tb_project — 2D `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])

tb_project: input → output

*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)

Usage

Projects 3D points (n,3) onto 2D (n,2) via a camera (rvec,t,K) (perspective division).

> The detailed description below is the original text — the summary and the headings are translated.

`X_cam = R(rvec) @ X + t、x = K @ X_cam、uv = x[:2] / x[2]` を全点まとめて計算する

(`project_points と同じ規約)。rvec` は回転ベクトル(軸 × 角 [rad]、scipy の

`Rotation.from_rotvec)、t は (3,) 並進、K` は (3,3) 内部行列。返り値は (n,2) float で

列 0 が u(横・列方向)、列 1 が v(縦・行方向)、単位は K に従いピクセル。

注意(検証なし): カメラ後方や像平面上の点(`Z_cam <= 0`)を弾かず、そのまま除算する。

`Z_cam = 0` は 0 割で inf/NaN、負の Z は画像内に見える偽の座標になるので、可視性の判定は

呼び出し側で行う。形状の検証もしない(`np.asarray` で float 化するのみ)。

`bundle_adjust / mean_reprojection_error` の再投影残差はこの関数で作られる。

2-D 進化レジストリへ橋渡しした 3d の op `project。実装は同じで、呼び出し規約だけ op(v, a, b) に合わせてある。この op に調整点は無く、a も b` も使われない。

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.

Try it in Studio

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

Runnable examples (verified samples that actually call this op)

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

Ops the type connects to (they accept `keypoints` as input)

identity · tb_keypoints_uv_to_points · tb_keypoints_to_image2d

Same category (`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).*

tb_project — 2D typed op