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ellipse-3d-anatomy-constrained

Reconstruct 3D circle geometry from 2D ellipse parameters using anatomical constraints.

6|1|Updated May 11, 2026
Search Tags:#computer vision#3d reconstruction#eye tracking#gaze estimation#ellipse fitting#rodrigues rotation#anatomical constraints
One-click install
npx skills add https://github.com/yakeworld/Synthos --skill ellipse-3d-anatomy-constrained-yakeworld
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: ellipse-3d-anatomy-constrained
Source: https://github.com/yakeworld/Synthos/tree/main/skills/private/mlops/ellipse-3d-anatomy-constrained
Command: npx skills add https://github.com/yakeworld/Synthos --skill ellipse-3d-anatomy-constrained-yakeworld

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve? Recovering 3D circle geometry (optical axis, iris center, eyeball center) from a 2D projected ellipse is underdetermined due to azimuth ambiguity. This Skill resolves that ambiguity by applying anatomical constraints (R_eyeball = 2*R_iris, d = sqrt(3)*R_iris), compressing the degrees of freedom from 2 to 0 for eye-tracking research. ## Core Features & Use Cases - 3D Normal Vector Recovery: Computes the unit optical-axis normal n = [sin(alpha)*sin(beta), -sin(alpha)*cos(beta), cos(alpha)] from ellipse axes (cos(alpha) = b/a) and rotation angle beta. - Multi-Frame Eyeball Center Solving: Intersects optical-axis projection lines from at least two frames with iterative convergence (estimate, compute, converge) to determine the eyeball center. - Constraint Validation and Error Handling: Detects contradictions between ellipse parameters and anatomical constraints (imaginary z1) and refuses single-frame eyeball-center requests with contextual recovery guidance. - Use Case: In an AKNE eye-tracking study, feed two frames of iris ellipse parameters plus the known iris radius to obtain the 3D optical axis, iris center depth, eyeball center, and a Rodrigues rotation matrix for gaze reconstruction. ## Quick Start Provide at least two frames of ellipse parameters (semi-axes a and b, rotation angle beta, 2D center) and the iris radius, then ask the agent to solve for the 3D normal vector, iris center, eyeball center, and Rodrigues rotation matrix.

Frequently Asked Questions about ellipse-3d-anatomy-constrained

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I recover a 3D circle from a 2D ellipse projection?▼

Compute cos(alpha) = b/a from the ellipse semi-axes, then build the unit normal n = [sin(alpha)*sin(beta), -sin(alpha)*cos(beta), cos(alpha)] using the ellipse rotation angle beta. This gives the 3D orientation of the circle plane from a single frame.

How to eliminate azimuth ambiguity in ellipse-to-3D circle fitting?▼

Apply anatomical constraints R_eyeball = 2*R_iris and d = sqrt(3)*R_iris, which compress the degrees of freedom from 2 to 0. This removes the two-fold ambiguity that pure geometric back-projection cannot resolve.

Can I determine the eyeball center from a single ellipse frame?▼

No. A single frame yields only one optical-axis projection line, so the eyeball center is indeterminate. You need at least two frames with different rotation angles; the intersection of their projection lines, refined iteratively, gives the center.

Why does the iris center depth z1 come out imaginary?▼

An imaginary z1 means 3*R_iris^2 - (x1-x0)^2 - (y1-y0)^2 is negative, so the ellipse parameters contradict the anatomical constraints. The Skill treats this as an error, reports the conflict with context, and prompts you to recheck input data rather than outputting an invalid value.

What is the Rodrigues rotation formula used for in gaze reconstruction?▼

It builds the 3D rotation matrix M = I + [v]_x + [v]_x^2 / (1 + O*O') relating two optical-axis orientations. The result is verified for orthogonality (M^T*M = I, determinant +1) before being accepted.

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