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])
*The figure is the actual output on a synthetic 128×128 input. Left: input, right: output. Point clouds are drawn as a top-down scatter (brightness = z), 1-D series as a line plot, volumes as the maximum-intensity projection along z, videos as the middle frame, complex images as magnitude; return values that are not pictures are shown as the values themselves.*
*Knob a does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
*Knob b does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
Stages (the ops that come before → this op, left to right):
▸ tb_stat_covariance: stages (docs site)
On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):
▸ tb_stat_covariance: other inputs (docs site)
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.
• 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.
The program below has been verified to run (same input as the figure). In Studio's help this block becomes buttons that load and run it on the spot.
img_to_matrix 0.50 0.50 tb_stat_covariance 0.50 0.50
▸ Load this pipeline · Load & run
The examples below call the underlying ledger op stat_covariance. This bridge op is the same implementation adapted to the fn(v, a, b) convention, so the behaviour carries over unchanged (only the call form differs).
• math_metrology — py -3.11 examples/math_metrology.py
• poc_thermal_radiometry — py -3.11 examples/poc_thermal_radiometry.py
matrix as input)identity · tb_mat_pinv · tb_mat_cond · tb_stat_correlation · matrix_to_img
typed)tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal · tb_voxel_grid_downsample
*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.