Retinal curl as a functional signal for heading estimation beyond the focus of expansion.
The 7 matches
- [1] § Results › Simulation results ↔ Python tree/curl-neural_model/ring_attractor_heading_v1.py, lines 144–266 · score 0.94 · Phase Portrait, drift dynamics, decoded heading, straight ahead prior, neural activity, ring attractor
- [2] § Results › Simulation results ↔ Python tree/curl-neural_model/ring_attractor_heading_v1.py, lines 144–266 · score 0.93 · neuron preferred headings, Phase portrait, sensory prior competition, normalized amplitude, straight ahead prior, ring position
- [3] § Appendix 2 › Neural network model of gaze-contingent heading bias ↔ Python tree/curl-neural_model/ring_attractor_heading_v1.py, lines 1–89 · score 0.92 · weak straight ahead, gaze modulated, bias emerges, neural model, heading representation, cortical
- [4] § Appendix 2 › Bias generation as sensory–prior competition ↔ Python tree/curl-neural_model/ring_attractor_heading_v1.py, lines 1–89 · score 0.83 · allows sensory evidence, weak straight ahead, weak prior, interaction, attractor, opposite
- [5] § Appendix 2 › Heading estimation and 3D path reconstruction ↔ Python tree/curl-neural_model/ring_attractor_heading_v1.py, lines 713–761 · score 0.71 · focal length, ring attractor, smoothed, horizontal, pixels, field
- [6] § Methods › Displays and conditions ↔ eLife-VOR-RA-2026-110770/3D_stimulus_generator.py, lines 102–163 · score 0.58 · simplex noise, stimulus generator, shaders, motion
- [7] § Appendix 2 › Local motion encoding ↔ Python tree/curl-neural_model/ring_attractor_heading_v1.py, lines 713–761 · score 0.51 · optical flow, encoding, V1, MT, motion, model
Paper
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The authors' code
Python · 947 lines · 40 KB · no license · 6 matches
ring_attractor_heading_v1.py, no license · at the source
Overview
Abstract
Prevailing models aiming at explaining heading assume that humans need to recover the Focus of Expansion (FoE) while accounting for eye-movement-induced rotation. We propose an alternative: the visual system utilizes mean retinal curl from fixations as a surrogate signal for heading, rendering the explicit recovery of the FoE unnecessary. Stationary participants viewed simulated walking paths on a large screen while fixating on points on the projected ground texture at varying eccentricities – a natural behavior inducing sustained retinal curl. Participants continuously reported perceived heading in 3D scene coordinates. To isolate the role of retinal curl, we employed a real-time manipulation that kept translational flow constant while the foveal curl component was either unaltered, canceled, or over-canceled. Under natural conditions (unaltered), participants exhibited systematic heading biases opposite the direction of gaze. Crucially, these biases vanished when we canceled the expected curl and flipped when we over-canceled it, identifying retinal curl as the specific driver of perceptual bias. We modeled these results using a simple feedback controller and a ring-attractor neural network featuring gaze-contingent inhibition and a ‘straight-ahead’ prior. These findings suggest that the brain exploits the geometry of gaze stabilization to simplify navigation, treating retinal curl as a functional signal rather than noise to be filtered.
Reproduced under the paper's license (CC BY), from the paper cited above.
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Its files are read in the Code ↔ Paper reader above, with 7 matches between paragraphs and lines of code.
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Availability: 1 check, the latest on 28 September 2026: the link answers (HTTP 200)
- 28 September 2026: the link answers (HTTP 200)
15 files, to read at the source
This repository has no license: its authors keep all rights. Read it at the source.
- Python tree/
curl-neural_model/ — Python, 947 lines, 6 matches, not shown herering_attractor_heading_v 1.py - Python tree/
curl-neural_model/ — Shell, 82 lines, not shown hererunCurlmodel_v2.sh - R/
loaddata.R — R, 238 lines, not shown here - R/
modelling.R — R, 1,091 lines, not shown here - R/
packages.R — R, 34 lines, not shown here - R/
plotting.R — R, 179 lines, not shown here - R/
prepdata.R — R, 169 lines, not shown here - R/
steering.R — R, 114 lines, not shown here - R/
utils.R — R, 24 lines, not shown here - docs/
controller_model.qmd — Quarto, 1,253 lines, not shown here - docs/
figures.qmd — Quarto, 954 lines, not shown here - docs/
index.qmd — Quarto, 449 lines, not shown here - docs/
neural_model_simulations — Quarto, 220 lines, not shown here.qmd - docs/
steering_simulation.qmd — Quarto, 163 lines, not shown here - readme.txt — Text, 74 lines, not shown here
supp:PMC13614786/elife-110770-code1.zip
Availability: 1 check, the latest on 28 September 2026: the link answers (HTTP 200)
- 28 September 2026: the link answers (HTTP 200)
1 file, to read at the source
This repository has no license: its authors keep all rights. Read it at the source.
- eLife-VOR-RA-2026-110770
/ — Python, 837 lines, 1 match, not shown here3D_stimulus_generator.py
The paper's code and data availability statement is in the Data section.
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- 15 scripts, each with its path and the digest of its content;
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Data
No dataset and no data link were found in the paper.
Data availability
All the data and code for the analysis are available through this link: https://
The following dataset was generated:
López-Moliner J, Zorpala KI. 2026. Beyond the Focus of Expansion: Retinal curl as a functional signal for heading estimation. Open Science Framework.
Reproduced under the paper's license (CC BY), from the paper cited above.
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Version 1, 28 September 2026: the first record
Recorded: type, language, journal, volume, pages, dates, 2 authors, 1 keyword, 7 MeSH terms, 2 funders, 71 references.
Cite
This paper
Zorpala, K. I., & López-Moliner, J. (2026). Retinal curl as a functional signal for heading estimation beyond the focus of expansion. eLife, 15, RP110770. https://
BibTeX
@article{zorpala2026reti
author = {Zorpala, Kontessa I and López-Moliner, Joan},
title = {{Retinal curl as a functional signal for heading estimation beyond the focus of expansion}},
journal = {eLife},
year = {2026},
month = sep,
volume = {15},
pages = {RP110770},
publisher = {eLife Sciences Publications, Ltd},
issn = {2050-084X},
doi = {10.7554/
url = {https://
pmid = {42788718},
pmcid = {PMC13614786}
}
RIS
TY - JOUR
AU - Zorpala, Kontessa I
AU - López-Moliner, Joan
TI - Retinal curl as a functional signal for heading estimation beyond the focus of expansion
T2 - eLife
J2 - Elife
PY - 2026
DA - 2026/
VL - 15
SP - RP110770
SN - 2050-084X
PB - eLife Sciences Publications, Ltd
DO - 10.7554/
UR - https://
LA - en
ER -
CSL-JSON
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