fundamental_8point — 3D `two_view` op

• Data kinds: image2d × image2d → matrix

• Call: import fullseye as fs; fs.ledger.fundamental_8point(pts1, pts2) (to call the implementation directly, import twoview; twoview.fundamental_8point(pts1, pts2); from the registry, ops3d.get("fundamental_8point"))

Usage

Estimate the fundamental matrix F by the normalised eight-point algorithm (rank 2 enforced). → F (3,3). At least eight points are needed.

Raises ValueError: points are not (N,2) / non-finite / fewer than 8 points / correspondence counts mismatch.

Procedure: Hartley-normalise the points of both images (centroid at the origin, mean distance √2) → take the smallest singular vector of the 9-column coefficient matrix as F → set the 3rd singular value to 0 to force rank-2 → denormalise with T2ᵀ F T1 → normalise by dividing by F[2,2] (if that is almost 0, divide by the Frobenius norm).

• Correspondences are (N,2) pixel coordinates (x, y). Convention: x2ᵀ F x1 = 0 (x1 is pts1, x2 is pts2).

• F is defined only up to scale (a constant multiple gives the same geometry) and its sign is not unique either.

• Least squares using all points equally; it is defenceless against outliers. Remove mismatches from the correspondences before this op, or check the residuals with sampson_distance, select, and refit.

• For a planar scene or pure rotation the correspondences can be explained by 1 homography and F is not uniquely determined (something is still returned). recover_pose detects this degeneracy at its entry and rejects it.

• Deterministic. Downstream: essential_8point / recover_pose / sampson_distance.

Background guides (the physics and conventions behind this op)

• depth_sensors — Depth sensors — ranging principles, real-device figures, how dropouts appear

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)

• two_view_pose — py -3.11 examples_3d/two_view_pose.py

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

fuse_to_voxel

Same category (`two_view`)

essential_8point · recover_pose · triangulate · sampson_distance

*Provenance: twoview.py — 3D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

fundamental_8point — 3D two_view op