Skip to content

Geometric Sampling Texture

Status: Analysis-only. No renderer changes. No simulation reruns. Raw validation truth remains separate from coherence previews.

This note synthesises the sampling-texture analysis performed on the wormhole checkpoint ladder (fixture_011, runs 2026-04-21 and 2026-04-24). It consolidates findings from adaptive tiling, polar tiling, edge-alignment measurements, geometric structure search, and log-polar orientation histograms into a unified recommendation.

Source: papers/paper_001_causal_observer_ladders/analysis/geometric_sampling_texture.md, papers/paper_001_causal_observer_ladders/analysis/phase_sampling_domain_update.md

Central Result

Two independent diagnostic objectives require different tile geometries:

Objective Best tile geometry Key metric
Preserve local edge direction Adaptive square direction similarity: 0.836 (mouth), 0.875 (bridge)
Maximise aperture edge recall Aperture polar recall: 1.000 / 1.000
Balance bridge direction + recall Incoherence or curvature polar direction: 0.656–0.660; recall near 1.000

No single geometry achieves both objectives. This is a fundamental trade-off, not a calibration issue.

Adaptive Square Tiles

Adaptive square tiles divide the image into tiles whose size and alignment respond to the local intensity-gradient field. Their primary advantage is direction fidelity: the tile boundaries align with locally dominant edge orientations.

Measured results: - mouth: visible-edge recall 0.712, gradient-direction similarity 0.836 - bridge: visible-edge recall 0.731, gradient-direction similarity 0.875

The bridge achieves higher direction similarity than the mouth despite being the more morphologically disrupted checkpoint. This suggests that the bridge's line-rich, radial-dominant edge field is well-matched to a gradient-aligned tile grid, even though its absolute coherence is lower.

Polar and Radial Tiles

Polar tiles divide the image into radial and angular sectors from a fixed centre. Their primary advantage is boundary recall: because any roughly circular or radial edge structure is guaranteed to fall near a tile boundary, they are difficult to fool.

Measured results (aperture-centred): - mouth: recall 1.000, direction 0.628 - bridge: recall 1.000, direction 0.642

Polar tiles are appropriate for aperture diagnostics where missing an edge is worse than having spurious matches. They are not appropriate as a replacement for adaptive tiles when directional accuracy matters.

Polar centre variants

Centre type mouth direction bridge direction Notes
Aperture centre 0.628 0.642 Global wormhole mouth estimate
Incoherence centre 0.624 0.656 Centroid of visible-band / phase-incoherence signal
Curvature centre 0.656 0.660 Hough circle/arc-fit centre candidates

Curvature-centred polar tiling gives the best polar direction results at both checkpoints, but still falls well below adaptive-square direction fidelity and reduces symmetric edge-distance alignment relative to aperture-centred polar.

Bridge Morphology

The bridge checkpoint is morphologically distinct from all others by three independent measures:

Measure Bridge Near-side range Far-side range
Hough line detections 214 71–86 90–106
Mean contour eccentricity 0.663 0.909–0.962 0.909–0.929
Visible-band components 190 91 56–107

The bridge has three times as many Hough line detections as the next-highest checkpoint, much rounder contours, and a highly fragmented visible-band mask. This is consistent with the transport finding that the bridge is a disordered, sparse regime rather than a clean photon-sphere-adjacent transition.

Orientation Persistence

Log-polar orientation histograms were computed for all six checkpoints. Key finding: orientation persistence does not break down at the bridge.

Checkpoint pair Cosine similarity
Bridge vs near-side mean 0.988
Bridge vs all-others mean 0.972
Non-bridge pairwise mean 0.961

The bridge remains radial-dominant (radial/tangential = 2.03), slightly more so than the near-side. The orientation transition occurs after the bridge: far-side checkpoints shift to tangential dominance (radial/tangential = 0.75 at exit-approach, 0.58 at exit-lookback).

This has a direct implication for render guidance: the far-side domain, not the bridge, is the location where an adaptive tile grid needs to be reoriented for tangential features.

Hybrid Architecture Recommendation

The evidence supports a layered rather than substituted architecture:

Raw row pass (scout truth)
    ↓ never overridden
Adaptive square tiles (local direction, coherence previews)
    + Aperture polar tiles (high-recall boundary diagnostics)
    + [Optional] Curvature-centred polar (geometric probe refinement)
    + [Future] Triangle/diagonal/annular (oblique edge families, ring persistence)

Coherence previews from any tiled layer must be labelled as interpretive and kept separate from Pass 1 classification truth.

Connection to Phase Sampling

The phase sampling domain update (2026-04-25) tested three polar recentring strategies as alternatives to aperture-centred polar. The key result: adaptive-square tiles remain the best directional match regardless of polar centre choice. Polar recentring improves geometric probe alignment modestly, especially for bridge-direction fidelity, but cannot close the gap to adaptive direction performance.

The next useful sampling texture is likely hybrid: adaptive square for local direction, plus multi-centre annular/curvature probes for high-recall geometry diagnostics.

Cross-References