17-EFT.WP.Methods.Imaging v1.0 | Chapter 1 Imaging Domain — Definition and Scope

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Chapter 1 Imaging Domain — Definition and Scope

One-Sentence Goal
Define the inputs/outputs, boundaries, and compliance gates of the EFT Imaging Methods volume; establish unified conventions for P20x-* / S20x-* / M20-* / I20-* that serve as prerequisites for subsequent chapters.

I. Scope & Objects

1. Input objects
   • Raw imaging payloads and metadata: D_raw_img = { frames, sensor_meta, optics_meta, timing, env }.
   • Key fields: I_raw(x,y,t), bpp, gain, offset, Δx, Δt, S_sensor(λ), QE(λ), K, R, t, dist_params, ts, tau_mono, RefCond.
2. Output objects
   • Standardized imaging data and the publication manifest: D_img_clean, manifest.imaging.*, contracts.tests, q_panel.
   • Typical derivatives: I_lin(x,y,t) (linearized radiometric response), I_denoised, I_geo, I_color, I_hdr, plus quality and gating tags.
3. Boundaries (out of scope for this volume)
   • Task-specific losses and training for downstream recognition/retrieval/generation are out of scope and governed by their respective method volumes.
   • Hardware design and manufacturing tolerances are treated as metadata inputs; optimization of hardware tolerances is not defined here.

II. Terms & Variables

1. Optics & spatial frequency domain
   • h(x,y) (PSF), H_otf(nu_x,nu_y), MTF(nu) = | H_otf(nu) |, F{•} is the 2-D Fourier operator.
   • aperture, f_number, focal, T_trans (transmission coefficient).
2. Radiometry & color
   L(x,omega,λ,t), E, H, S_sensor(λ), QE(λ), I_lin; color bases RGB/XYZ/LinearRGB and white point Wp are explicit.
3. Sampling & noise
   Δx, Δt, bpp, gain, offset, σ_shot, σ_read, σ_total, PRNU, DSNU.
4. Geometry & registration
   Intrinsics K, extrinsics R,t, distortion parameters k1,k2,k3,p1,p2,…, reprojection error eps_reproj.
5. Time & path
   ts, tau_mono, gamma(ell), T_arr; two forms:
   T_arr = ( 1 / c_ref ) * ( ∫_{gamma} n_eff d ell ) and T_arr = ( ∫ ( n_eff / c_ref ) d ell ), with difference delta_form.
6. Quality & compliance
   q_score ∈ [0,1], SLO, P99, ghost_rate, DR, ΔE, SSIM, NIQE, and hash_sha256(blob), signature, TraceID.

*III. Axioms P201- **

• P201-1 (Dimensional consistency): Any quantity entering an equation must declare unit(x) and dim(x), and satisfy check_dim( y - f(x) ).
• P201-2 (Two-form arrival in parallel): Whenever T_arr is involved, evaluate both forms in parallel and record delta_form ≤ tol_Tarr.
• P201-3 (Unified time base): Evaluate internally on tau_mono, publish on ts, and record offset/skew/J.
• P201-4 (Energy & normalization): ( ∫∫ h dx dy ) = 1, MTF(0) = 1; use I_lin as the unified radiometric linear domain.
• P201-5 (Traceable & revertible): The manifest must include versioning, dependency closure, signatures, and quality assertions to support freeze and rollback.

*IV. Minimal Equations S201- **

• S201-1 (Imaging convolution): I_lin(x,y,t) = ( h * scene )(x,y,t), and in frequency, F{I_lin} = H_otf • F{scene}.
• S201-2 (Noise synthesis): σ_total^2 = σ_shot^2 + σ_read^2 + σ_fixed^2 + σ_proc^2.
• S201-3 (Linearization & black level): I_lin = gain * ( I_raw - offset ), with unit(I_lin) = "e-".
• S201-4 (Color transform): RGB_lin = M_xyz2rgb • XYZ, with explicit white-point adaptation via CAT.
• S201-5 (HDR exposure fusion): I_hdr = ( ∑ w_i • I_lin_i / t_i ) / ( ∑ w_i ), with w_i defined by saturation and SNR.
• S201-6 (Arrival two-form gap): delta_form = | ( 1 / c_ref ) * ( ∫ n_eff d ell ) - ( ∫ ( n_eff / c_ref ) d ell ) |.
• S201-7 (Geometric projection): u ~ K [ R | t ] X, reprojection error eps_reproj = mean || u_obs - u_pred ||.

*V. Imaging Process M20- **

• M20-1 Standard inputs & schema binding: register_schema → standardize_names → validate_dataset (see EFT.WP.Core.DataSpec v1.0).
• M20-2 Metrology & linearization: repair_units → black-level removal and I_lin construction → check_dim.
• M20-3 Time & gating alignment: align_timebase; if ToF/shutter gating is present, compute two-form T_arr and delta_form.
• M20-4 Optics & geometry calibration: estimate K,R,t,dist_params; assess eps_reproj and MTF.
• M20-5 Noise modeling & correction: dark/flat, PRNU/DSNU, denoising, and residual auditing.
• M20-6 Color management: spectral-to-target gamut mapping, white point and gamma, audit ΔE.
• M20-7 HDR / multi-frame fusion: weights, saturation masks, de-ghosting, and dynamic-range metrics.
• M20-8 Quality panel & release freeze: assert_contract → q_panel → freeze_release(tag).

VI. Contracts & Assertions

1. Structure & monotonicity
   unique(pk), non_decreasing(ts); if a path exists, non_decreasing(ell) and L_gamma = ( ∫_gamma 1 d ell ) are persisted.
2. Metrology & energy
   check_dim(I_lin - gain*(I_raw-offset)) = true; ( ∫∫ h dx dy ) = 1; MTF(0)=1.
3. Quality & publication
   • delta_form ≤ tol_Tarr; eps_reproj ≤ eps_reproj_max; ΔE ≤ ΔE_max; mtf50 ≥ mtf50_min; ghost_rate ≤ ghost_max; DR ≥ DR_min; q_score ≥ q_min.
   • manifest_signed = true and hash_sha256(blob) consistent.

*VII. Implementation Bindings I20- **

• I20-1 standardize_names(ds, registry) -> ds'
• I20-2 repair_units(ds, policy) -> report
• I20-3 linearize_response(frames, gain, offset) -> I_lin
• I20-4 align_timebase(ds, sync_ref) -> ds'
• I20-5 compute_arrival_forms(path, n_eff, c_ref) -> { T_arr_forms, delta_form }
• I20-6 calibrate_geometry(frames, pattern) -> { K,R,t,dist_params, eps_reproj }
• I20-7 estimate_psf_mtf(frames) -> { h, MTF }
• I20-8 denoise_and_flatfield(I_lin, dark, flat) -> I_corr
• I20-9 color_pipeline(I_corr, profile) -> I_color, ΔE
• I20-10 hdr_merge(frames, weights) -> I_hdr
• I20-11 assert_contract(ds, tests) -> report
• I20-12 freeze_release(ds, tag) -> manifest

VIII. Cross-References

• Schema/manifests & keys: see standard schemas and manifest keys in EFT.WP.Core.DataSpec v1.0.
• Acquisition & arrival time: see EFT.WP.Core.Sea v1.0 for arrival time and gated acquisition flows.
• Streaming & backpressure: see EFT.WP.Core.Threads v1.0 for thr/chan execution graphs and SLI/SLOs.
• Spectra & conservation: see EFT.WP.Core.Density v1.0 and Methods.Cleaning v1.0, Chapter 13.
• Units/dimensions & uncertainty propagation: see Methods.Cleaning v1.0, Chapter 4 and Appendix E.

IX. Quality Metrics & Risk Control

1. Metric set
   • Optics: mtf50, MTF(nu) curve, consistency drift drift_mtf.
   • Noise: σ_total, PRNU, DSNU, spectral density of denoising residuals.
   • Geometry: eps_reproj, edge deformation edge_warp.
   • Color: ΔE95, gray-card neutrality bias.
   • HDR/Dynamics: DR, ghost_rate, saturation coverage.
   • Time/Path: delta_form, offset/skew/J.
   • Aggregate: q_score, P99, SLO attainment rate.
2. Risk & rollback
   Guardrails: upon contract_fail or SLO degradation, roll back to the latest freeze_release(tag_prev) and issue audit plus postmortem.

Summary
This chapter establishes the objects, boundaries, and minimal P/S/M/I conventions for the imaging domain. Subsequent chapters follow this scaffold—covering metrology and time-base unification, two-form arrival time, and the optics/geometry/color/HDR/quality & compliance stack—together with their implementation bindings.