Region out-of-Interest Preserving (NERP)

• NERP is a framework that enforces preservation of data outside a defined region using mask-based constraints to ensure unchanged or purposefully altered out-of-interest areas.
• It applies across modalities such as medical imaging, generative editing, and data anonymization by integrating ROI-specific losses and architectural constraints.
• NERP methods leverage latent disentanglement and targeted regularization techniques to guarantee ROI fidelity while controlling modifications on the out-of-interest regions.

Region out of Interest Preserving (NERP) designates algorithmic paradigms and model architectures that explicitly ensure the integrity or non-modification of image, signal, or data content outside a defined Region of Interest (ROI). The primary motivation is to enforce locality of transform, editing, or anonymization, as required in medical imaging, generative editing, privacy-preserving computation, and scientific data reduction. Across diverse modalities—deep tomography, generative adversarial inversion, learned compression, 3D scene inpainting, diffusion-based editing, and unsupervised physics-based data selection—NERP frameworks formalize the requirement that out-of-interest regions remain either provably unchanged or are manipulated according to a secondary objective (e.g., maximal obfuscation or minimal distortion), often via mask-based decomposition, specialized loss functions, or architectural constraints that enforce region-specific behavior.

1. Formal Definitions and Taxonomy

NERP, as a technical term, encompasses algorithms that guarantee the preservation, controlled degradation, or selective transformation of signals outside predefined regions. Let $I$ denote a data sample (image, volume, sinogram, etc.), $M$ a binary ROI indicator with $M(x)=1$ for ROI pixels, and $\bar M=1-M$ the out-of-interest mask. NERP imposes for a model $\mathcal{F}$ that

$$\mathcal{F}(I)\odot \bar M \approx I\odot \bar M \qquad \text{(preservation)}$$

or, more generally, that loss or transformation of out-of-interest regions is regulated independently from the ROI. Across applications, this manifests as:

• Exact region conservation: Out-of-interest pixels are unchanged (image editing, inpainting).
• Targeted regularization: Out-of-interest signal is suppressed or decorrelated from ROI (disentanglement, anonymization).
• Controlled measurement or computation: Only ROI data is acquired or reconstructed, with non-ROI data neglected (physics-driven selection, data-efficient imaging).

NERP stands in contrast to global optimization or unconstrained generative approaches, where all regions may be altered to minimize total loss.

2. Core Methodologies Across Modalities

NERP frameworks span multiple technical domains. Representative instantiations include:

A. Deep Interior Tomography

In sparse-data CT, only central line integrals ($s\in(-\mu,\mu)$) are measured, creating a nontrivial null-space $\mathcal{N}_\mu$ associated with unmeasured data. Analytic inversion (e.g., Filtered Backprojection) yields artifacts in the ROI due to the null-space. Deep NERP architectures (Han et al., 2017) use an FBP-to-U-Net pipeline, where the input is the truncated FBP image ($\tilde f=f^*+g, \; g\in\mathcal N_\mu$), and the network $\mathcal Q$ is trained so that

$$\mathcal{Q}(f^*+g)=f^*,\quad \forall g\in\mathcal N_\mu,$$

eliminating the null-space component and thus ensuring ROI reconstruction is independent of invisible, out-of-interest data.

B. GAN Inversion and ROI Focusing

In generative image inversion (Moon et al., 2022), encoders may overfit both interest and uninterest regions, with OOD backgrounds corrupting ROI features. “IntereStyle” introduces an Uninterest Filter (heavy blurring on $\bar M$) in the input chain and a disentanglement loss ensuring latent codes for $\bar M$ do not affect ROI reconstructions: $G(w_N + \Delta_b)\odot M \approx G(w_N)\odot M,$ with $\Delta_b$ representing the “non-interest” style code, so that only the ROI is faithfully reconstructed.

C. Learned Compression with ROI Loss

In image compression-anonymization pipelines (Liebender et al., 9 Jun 2024), NERP is realized by joint optimization of compression rate, global distortion, and ROI-specific loss: $$L = \lambda_r R + \lambda_{bg} D + \lambda_{hbox} L_{hbox} + \lambda_{vbox} L_{vbox},$$ where $L_{hbox}$ (on face head-boxes) uses an “inverted MSE” (maximizing error, i.e., minimizing reconstruction fidelity), while $L_{vbox}$ (on person-boxes) uses standard MSE, resulting in selective anonymization (face obfuscation) while maintaining recognizability of people and background.

D. Masked Training for Privacy-Preserving Detection

NERP in medical AI (Yang et al., 11 Sep 2025) employs a fixed mask $M$ derived from population-level redness statistics. This mask zeroes all identity features and preserves only diagnostically relevant facial regions (e.g., cheeks, nose, forehead). The downstream detection network is trained and deployed only on masked content, yielding improved recall and F1 while minimizing pixelwise identity leakage.

E. Diffusion and Latent Editing with Explicit Region Preservation

Region-aware diffusion models (Huang et al., 2023) produce entity-level RoI segmentations automatically and enforce loss terms: $$L_{NERP}(x_0, \hat{y}_t, m) = d(x_0 \odot (1-m), \hat{y}_t \odot (1-m)),$$ with $d(\cdot,\cdot)$ combining LPIPS and MSE, penalizing deviation from the unedited out-of-interest region in each diffusion step.

F. 3D Scene Inpainting and Multi-View Consistency

In NeRF inpainting (Liu et al., 2022), a user-defined mask is propagated to all views; former object regions are replaced using guidance (inpainted color/depth). Out-of-interest pixels drive a loss enforcing

$$L_{color}^{out}(\theta) = \sum_{s=1}^K \|F_\theta^{image}(o_s) - I_s\|^2 \odot M_s,$$

forcing unchanged appearance outside edited regions across all camera views.

G. Physics-Driven Data Selection in Imaging

In ptychography (Lin et al., 2022), a two-feature unsupervised classifier selects detector positions within the ROI, discarding redundant measurements outside. This physically-informed filtering focuses computation solely on the ROI without loss of reconstructive accuracy in that region.

3. Algorithmic and Architectural Details

NERP systems are unified by explicit mask-based partitioning or implicit disentanglement. Key algorithmic devices include:

• Mask-based input pipelines: Multiplicative masking or blurring of $\bar M$ enforces region separation at the input or feature level.
• Region-weighted losses: Objective terms are evaluated with mask $M$ or $\bar M$, e.g., MSE on $M$, inverted or adversarial loss on $\bar M$.
• Latent disentanglement: Separate latent codes are learned or regularized such that ROI encoding is invariant to changes in out-of-interest regions.
• Framelet or implicit basis constraints: Networks are constructed (e.g., U-Net/encoder-decoder) to filter out null-space signals or to serve as learned projectors onto the space of ROI-preserving representations.
• Multiview consistency: In 3D/scene-editing contexts, all rays/pixels outside the ROI in every view are directly constrained to maintain global coherence.
• Physics-inspired feature clustering: In scientific imaging, NERP may be enforced without explicit masks, instead using features (intensity, center-of-mass) to cluster data by ROI relevance, minimizing unnecessary data acquisition or computation.

Representative architectures are summarized below.

Application Domain	Masking/Partition Mechanism	Loss/Constraint on Out-of-Interest
Deep CT reconstruction	Null-space framelet filtering	Network outputs $f^*$, discards $g\in\mathcal N_\mu$
GAN inversion, editing	Blurred $\bar M$ + latent separation	Disentanglement loss: non-impact of $\bar M$
Compression-anonymization	ROI-specific loss (inverted MSE, MSE)	Maximal destruction (faces), preservation (persons)
Medical detection	Fixed redness-based mask	All identity features zeroed
Diffusion-based editing	CLIP-based segmentation, blended latent	LPIPS/MSE outside-ROI preservation
Scene inpainting (NeRF)	User mask, multi-view propagation	MSE on unmasked regions across all views
Physics-based selection	Feature clustering on raw data	Non-ROI positions excluded

4. Quantitative Performance and Evaluation Protocols

NERP approaches are evaluated not only on target region performance (restoration, editing fidelity, anonymization) but crucially on the preservation or controlled modification of out-of-interest regions. Metrics and results include:

• CT interior tomography (Han et al., 2017):
  • PSNR (dB) in the ROI: 37.46 (CNN), 30.20 (TV), 27.03 (L-spline), 9.41 (FBP truncated).
  • NMSE: 1.30e-3 (CNN), 6.91e-3 (TV).
  • Run-time: 0.05 s/slice (CNN), 1.83 s/slice (TV).
• StyleGAN inversion (Moon et al., 2022):
  • Interest region $L_2$ (MSE): 0.013; LPIPS: 0.075; ID similarity: 0.68; outperforming baselines.
• Anonymizing compression (Liebender et al., 9 Jun 2024):
  • Person AP: 19% at 0.24 bpp (comparable to AV1@10%, JPEG@10%).
  • Face AP: 0.1% (near-zero successful face detection).
  • Encoding: 21 ms (DGX GPU), 239 ms (Jetson Nano/edge).
• Privacy-preserving dermatology (Yang et al., 11 Sep 2025):
  • Accuracy (test real): Masked 95.5%, Unmasked 83.5%.
  • Recall: 82.0% (Masked), 34.0% (Unmasked).
  • Precision: 97.78% (Masked), 100% (Unmasked).
  • F1: 90.11% (Masked), 50.75% (Unmasked).
• Region-aware diffusion (Huang et al., 2023):
  • CLIP score: 0.849 (RDM), outperforming all baselines.
  • SFID: 6.54 (RDM, lowest).
  • LPIPS (outside ROI): 0.039 (NERP), 0.143 (no NERP).
  • Inference: 3 s (256×256, RTX 3090).
• NeRF inpainting (Liu et al., 2022):
  • PSNR (masked region): 27.2 dB (Ours), 22.4/24.3 dB (baselines).
  • SSIM (masked): 0.91 (Ours); >0.95 outside the mask.
  • Optimization: 5 hours (GTX-1080), preserving multiview consistency.
• Ptychography data selection (Lin et al., 2022):
  • Data retained: 20% (from 15,980 to 3,260).
  • SSIM: $\geq$0.95 at 20% data, 0.98 plateau with wider borders.
  • Runtime: 23 min (NERP), 104 min (full), 10 s pre-filtering.

These results indicate that rigorous NERP methods preserve or enhance performance within the ROI while tightly controlling or minimizing distortion, information leakage, or computational cost in out-of-interest regions.

5. Applications and Theoretical Guarantees

NERP methods are critical in:

• Medical Imaging: Ultra-localized reconstruction with minimized radiation and artifact-free ROI (interior CT).
• Generative Editing: Region-local attribute transfer, obstacle-invariant style mixing, robust inpainting, and inversion (face, background, texture).
• Data Anonymization: Regulatory-compliant de-identification by targeted distortion of sensitive regions (face box), with scene context retained for detection or analytics.
• Privacy by Design in Clinical AI: Fixed-masking to guarantee zero transmission of identifying features in medical AI pipelines.
• Scientific Data Acquisition: Efficient ptychographic reconstructions by pre-filtering data only to fields-of-interest, dramatically reducing computation.
• Interactive and Automated Editing: User- or CLIP-driven mask selection with robust multiview, multiobject NERP (scene editing, object removal).

Theoretical properties depend on modality. For framelet-based learning (deep tomography), the U-Net acts as a null-space annihilator, with the guarantee

$$\mathcal{Q}(f^*+g) = f^*\quad\forall\,g\in\mathcal{N}_\mu,$$

But formal robustness to mask errors, generalization to unseen mask shapes, or full guarantee of information-theoretic privacy (e.g., pixelwise identity leakage) remains an open question in several domains.

6. Limitations and Open Questions

Common limitations across NERP frameworks include:

• Generalization beyond fixed or learned mask shapes: Most methods assume static or dataset-sampled distributions of ROI; adaptivity to arbitrary user, task, or detector-driven mask changes is not always established.
• Robustness to OOD content: OOD backgrounds or domain shifts may violate latent disentanglement or lead to spurious hallucinations.
• Scalability: Training with region losses or multiview consistency is more resource-intensive; inference speed is generally fast but may be bottlenecked by segmentation or mask propagation.
• Theoretical rigor: Guarantees for null-space removal (tomography) and no-leakage guarantees (privacy) are partly empirical or rely on observed performance, with unsolved problems in formalizing under what conditions NERP retains analytic correctness or privacy guarantees.
• Edge case failure modes: In imaging, objects with negligible contrast (e.g., phase-only objects) or inpainting of thin/reflective structures may not be preserved; in ptychography, clustering may misclassify heterogeneous samples.

A plausible implication is that hybrid methods—combining mask-based, feature-driven, and learned disentanglement—may address the major gaps in robustness and guarantee derivation for broader NERP adoption in critical, safety-sensitive domains.

7. Outlook and Extensions

NERP continues to expand into domains such as federated/fog computing (masking privacy-critical regions before transmission), 3D/scene graph editing, and multi-modal sensor fusion, often combining region-preserving principles from segmentation, physical feature engineering, and deep representation learning. Extensions proposed include:

• Dynamic or per-subject ROI adaptation (e.g., demographically adaptive masks, 3D-driven segmentation).
• Integration into interactive editors for real-time, user-guide mask specification with immediate NERP-compliant feedback.
• Data-efficient, online acquisition in experimental science: active mask suggestion and on-the-fly NERP-driven scanning.
• Advanced adversarial regularization guaranteeing pixelwise privacy (differential privacy, information-theoretic secrecy) via masked or noise-injected ROIs.

The breadth of NERP implementations underlines its central role at the intersection of interpretability, privacy, computational efficiency, and robust model design for regionally limited or safety-critical tasks.