Multi-Focus / Panorama Fusion (all-in-focus composite imaging) L1-076
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
A sequence of K images {y_k} of the same scene is captured with varying focus distance z_k (multi-focus) or camera pose (panorama). Each y_k blurs the 3D scene x(u,v,z) through a depth-dependent PSF_k and an affine warp W_k. Fusion recovers an all-in-focus, globally aligned image X.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 800
Well-conditioned when scenes are Lambertian, inter-frame parallax is small (pure rotation or small translation), and focus distances span the scene depth range. Degrades catastrophically for moving subjects (ghosting) and unconstrained parallax (depth ambiguity).
Solvability C
- Solver class:
- Laplacian-pyramid fusion, gradient-based focus measure (SML, ML, tenengrad), Poisson-blend stitching, learned fusion (MFIF-GAN, U2Fusion), graph-cut seam selection
- Convergence rate q:
- 2
- Complexity:
- O(K * H * W * log(max(H,W))) for pyramid; O(K * H * W) for gradient fusion