Support Scoring

Overview

Support scoring quantifies how strongly local image evidence supports a geometric hypothesis (circle or ellipse). The output is a SupportScore with component breakdown, used to rank hypotheses and reject weak detections.

Score components

Ringness

The ringness component measures gradient alignment within the annulus. It is the mean absolute radial alignment across all valid gradient samples:

$$\text{ringness} = \frac{1}{N} \sum_{i=1}^{N} |a_i|,$$

where $a_i$ is the radial alignment of the $i$-th sample (see annulus sampling). A value near 1.0 indicates strong ring-like support; values near 0.0 indicate random or tangential gradients.

Angular coverage

The angular_coverage component measures what fraction of the angular range $[0, 2\pi)$ is covered by sufficiently strong gradient responses. The annulus is divided into angular bins, and each bin is considered “covered” if at least one sample in that bin has a gradient magnitude above a threshold. Coverage is the fraction of covered bins.

This component guards against the case where a few strong edge fragments dominate the ringness score despite most of the ring being absent.

Weighted total

The combined score is a weighted sum clamped to $[0, 1]$:

$$\text{total} = \text{clamp}\bigl(w_r \cdot \text{ringness} + w_c \cdot \text{coverage},; 0,; 1\bigr),$$

where $w_r$ = weight_ringness (default 0.6) and $w_c$ = weight_coverage (default 0.4).

Degeneracy detection

If the number of valid gradient samples falls below min_samples (default 8), the score is flagged as degenerate (is_degenerate = true) and the total is set to 0.0. This prevents small hypotheses near image borders or in flat regions from receiving artificially high scores.

Rectified variant

score_rectified_circle_support computes the support score for a circle defined in rectified space (via a Homography). It transforms sample positions from the rectified circle into image coordinates, reads the gradient in image space, and pulls back the radial direction through the homography Jacobian to compute alignment. This ensures correct scoring even under perspective distortion.

Configuration

#![allow(unused)]
fn main() {
pub struct ScoringConfig {
    /// Annulus sampling parameters.
    pub sampling: AnnulusSamplingConfig,
    /// Fractional margin around the radius. Default: 0.3.
    pub annulus_margin: f32,
    /// Minimum samples to avoid degeneracy. Default: 8.
    pub min_samples: usize,
    /// Weight for ringness in total score. Default: 0.6.
    pub weight_ringness: f32,
    /// Weight for angular coverage in total score. Default: 0.4.
    pub weight_coverage: f32,
}
}