tb_stat_covariance — 2D typed op

• Data kinds: matrix → matrix

• Call: fullseye.apply(img, "tb_stat_covariance", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])

Usage

Sample covariance matrix of `(N, D) observations → (D, D)`.

Rows are observations, columns are variables — the `(N, D)` orientation

every Fullseye point/sample API uses (note `np.cov` defaults to the

*transposed* convention). Uses the unbiased `ddof=1` estimator (divides

by `N - 1), hence the N >= 2` requirement. The diagonal holds the

per-variable sample variances; the result is symmetric positive

semi-definite by construction, so it can go straight into

:func:mat_eigh for principal axes (the covariance-ellipse workflow).

HALCON: no public tuple/matrix operator — covariance lives inside HALCON's

calibration and matching internals only.

Typed bridge of the math op `stat_covariance into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. This op has no tunable parameter; a and b` are unused.

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

Runnable examples (verified samples that actually call this op)

• (none yet)

Ops the type connects to (they accept matrix as input)

identity · tb_mat_pinv · tb_mat_cond · tb_stat_correlation

Same category (typed)

tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_angle_3points · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal

*Provenance: ops.py — 2D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.