Certified Abstention for Provably-Unidentifiable Index-Phase Recovery in Image Registration
Authors: Dinh Tuan Nguyen, Trong Nhan Nguyen, Vu Nguyen Minh Hung, Tien Minh Khoi Nguyen, Jaeyeop Choi, Sudip Mondal, Jae Sung Ahn, Junghwan Oh
Organizations: Industry 4.0 Convergence Bionics Engineering, Department of Biomedical Engineering, Pukyong National University, Busan 48513, Republic of Korea. · Smart Gym-Based Translational Research Center for Active Senior’s Healthcare, Pukyong National University, Busan 48513, Republic of Korea. · Digital Healthcare Research Center, Institute of Information Technology and Convergence, Pukyong National University, Busan 48513, Republic of Korea. · Ohlabs Corp., Busan, Republic of Korea.
Image registration underpins measurement across scanning, camera, and microscopy imaging, yet a fundamental question is rarely posed: when is the sample-to-position map recoverable at all, and when does any estimator that reports a position necessarily fabricate one? We show that in reference-perturbed sampled imaging, where samples are localized through a perturbed reference, position fidelity (where samples land) and phase fidelity (which reference index becomes each block's origin) are logically independent: no policy acting on position information alone can guarantee phase fidelity. We derive a tight resolution threshold separating recoverable from provably-unidentifiable registration, and a recovery framework that certifies identifiable regions--recovering them exactly--while abstaining on provably-unidentifiable regions rather than hallucinating structure. On a deployed scanning system we measure a direction-bimodal registration offset consistent with the theory. Against classical and learned restoration baselines, certificate-free offset estimators fabricate structure on the unidentifiable regime, whereas the certified method abstains rather than fabricating. Finally, the certified-abstention mechanism carries across scanning, rolling-shutter, and cryo-electron-microscopy imaging--declining rather than fabricating on the regime it flags--though how completely it abstains and how tightly it bounds kept-region risk stay modality-specific (at extreme SNR the cryo-EM certificate abstains only partially): a structural-versus-statistical boundary in registration reliability.
Figures & tables
Fig. 1: Qualitative illustration of the recovery channel on a real capture ( 5μ m pitch). (a) unregistered: an illustration of continuous intra-row warp (an L1/P3 regime we bracket out, Supplementary Material, Sec. S-C), not the L2 measurement—this state was not logged, and its per-row distortion varies within each row (left/mid/right sub-window shifts of a single row disagree by ≈9 px, exceeding the ≈6 px median row shift), so it is warp-dominated rather than a rigid per-block offset. A rendered-image proxy gives same-direction row-shift std ≈8.8 px. (b) image-based registration: the image channel of Section V (a Robinson–Milanfar/CRLB-limited estimator with an identifiability certificate) estimates and inverts the per-row shift where it is identifiable, aligning the rows ( ≈0.5 px) but leaving a residual blur. The discrete per-block L2 offset is evidenced separately by the logged ki of Table I (a 17.3 -column bidirectional index offset), not by this figure; the two panels are rendered-image proxies (mixing L1/L2), shown to illustrate the recovery channel, not to quantify L2.
Fig. 2: Logged per-block index offset ki for the position-only configuration ( 5μ m), bimodal by scan direction : forward sweeps centre at +6.9 columns, reverse at −10.4 —a rigid 17.3 -column bidirectional index offset (the L2 signal), about which the within-direction std is only ≈1 column. The column spacing is simultaneously on grid. Columns are 5μ m.
scan direction
mean ki (col)
std ki (col)
lag-1 autocorr
forward (FWD)
+6.9
0.97
0.40
reverse (REV)
−10.4
1.19
0.56
TABLE I: Logged per-block index offset ki , position-only configuration ( 903 blocks, 5μ m pitch, ≈390 mm/s). Bimodal by scan direction (FWD +6.9 , REV −10.4 columns): a rigid 17.3 -column bidirectional index offset —the real-system L2 evidence (Theorems 1 , 3 ), no origin-coupled reference applied. Full interpretation in Section VI-A ; L1 warp in Supplementary Table S5.
Fig. 3: Synthetic studies S1 and S3 (Algorithm A; Δy=1μ m, vmax=200 mm/s; the S2 cadence study is Supplementary Fig. S1). S1: the probability that every block is correctly phased steps from 1 to 0 exactly at δ=Δy/(2vmax) (empirical transition within one grid step of the predicted 2.5μ s; zero below-threshold failures over 200 blocks ×100 seeds), confirming Theorem 5 ; the adversarial and stochastic curves coincide (both step at the same half-cell threshold), so the stochastic curve is drawn dashed with open markers over the solid adversarial one. S3: the all-block exact-recovery knee sits at ΛΔy2/(2σ2)≈22.2 , matching the exact-Gaussian union-bound prediction ρ⋆≈21.7 (the root of R⋅2KmaxΦ(−ρ⋆/2)=1 ) to within 3% —confirming ( 6 ) with its exact constant; logR(2Kmax+1)≈7.7 is the order-only prediction.
Fig. 4: Synthetic studies S4–S5. S4: on textured bands the image channel decodes exactly and the certificate keeps; on texture-free and p -periodic bands (Proposition 3 ) the image channel fails ( 0.11 / 0.34 accuracy) and the certificate abstains ( 100% ), while the metadata channel stays exact everywhere. S5: the conformally calibrated kept-region error stays at or below the target risk α across 20 splits (Proposition 5 ). The image-restoration reliability evaluation (recovery vs. fabrication vs. abstention across baselines) is Fig. 5 .
Method
exact (ident.)
fab. (per.)
abst. (per.)
metadata-only (oracle)
1.00
0.00
0.00
image-only ML ⋆
1.00
0.88
0.00
image + certificate ⋆
1.00
0.00
1.00
rigid registration
0.43
0.98
0.00
destriping (col-mean)
0.43
0.00
0.00
smooth-prior
0.67
0.63
0.00
TABLE II: Image-restoration reliability on the synthetic benchmark (gated; Fig. 5 ; full version Supplementary Table S1). exact : exact-recovery over the identifiable band; fab. : fraction of p -periodic-band lines given a nonzero wrong shift; abst. : abstention coverage on the texture-free/periodic bands. Destriping/PCA fabricate little only because they are inert , not certified abstention. ⋆ ours; † added data-driven baselines.
Fig. 5: Image-restoration reliability on the synthetic benchmark (Table II ; full version Supplementary Table S1). Per restorer: exact-recovery rate on the identifiable band, fabrication rate on the provably-unidentifiable p -periodic band, and abstention coverage on that band. Every restorer without an abstention certificate—rigid registration, destriping, smooth-prior, and the two data-driven baselines (learned-template, low-rank PCA)—fabricates structure on the periodic band, whereas the certified method ( image+cert ) abstains ( 1.00 ) and still recovers the identifiable band exactly. Starred rows ( ⋆ ) are ours; the low fabrication of destriping/PCA reflects inertness (they apply no shift or average it out), not certified abstention.
Fourier phase encodes important spatial image structure, but recovering an image without measured spectral magnitude requires additional constraints and leaves absolute intensity ambiguous. We propose a projection-based two-stage framework that combines Fourier-phase and spatial-support constraints with an image-specific neural prior. The first stage alternates constraint enforcement with regularized neural-prior updates, while the second performs phase/support refinement alone with guaranteed convergence. We evaluate two neural-prior implementations on the same 77 microscopy images and compare them with a constraint-only baseline. After 500 final refinement passes, the best-performing variant achieves 31.41 dB pooled PSNR, 35.75 dB mean PSNR, and 0.9531 mean SSIM, improving pooled PSNR by 1.51~dB and reducing pooled MSE by 29.3% relative to the baseline. The results demonstrate the benefit of combining neural guidance with explicit constraint refinement at the evaluated iteration budget, while showing that lower phase residual alone does not guarantee greater reconstruction accuracy.
Ene Meco, Ahmet Enis Cetin
Dept. of Electrical and Computer Engineering, University of Illinois at Chicago, IL, 60607, USA
Conventional image registration algorithms are robust to domain shifts and achieve low errors, but they are slow and computationally expensive. Deep-learning methods are efficient at inference-time, but face challenges in out-of-domain samples. We propose Recursive Uncertainty-Gated Image Registration (RUGI), an algorithm for iteratively refining deformation fields predicted by learning-based registration models. At each iteration, the registration model predicts an incremental deformation, and a gating map modulates the update. Refinements are hence concentrated in regions that remain difficult to register. We explore two gating strategies: a learned uncertainty-based approach and an image residual error approach. We evaluate RUGI on cardiac MRI and echocardiography datasets and show consistent improvements over single-step inference. Ablation experiments demonstrate that iterative refinement alone improves registration, but informative spatial gating provides a significant additional benefit. The error-gated variant of RUGI can also be applied directly to existing pretrained models; applied to VoxelMorph, TransMorph, and CycleMorph, it yields MSE reductions of 27-37% with no modification to the original training procedure. The improvements in registration performance are reflected in decreased errors in ejection fraction estimation relative to ground truths. These results demonstrate that spatially selective iterative refinement provides an effective strategy to improve registration accuracy at inference-time.
Clara Rodrigo González, Oscar Bates, Fu Siong Ng +1
Department of Bioengineering, Imperial College London, London, UK · Department of Earth Science and Engineering, Imperial College London, London, UK · National Heart and Lung Institute, Imperial College London, London, UK
Image registration is essential in applications such as electronic image stabilization. Scale-Invariant Feature Transform (SIFT), a widely used local keypoint detector and descriptor, typically provides accurate registration; however, it often fails in scenes with strong linear structures (e.g., shutters), where local features become ambiguous. We propose Hough-SIFT, a robust registration method that performs SIFT descriptor matching in Hough space. In this domain, linear structures form distinctive peaks that restore descriptor discriminability. Experiments demonstrate that Hough-SIFT is robust in linear scenes where SIFT frequently fails, while maintaining accuracy comparable to SIFT in normal scenes.