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Scale Equivariance Regularization and Feature Lifting in High Dynamic Range Modulo Imaging

Brayan Monroy, Jorge Bacca

TL;DR

The paper tackles reconstructing high-dynamic-range scenes from modulo-wrapped measurements, where wrap discontinuities hinder edge recovery. It introduces a learning-based HDR restoration framework that combines scale-equivariant regularization with a feature-lifting input (raw modulo image, wrapped finite differences, and a closed-form initialization) to better separate true structure from wrapping artifacts. The method optimizes a reconstruction loss together with an equivariance penalty and is evaluated on the UnModNet dataset, achieving state-of-the-art perceptual (PU21) and linear HDR metrics, with notable gains over strong baselines. By enforcing exposure-scale consistency and supplying physics-informed input priors, the approach enhances robustness to varying exposures and wrapping artifacts, with practical implications for HDR imaging pipelines in constrained hardware settings.

Abstract

Modulo imaging enables high dynamic range (HDR) acquisition by cyclically wrapping saturated intensities, but accurate reconstruction remains challenging due to ambiguities between natural image edges and artificial wrap discontinuities. This work proposes a learning-based HDR restoration framework that incorporates two key strategies: (i) a scale-equivariant regularization that enforces consistency under exposure variations, and (ii) a feature lifting input design combining the raw modulo image, wrapped finite differences, and a closed-form initialization. Together, these components enhance the network's ability to distinguish true structure from wrapping artifacts, yielding state-of-the-art performance across perceptual and linear HDR quality metrics.

Scale Equivariance Regularization and Feature Lifting in High Dynamic Range Modulo Imaging

TL;DR

The paper tackles reconstructing high-dynamic-range scenes from modulo-wrapped measurements, where wrap discontinuities hinder edge recovery. It introduces a learning-based HDR restoration framework that combines scale-equivariant regularization with a feature-lifting input (raw modulo image, wrapped finite differences, and a closed-form initialization) to better separate true structure from wrapping artifacts. The method optimizes a reconstruction loss together with an equivariance penalty and is evaluated on the UnModNet dataset, achieving state-of-the-art perceptual (PU21) and linear HDR metrics, with notable gains over strong baselines. By enforcing exposure-scale consistency and supplying physics-informed input priors, the approach enhances robustness to varying exposures and wrapping artifacts, with practical implications for HDR imaging pipelines in constrained hardware settings.

Abstract

Modulo imaging enables high dynamic range (HDR) acquisition by cyclically wrapping saturated intensities, but accurate reconstruction remains challenging due to ambiguities between natural image edges and artificial wrap discontinuities. This work proposes a learning-based HDR restoration framework that incorporates two key strategies: (i) a scale-equivariant regularization that enforces consistency under exposure variations, and (ii) a feature lifting input design combining the raw modulo image, wrapped finite differences, and a closed-form initialization. Together, these components enhance the network's ability to distinguish true structure from wrapping artifacts, yielding state-of-the-art performance across perceptual and linear HDR quality metrics.
Paper Structure (11 sections, 9 equations, 2 figures, 2 tables)

This paper contains 11 sections, 9 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Modulo Imaging
  3. Method
  4. Restoration Model Formulation
  5. Input Construction ${\boldsymbol{z}}$
  6. Scale Equivariance Regularization $\mathcal{R}_{\mathrm{eq}}$
  7. Simulations
  8. Dataset and Experimental Setup
  9. Input Construction Analysis
  10. State-of-the-art Comparison
  11. Conclusions

Figures (2)

  • Figure 1: Input alternatives. (a) raw modulo image $\boldsymbol{y}$, exhibiting wrapping edges; (b) wrapped finite differences $\mathcal{M}_b(\Delta\boldsymbol{y})$, which accentuate true edges; and (c) closed‑form initialization $\boldsymbol{x}_0$, capturing large‑scale illumination.
  • Figure 2: Visual Results of HDR Recovery Methods. Qualitative comparison of unwrapped images from various methods, demonstrating the proposed approach achieves superior visual fidelity and quantitative metrics (PSNR-Y$\vert$SSIM$\vert$MS-SSIM) on PU21 encoding and compared to state-of-the-art alternatives. Visual HDR images are displayed using Reinhard tone mapping.