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docs(sparse-sfm): freeze Gate E Huber cost

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fy59 2026-08-24 19:54:09 +02:00
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docs/architecture/sparse_sfm.md
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@ -294,13 +294,38 @@ optimized; its Gate D data is retained with a gauge/degenerate diagnostic.
### Objective and solver
Every valid observation contributes the two-dimensional source-pixel residual
defined above. Gate E uses binary64 throughout and minimizes their robustified
sum with Huber loss and `delta = 2.0` source pixels. The Huber kind and scale are
Gate E scientific policy, not Governor parameters, Resource parameters or a
Gate E fingerprint. Non-finite poses, landmarks, projections, residuals or
costs, and camera-frame depth invalid under the frozen camera invariants,
reject the candidate.
Every valid observation contributes one two-dimensional source-pixel residual
block `f_i = [dx, dy]`, where `dx = predicted_x - observed_x` and
`dy = predicted_y - observed_y`. Gate E uses binary64 throughout. Define:
```text
s_i = dx*dx + dy*dy
delta = 2.0
delta2 = 4.0
rho_delta(s) = s if s <= delta2
rho_delta(s) = 2*delta*sqrt(s) - delta2 if s > delta2
robust_cost = 0.5 * sum_i(rho_delta(s_i))
```
Thus, with `delta = 2.0` source pixels, the second branch is
`4.0*sqrt(s) - 4.0`. The Huber loss applies once to the norm squared of the
complete 2D observation, never independently to `dx` and `dy`; the factor
`0.5` is contractual. Each observation must likewise be one 2D Ceres residual
block, not two scalar blocks.
Lardon3D computes initial and final robust costs independently of the solver
using exactly this formula, and those values govern acceptance. Ceres summary
costs may only diagnose or cross-check them. With the identical problem, a
disagreement beyond the applicable numerical tolerance stops implementation
for contract review; neither value silently replaces the other. Non-finite
`dx`, `dy`, `s_i`, `rho_delta(s_i)`, accumulation, pose, landmark or projection,
and camera-frame depth invalid under the frozen camera invariants, reject the
candidate. No clamp or fallback is permitted.
The Huber kind and scale are Gate E scientific policy, not Governor parameters,
Resource parameters or a Gate E fingerprint.
Gate E v1 selects the Ceres Solver 2.2.x API, CPU-only, with these explicit
options: