typed op• Data kinds: points → keypoints
• Call: fullseye.apply(img, "tb_project_points", 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_points: stages (docs site)
On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):
▸ tb_project_points: other inputs (docs site)
3D point cloud (N,3) → image coordinates (u,v) and depth. Pinhole model (the forward direction of depth_to_points).
K = camera intrinsic matrix [[fx,0,cx],[0,fy,cy],[0,0,1]]. R,t give the extrinsic pose. The observation mapping of the world model.
P_cam = R @ P + t (R (3,3), t (3,); None means identity / zero) is projected by u = fx·X/Z + cx, v = fy·Y/Z + cy. Returns (uv (N,2), depth (N,)): uv[:,0] = u (column), uv[:,1] = v (row), depth is Z in camera coordinates (the raw value before clipping, negatives kept as they are). K is indexed as K[0,0] etc., so it must be a numpy array (a nested list is not allowed). Z is clipped to at least 1e-6 before dividing, so points behind the camera are not discarded either and get huge u,v (the caller removes them with depth > 0). Points outside the image are also returned (render_point_depth cuts by range). The inverse of depth_to_points; depth_to_points(render_point_depth(...)) makes a round trip.
The 3d op project_points 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 tuning points; 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_points 0.50 0.50
▸ Load this pipeline · Load & run
The examples below call the underlying ledger op project_points. 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).
• pnp_pose_outliers — py -3.11 examples_3d/pnp_pose_outliers.py
• pose_estimation — py -3.11 examples_3d/pose_estimation.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_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal · tb_voxel_grid_downsample · tb_mls_smooth
*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.