typed op• Data kinds: points → keypoints
• Call: fullseye.apply(img, "tb_project", 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_project: stages (docs site)
On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):
▸ tb_project: other inputs (docs site)
Projects 3D points (n,3) onto 2D (n,2) via a camera (rvec,t,K) (perspective division).
X_cam = R(rvec) @ X + t, x = K @ X_cam, uv = x[:2] / x[2] are computed for all points at once (same convention as project_points). rvec is a rotation vector (axis × angle [rad], scipy's Rotation.from_rotvec), t is the (3,) translation, K is the (3,3) intrinsic matrix. The return value is an (n,2) float where column 0 is u (horizontal, column direction) and column 1 is v (vertical, row direction), in pixels as given by K.
Caution (no validation): points behind the camera or on the image plane (Z_cam <= 0) are not rejected; the division is done as is. Z_cam = 0 gives inf/NaN from division by 0, and a negative Z gives a false coordinate that appears inside the image, so visibility must be decided by the caller. The shape is not validated either (only converted to float by np.asarray). The reprojection residuals of bundle_adjust / mean_reprojection_error are built with this function.
The 3d op project bridged into the 2-D evolution registry. The implementation is the same; only the calling convention is adapted to op(v, a, b). This op has no tunable parameters; neither a nor b is used.
• 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_points 0.50 0.50 tb_project 0.50 0.50
▸ Load this pipeline · Load & run
The examples below call the underlying ledger op project. 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).
• bundle_adjust — py -3.11 examples_3d/bundle_adjust.py
keypoints as input)identity · tb_keypoints_uv_to_points · tb_keypoints_to_image2d
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.