2013EBRAINS-Italy"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>Depth estimation is an ill-posed problem; objects of different shapes or dimensions, even if at different distances, may project to the same image on the retina. Our brain uses several cues for depth estimation, including monocular cues such as motion parallax and binocular cues such as diplopia. However, it remains unclear how the computations required for depth estimation are implemented in biologically plausible ways. State-of-the-art approaches to depth estimation based on deep neural networks implicitly describe the brain as a hierarchical feature detector. Instead, in this paper we propose an alternative approach that casts depth estimation as a problem of active inference. We show that depth can be inferred by inverting a hierarchical generative model that simultaneously predicts the eyes\u2019 projections from a 2D belief over an object. Model inversion consists of a series of biologically plausible homogeneous transformations based on Predictive Coding principles. Under the plausible assumption of a nonuniform fovea resolution, depth estimation favors an active vision strategy that fixates the object with the eyes, rendering the depth belief more accurate. This strategy is not realized by first fixating on a target and then estimating the depth; instead, it combines the two processes through action\u2013perception cycles, with a similar mechanism of the saccades during object recognition. The proposed approach requires only local (top-down and bottom-up) message passing, which can be implemented in biologically plausible neural circuits.<\/jats:p>","DOI":"10.3390\/biomimetics8050445","type":"journal-article","created":{"date-parts":[[2023,9,21]],"date-time":"2023-09-21T21:16:49Z","timestamp":1695331009000},"page":"445","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Active Vision in Binocular Depth Estimation: A Top-Down Perspective"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-4481-8727","authenticated-orcid":false,"given":"Matteo","family":"Priorelli","sequence":"first","affiliation":[{"name":"Institute of Cognitive Sciences and Technologies, National Research Council of Italy, 35137 Padova, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6813-8282","authenticated-orcid":false,"given":"Giovanni","family":"Pezzulo","sequence":"additional","affiliation":[{"name":"Institute of Cognitive Sciences and Technologies, National Research Council of Italy, 00185 Rome, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0642-259X","authenticated-orcid":false,"given":"Ivilin Peev","family":"Stoianov","sequence":"additional","affiliation":[{"name":"Institute of Cognitive Sciences and Technologies, National Research Council of Italy, 35137 Padova, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/S0896-6273(00)81238-6","article-title":"Binocular disparity and the perception of depth","volume":"18","author":"Qian","year":"1997","journal-title":"Neuron"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1038\/nrn2131","article-title":"Binocular depth perception and the cerebral cortex","volume":"8","author":"Parker","year":"2007","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1016\/j.neuron.2007.06.040","article-title":"Anterior Regions of Monkey Parietal Cortex Process Visual 3D Shape","volume":"55","author":"Durand","year":"2007","journal-title":"Neuron"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"820","DOI":"10.1038\/nn1461","article-title":"3D shape perception from combined depth cues in human visual cortex","volume":"8","author":"Welchman","year":"2005","journal-title":"Nat. Neurosci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s00221-007-1081-2","article-title":"Depth cues, rather than perceived depth, govern vergence","volume":"184","author":"Wismeijer","year":"2008","journal-title":"Exp. Brain Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2390","DOI":"10.1162\/neco_a_01239","article-title":"Bayesian filtering with multiple internal models: Toward a theory of social intelligence","volume":"31","author":"Isomura","year":"2019","journal-title":"Neural Comput."},{"key":"ref_7","first-page":"279","article-title":"Perceptual illusions and brain models","volume":"171","author":"Gregory","year":"1968","journal-title":"Proc. R. Soc. Lond. Ser. Biol. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1038\/4580","article-title":"Predictive coding in the visual cortex: A functional interpretation of some extra-classical receptive-field effects","volume":"2","author":"Rao","year":"1999","journal-title":"Nat. Neurosci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1098\/rstb.2005.1622","article-title":"A theory of cortical responses","volume":"360","author":"Friston","year":"2005","journal-title":"Philos. Trans. R. Soc. Lond. Ser. B Biol. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Parr, T., Pezzulo, G., and Friston, K.J. (2022). Active Inference: The Free Energy Principle in Mind, Brain, and Behavior, MIT Press.","DOI":"10.7551\/mitpress\/12441.001.0001"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1162\/NECO_a_00912","article-title":"Active inference: A process theory","volume":"29","author":"Friston","year":"2017","journal-title":"Neural Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.tics.2018.01.009","article-title":"Hierarchical active inference: A theory of motivated control","volume":"22","author":"Pezzulo","year":"2018","journal-title":"Trends Cogn. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.pneurobio.2015.09.001","article-title":"Active inference, homeostatic regulation and adaptive behavioural control","volume":"134","author":"Pezzulo","year":"2015","journal-title":"Prog. Neurobiol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.neuroimage.2006.08.035","article-title":"Variational free energy and the Laplace approximation","volume":"34","author":"Friston","year":"2007","journal-title":"NeuroImage"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1162\/NETN_a_00018","article-title":"The graphical brain: Belief propagation and active inference","volume":"1","author":"Friston","year":"2017","journal-title":"Netw. Neurosci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1007\/s00429-012-0475-5","article-title":"Predictions not commands: Active inference in the motor system","volume":"218","author":"Adams","year":"2013","journal-title":"Brain Struct. Funct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/j.neuropsychologia.2018.01.041","article-title":"Active inference and the anatomy of oculomotion","volume":"111","author":"Parr","year":"2018","journal-title":"Neuropsychologia"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jneumeth.2015.01.003","article-title":"Active inference and oculomotor pursuit: The dynamic causal modelling of eye movements","volume":"242","author":"Adams","year":"2015","journal-title":"J. Neurosci. Methods"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Lanillos, P., and Cheng, G. (2018, January 1\u20135). Adaptive Robot Body Learning and Estimation Through Predictive Coding. Proceedings of the 2018 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain.","DOI":"10.1109\/IROS.2018.8593684"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"20160616","DOI":"10.1098\/rsif.2016.0616","article-title":"Active inference and robot control: A case study","volume":"13","author":"Nizard","year":"2016","journal-title":"J. R. Soc. Interface"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Priorelli, M., Pezzulo, G., and Stoianov, I.P. (2023). Deep kinematic inference affords efficient and scalable control of bodily movements. bioRxiv, 1\u201333.","DOI":"10.1101\/2023.05.04.539409"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1128694","DOI":"10.3389\/fncom.2023.1128694","article-title":"Flexible Intentions: An Active Inference Theory","volume":"17","author":"Priorelli","year":"2023","journal-title":"Front. Comput. Neurosci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Priorelli, M., and Stoianov, I.P. (2023, January 13\u201315). Efficient motor learning through action-perception cycles in deep kinematic inference. Proceedings of the 4th International Workshop on Active Inference, Ghent, Belgium.","DOI":"10.1007\/978-3-031-47958-8_5"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1016\/j.tics.2016.07.006","article-title":"Perceptual cycles","volume":"20","author":"VanRullen","year":"2016","journal-title":"Trends Cogn. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.visres.2016.06.015","article-title":"Distribution differences of macular cones measured by AOSLO: Variation in slope from fovea to periphery more pronounced than differences in total cones","volume":"132","author":"Elsner","year":"2017","journal-title":"Vis. Res."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhu, Q., Triesch, J., and Shi, B.E. (2020, January 26\u201330). Integration of Vergence, Cyclovergence, and Saccades through Active Efficient Coding. Proceedings of the ICDL-EpiRob 2020\u201410th IEEE International Conference on Development and Learning and Epigenetic Robotics, Valparaiso, Chile.","DOI":"10.1109\/ICDL-EpiRob48136.2020.9278126"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Lugtigheid, A.J., Wilcox, L.M., Allison, R.S., and Howard, I.P. (2013). Vergence eye movements are not essential for stereoscopic depth. Proc. R. Soc. Biol. Sci., 281.","DOI":"10.1098\/rspb.2013.2118"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3176","DOI":"10.3758\/s13414-020-02006-1","article-title":"Does vision extract absolute distance from vergence?","volume":"82","author":"Linton","year":"2020","journal-title":"Atten. Percept. Psychophys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1163\/15685680152692024","article-title":"The role of vergence in the perception of distance: A fair test of bishop Berkeley\u2019s claim","volume":"15","author":"Logvinenko","year":"2002","journal-title":"Spat. Vis."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1111\/j.1475-1313.1997.tb00064.x","article-title":"Fixation disparity and accommodation as a function of viewing distance and prism load","volume":"17","author":"Jaschinski","year":"1997","journal-title":"Ophthalmic Physiol. Opt."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1038\/38496","article-title":"Vergence eye movements in response to binocular disparity without depth perception","volume":"389","author":"Masson","year":"1997","journal-title":"Nature"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/j.neunet.2021.08.037","article-title":"Active inference through whiskers","volume":"144","author":"Mannella","year":"2021","journal-title":"Neural Netw."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.copsyc.2018.10.006","article-title":"Attention or salience?","volume":"29","author":"Parr","year":"2019","journal-title":"Curr. Opin. Psychol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1006\/cviu.2001.0924","article-title":"Disparity Estimation on Log-Polar Images and Vergence Control","volume":"83","author":"Manzotti","year":"2001","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s11263-016-0936-z","article-title":"A Portable Bio-Inspired Architecture for Efficient Robotic Vergence Control","volume":"121","author":"Gibaldi","year":"2017","journal-title":"Int. J. Comput. Vis."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"151","DOI":"10.3389\/fpsyg.2012.00151","article-title":"Perceptions as hypotheses: Saccades as experiments","volume":"3","author":"Friston","year":"2012","journal-title":"Front. Psychol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"896229","DOI":"10.3389\/fnbot.2022.896229","article-title":"Reclaiming saliency: Rhythmic precision-modulated action and perception","volume":"16","author":"Novicky","year":"2022","journal-title":"Front. Neurorobot."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.1016\/j.neuron.2013.03.007","article-title":"The theta-gamma neural code","volume":"77","author":"Lisman","year":"2013","journal-title":"Neuron"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood from incomplete data via the EM algorithm","volume":"39","author":"Dempster","year":"1977","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.tics.2018.12.005","article-title":"Theories of Error Back-Propagation in the Brain","volume":"23","author":"Whittington","year":"2019","journal-title":"Trends Cogn. Sci."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1329","DOI":"10.1162\/neco_a_01497","article-title":"Predictive Coding Approximates Backprop Along Arbitrary Computation Graphs","volume":"34","author":"Millidge","year":"2022","journal-title":"Neural Comput."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1109\/TPAMI.2012.89","article-title":"State-of-the-art in visual attention modeling","volume":"35","author":"Borji","year":"2013","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1006\/cviu.1996.0034","article-title":"Analysis of Error in Depth Perception with Vergence and Spatially Varying Sensing","volume":"63","author":"Sahabi","year":"1996","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1167\/9.13.11","article-title":"Latitude and longitude vertical disparities","volume":"9","author":"Read","year":"2009","journal-title":"J. Vis."},{"key":"ref_45","unstructured":"Lanillos, P., and Cheng, G. (2020). Robot self\/other distinction: Active inference meets neural networks learning in a mirror. arXiv."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2025","DOI":"10.1162\/neco_a_01228","article-title":"A novel predictive-coding-inspired variational RNN model for online prediction and recognition","volume":"31","author":"Ahmadi","year":"2019","journal-title":"Neural Comput."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1080\/01691864.2023.2225232","article-title":"World models and predictive coding for cognitive and developmental robotics: Frontiers and challenges","volume":"37","author":"Taniguchi","year":"2023","journal-title":"Adv. Robot."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.neunet.2021.05.010","article-title":"Robot navigation as hierarchical active inference","volume":"142","author":"Verbelen","year":"2021","journal-title":"Neural Netw."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"103474","DOI":"10.1016\/j.robot.2020.103474","article-title":"Learning robots to grasp by demonstration","volume":"127","author":"Verbelen","year":"2020","journal-title":"Robot. Auton. Syst."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Rood, T., van Gerven, M., and Lanillos, P. (2020, January 14). A Deep Active Inference Model of the Rubber-Hand Illusion. Proceedings of the Active Inference: First International Workshop, IWAI 2020, Co-located with ECML\/PKDD 2020, Ghent, Belgium.","DOI":"10.1007\/978-3-030-64919-7_10"}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/8\/5\/445\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:54:51Z","timestamp":1760129691000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/8\/5\/445"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,21]]},"references-count":50,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["biomimetics8050445"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics8050445","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2023.07.15.549132","asserted-by":"object"}]},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,21]]}}}