[Paper Review] Curvature Blindness from Polarity Breaks and Orientation Channel Fragmentation in V1

Michael Menke|arXiv (Cornell University)|Mar 10, 2026

Visual perception and processing mechanisms0 citations

TL;DR

A mathematical model explains curvature blindness as a product of polarity-segmented contour representations and fragmented orientation channels in V1, predicting a zigzag percept under specific contrast and curvature conditions. The model generalizes to curves with sign-changing curvature and inflection points between polarity reversals.

ABSTRACT

We present a mathematical model of the curvature blindness illusion in which sinusoids appear as angular zigzags when drawn with alternating contrast polarity against a gray background. The model identifies two complementary mechanisms, both operating in V1. First, polarity channel separation: simple cells are selective for contrast polarity, and lateral connections link only same polarity neurons; where the line switches from darker than background to lighter than background at each peak and trough, the encoding population changes and the lateral chain is broken, segmenting the contour into half-wavelength pieces. Second, orientation channel fragmentation: at moderate contrast, the active orientation window is narrow, and within each half-wavelength segment no single orientation channel spans the full range of edge normals; the inflection point at the center of each segment anchors a locally straight percept. Together, the two mechanisms produce a zigzag: polarity breaks supply the corners, and fragmentation straightens the segments between them.

Motivation & Objective

• Explain the neural mechanisms that generate curvature blindness in the Takahashi stimulus.
• Formalize how polarity segmentation and orientation channel fragmentation interact within V1 to distort curvature perception.
• Derive essential conditions and testable predictions for when the illusion occurs.
• Link the model to general curve forms with polarity alternation and sign-changing curvature.

Proposed method

• Model V1 edge detectors as orientation-tuned, polarity-specific simple cells with Gabor-like responses.
• Use divisive normalization and a Gaussian orientation tuning to compute edge responses.
• Define active orientation windows with a threshold condition based on a derived tau_eff(c) and alpha(c).
• Describe polarity segmentation at polarity reversals and fragmentation within half-wavelength segments when 2*alpha < theta_max.
• Show how inflection points anchor straight segments within fragments, yielding a piecewise-linear zigzag perception.
• Derive three necessary conditions for the illusion and corresponding predictions.

Experimental results

Research questions

• RQ1 What conditions are necessary for curvature blindness to occur with polarity-alternating sinusoids?
• RQ2 How do polarity segmentation and orientation channel fragmentation interact to produce a zigzag percept?
• RQ3 How does Michelson contrast influence the width of the active orientation window and the illusion strength?
• RQ4 Can the curvature blindness illusion generalize to curves with sign-changing curvature beyond simple sinusoids?

Key findings

• The illusion requires: (a) polarity reversals along the curve, (b) moderate contrast that narrows the active orientation window, and (c) inflection points between polarity reversals to anchor straight segments.
• Polarity segmentation breaks the contour at peaks and troughs, while orientation fragmentation prevents a single orientation channel from spanning a half-wavelength segment under moderate contrast.
• Inflection points anchor the straight segments by aligning the local fragment with zero curvature, enabling a zigzag percept.
• The model predicts generalization to any polarity-alternating curve with sign-changing curvature (e.g., S-curves, damped oscillations).
• There exists a contrast window [c_vis, c_crit] within which the illusion occurs, and c_crit grows with amplitude A/λ, extending visibility for larger amplitudes.