NOIR: Neural Operator mapping for Implicit Representations
| Authors | Sidaty El Hadramy et al. |
| Year | 2026 |
| Field | Computer Vision |
| arXiv | 2603.13118 |
| Download | |
| Categories | cs.CV |
Abstract
This paper presents NOIR, a framework that reframes core medical imaging tasks as operator learning between continuous function spaces, challenging the prevailing paradigm of discrete grid-based deep learning. Instead of operating on fixed pixel or voxel grids, NOIR embeds discrete medical signals into shared Implicit Neural Representations and learns a Neural Operator that maps between their latent modulations, enabling resolution-independent function-to-function transformations. We evaluate NOIR across multiple 2D and 3D downstream tasks, including segmentation, shape completion, image-to-image translation, and image synthesis, on several public datasets such as Shenzhen, OASIS-4, SkullBreak, fastMRI, as well as an in-house clinical dataset. It achieves competitive performance at native resolution while demonstrating strong robustness to unseen discretizations, and empirically satisfies key theoretical properties of neural operators. The project page is available here: https://github.com/Sidaty1/NOIR-io.
Engineering Breakdown
Plain English
NOIR reframes medical imaging tasks as operator learning problems by embedding discrete medical images into continuous implicit neural representations and learning neural operators that map between them, rather than processing fixed pixel/voxel grids. This approach enables resolution-independent transformations—the same learned operator works across different input resolutions without retraining. The paper evaluates NOIR on segmentation, shape completion, image-to-image translation, and synthesis tasks across multiple public datasets (Shenzhen, OASIS-4, SkullBreak, fastMRI) and achieves competitive performance while maintaining flexibility across different resolutions and modalities.
Core Technical Contribution
The core novelty is reframing medical imaging as function-to-function mapping rather than discrete grid-to-grid processing. Instead of learning CNN operators on fixed resolution grids, NOIR embeds both source and target medical signals into a shared latent space of implicit neural representations, then learns a neural operator that transforms latent modulations between representations. This shift from discrete grids to continuous function spaces enables true resolution independence—a single learned operator generalizes across different input/output resolutions without architectural changes. The technical innovation combines neural implicit representations (coordinate-based MLPs that define continuous functions) with neural operator theory (learning mappings in infinite-dimensional function spaces).
How It Works
The pipeline begins by encoding discrete medical images into Implicit Neural Representations (INRs)—coordinate-based neural networks that map spatial coordinates to pixel/voxel values, creating a continuous function representation of each discrete image. These INRs are trained to reconstruct the original images while capturing their structure in learned weights. The latent modulations (learned parameters) of corresponding source and target INRs are extracted and paired as training data. A neural operator network then learns the mapping from source latent modulations to target latent modulations, operating in this lower-dimensional learned space rather than the original pixel space. At inference, given a new source image: (1) encode it to an INR, (2) extract its latent modulation, (3) apply the learned operator to get the target modulation, (4) decode the target modulation back to a continuous function and sample at desired resolution. This decouples the learned transformation from any specific resolution, enabling evaluation at native or arbitrary resolutions.
Production Impact
For clinical systems, this approach solves the resolution inflexibility problem that plagues standard CNNs—models trained on 512×512 images cannot efficiently process 1024×1024 or 256×256 variants without retraining. NOIR would allow a single segmentation or translation model to handle varying acquisition resolutions across different clinical sites without architectural changes. The implicit representation encoding adds computational overhead (training an INR per image during preprocessing), but inference is potentially faster since the operator works in compressed latent space rather than full resolution. Storage is reduced—you store learned modulations instead of full resolution feature maps. Integration requires: (1) preprocessing pipeline to convert discrete images to INRs, (2) latent space database for training, (3) operator inference serving. Trade-off: slower offline preprocessing but more flexible, efficient online inference; requires tuning INR architecture and operator depth for your specific resolution ranges and modality types.
Limitations and When Not to Use This
The paper does not address how to choose INR architecture complexity or modulation dimensionality—overly simple INRs lose medical detail, overly complex ones create noisy modulation spaces for operator learning. There's no analysis of failure modes when source and target domains are highly misaligned (e.g., CT to MRI with different contrast properties), or when fine anatomical details are critical but get smoothed by the continuous function representation. Computational cost of the INR encoding stage is glossed over—for large-scale deployment, encoding every image to an implicit representation could become a bottleneck. The approach assumes latent modulations form a smooth, learnable manifold; this may break down for rare pathologies or out-of-distribution cases not represented in training. Limited discussion of how to validate that the continuous representation preserves diagnostic-critical details versus simply reconstructing average anatomy.
Research Context
This work builds on three research threads: (1) implicit neural representations (INRs/neural radiance fields), which have shown that coordinate MLPs can compactly represent signals; (2) neural operator learning (DeepONet, Fourier Neural Operators), which extend deep learning to infinite-dimensional function spaces; and (3) medical imaging deep learning, where resolution flexibility and modality generalization remain open challenges. NOIR's contribution is unifying these—using INRs as a shared embedding space and neural operators for cross-space mappings rather than pixel-space CNNs. This opens research directions: scaling to higher-dimensional operators, learning operators that generalize across multiple modalities simultaneously, combining with uncertainty quantification for clinical workflows, and exploring whether implicit representations preserve anatomically-critical information better than standard feature pyramids for rare disease detection.
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