Annulus Sampling

Overview

Annulus sampling extracts local gradient evidence from a ring-shaped region around a hypothesis center. This evidence feeds into the support scoring stage, which determines how strongly the image supports the hypothesis.

Sampling strategy

The annulus is defined by an inner radius and an outer radius (typically computed as $(1 - m) \cdot r$ and $(1 + m) \cdot r$, where $r$ is the hypothesized radius and $m$ is the annulus_margin). Sample points are placed on a regular grid in polar coordinates:

• Angular axis: num_angular_samples evenly spaced angles in $[0, 2\pi)$.
• Radial axis: num_radial_samples linearly interpolated offsets between the inner and outer radii.

For each sample at angle $\theta$ and radius $\rho$, the image-space coordinates are

$$x = c_x + \rho \cos\theta, \qquad y = c_y + \rho \sin\theta.$$

Gradient readout

At each sample point, the gradient $(g_x, g_y)$ is read from the precomputed GradientField using bilinear interpolation, giving sub-pixel accuracy. Samples that fall outside image bounds are silently skipped.

The radial alignment at each sample is

$$a = \frac{|g_x \cos\theta + g_y \sin\theta|}{|\mathbf{g}|},$$

measuring how well the gradient direction agrees with the radial direction from the center. A perfect ring gives $a = 1$ at every sample.

Circular and elliptical variants

Two sampling functions are provided:

• sample_annulus – circular annulus, parameterized by center and inner/outer radii.
• sample_elliptical_annulus – elliptical annulus, parameterized by an Ellipse and margin. The radial direction at each angle is computed from the ellipse geometry, stretching sample placement along the appropriate axes.

Both return a SupportEvidence struct containing the individual gradient samples, the total sample count, and the mean gradient alignment.

Configuration

#![allow(unused)]
fn main() {
pub struct AnnulusSamplingConfig {
    /// Number of angular samples around the annulus. Default: 64.
    pub num_angular_samples: usize,
    /// Number of radial samples across the annulus width. Default: 9.
    pub num_radial_samples: usize,
}
}

The total number of sample points is num_angular_samples * num_radial_samples (576 by default). Increasing angular samples improves coverage estimation; increasing radial samples captures more of the annulus width, which is useful for thick rings or uncertain radius estimates.

Validation requires num_angular_samples >= 4 and num_radial_samples >= 1.