Outer Ellipse Fit
Once a radius hypothesis is available from the outer estimation stage, the detector fits an ellipse to the outer ring boundary using RANSAC with the Fitzgibbon direct least-squares solver.
Edge Point Sampling
For each proposal center, the detector casts radial rays outward at uniformly spaced angles and locates the intensity transition along each ray. The edge detection uses the Scharr gradient magnitude — each ray is sampled at sub-pixel resolution, and the point of maximum gradient response within the expected radius range is recorded as an edge point.
Key parameters from EdgeSampleConfig:
| Parameter | Description |
|---|---|
n_rays | Number of uniformly spaced radial rays (typically 64–128) |
r_min | Minimum search radius in pixels |
r_max | Maximum search radius in pixels |
When a PixelMapper is active, edge sampling operates in the working (undistorted) frame. The ray endpoints are mapped from working coordinates to image coordinates for pixel lookups, then the edge points are recorded in working-frame coordinates.
RANSAC Ellipse Fitting
The edge points are passed to a RANSAC loop that uses the Fitzgibbon ellipse fitter as the minimal solver:
- Sample: randomly select 6 edge points (the minimum for Fitzgibbon)
- Fit: compute the direct least-squares ellipse
- Score: count inliers using Sampson distance as the error metric
- Iterate: repeat for
max_itersiterations, keeping the best model - Refit: fit a final ellipse from all inliers of the best model
The Sampson distance provides a first-order approximation of the geometric distance from a point to the conic. It is cheaper to compute than the true geometric distance while being a much better approximation than algebraic distance.
See RANSAC Robust Estimation and Fitzgibbon Ellipse Fitting for mathematical details.
Validation Gates
After RANSAC fitting, the resulting ellipse must pass several validation checks:
| Gate | Default | Purpose |
|---|---|---|
| Semi-axis bounds | min_semi_axis = 3.0, max_semi_axis = 15.0 (derived from scale prior) | Reject fits that are too small or too large |
| Aspect ratio | max_aspect_ratio = 3.0 | Reject highly elongated fits (likely not a ring) |
| Inlier ratio | Minimum fraction of edge points that are inliers | Reject poor fits |
These bounds are automatically derived from the MarkerScalePrior via apply_marker_scale_prior.
Output
A successful outer fit produces an Ellipse struct:
#![allow(unused)]
fn main() {
pub struct Ellipse {
pub cx: f64, // center x
pub cy: f64, // center y
pub a: f64, // semi-major axis
pub b: f64, // semi-minor axis
pub angle: f64, // rotation angle (radians)
}
}The ellipse center (cx, cy) serves as the initial marker center estimate. This center is later refined by projective center correction if both inner and outer ellipses are available.
Source: detector/outer_fit.rs, ring/edge_sample.rs, conic/ransac.rs