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An Adaptive Method for Camera Attribution under Complex Radial Distortion Corrections

Andrea Montibeller, Fernando Pérez-González

TL;DR

The paper tackles PRNU-based camera attribution under complex radial distortion corrections by introducing an adaptive, annulus-based divide-and-conquer framework. Each annulus uses a locally simple distortion model (cubic or linear) with per-annulus parameter estimation guided by a maximum-likelihood objective and an adaptive LS-like predictor to propagate estimates across annuli. A CPCE-driven early stopping mechanism enables substantial computational savings while maintaining high detection power, and parameter inheritance across direct/inverse PCE computations further reduces cost. Experimental results on a large, diverse dataset show that the proposed method yields higher accuracy than prior state-of-the-art approaches while substantially reducing runtime, especially for complex out-camera corrections like those from Lightroom and similar tools.

Abstract

Radial correction distortion, applied by in-camera or out-camera software/firmware alters the supporting grid of the image so as to hamper PRNU-based camera attribution. Existing solutions to deal with this problem try to invert/estimate the correction using radial transformations parameterized with few variables in order to restrain the computational load; however, with ever more prevalent complex distortion corrections their performance is unsatisfactory. In this paper we propose an adaptive algorithm that by dividing the image into concentric annuli is able to deal with sophisticated corrections like those applied out-camera by third party software like Adobe Lightroom, Photoshop, Gimp and PT-Lens. We also introduce a statistic called cumulative peak of correlation energy (CPCE) that allows for an efficient early stopping strategy. Experiments on a large dataset of in-camera and out-camera radially corrected images show that our solution improves the state of the art in terms of both accuracy and computational cost.

An Adaptive Method for Camera Attribution under Complex Radial Distortion Corrections

TL;DR

The paper tackles PRNU-based camera attribution under complex radial distortion corrections by introducing an adaptive, annulus-based divide-and-conquer framework. Each annulus uses a locally simple distortion model (cubic or linear) with per-annulus parameter estimation guided by a maximum-likelihood objective and an adaptive LS-like predictor to propagate estimates across annuli. A CPCE-driven early stopping mechanism enables substantial computational savings while maintaining high detection power, and parameter inheritance across direct/inverse PCE computations further reduces cost. Experimental results on a large, diverse dataset show that the proposed method yields higher accuracy than prior state-of-the-art approaches while substantially reducing runtime, especially for complex out-camera corrections like those from Lightroom and similar tools.

Abstract

Radial correction distortion, applied by in-camera or out-camera software/firmware alters the supporting grid of the image so as to hamper PRNU-based camera attribution. Existing solutions to deal with this problem try to invert/estimate the correction using radial transformations parameterized with few variables in order to restrain the computational load; however, with ever more prevalent complex distortion corrections their performance is unsatisfactory. In this paper we propose an adaptive algorithm that by dividing the image into concentric annuli is able to deal with sophisticated corrections like those applied out-camera by third party software like Adobe Lightroom, Photoshop, Gimp and PT-Lens. We also introduce a statistic called cumulative peak of correlation energy (CPCE) that allows for an efficient early stopping strategy. Experiments on a large dataset of in-camera and out-camera radially corrected images show that our solution improves the state of the art in terms of both accuracy and computational cost.
Paper Structure (18 sections, 49 equations, 7 figures, 2 tables)

This paper contains 18 sections, 49 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation and Modeling
  3. Notation
  4. PRNU estimation
  5. Lens Distortion Models
  6. Direct and inverse approaches to PCE computation
  7. State of the Art
  8. Proposed Method
  9. Set partitioning and transform computation
  10. Optimization with respect to $\alpha_k$
  11. Adaptive optimization
  12. PCE computation for the optimal $\boldsymbol \alpha$
  13. Early stopping
  14. Parameter inheritance
  15. Parameter default values
  16. ...and 3 more sections

Figures (7)

  • Figure 1: Values of $\alpha$ maximizing $\text{PCE}_{\mathsf{inv}}(\alpha)$ vs inner radius of the annulus. Values are linearly interpolated. Canon 1200D camera with EF-S 10-18mm lens, corrected with Adobe Lightroom. Focal length: 10mm. Shutter speed: 1/100 sec. Aperture: f7.1. ISO 800. The PRNU is estimated with 20 natural images all taken with those settings.
  • Figure 2: $\text{PCE}_{\mathsf{max}}$ as a function of $\alpha$ for a Panasonic DMC-ZS7 camera.
  • Figure 3: $\text{PCE}_\mathsf{inv}(\alpha)$ for: $\alpha=-0.01$ and $\alpha=0.05$.
  • Figure 4: Annular partition used in the proposed method.
  • Figure 5: Illustration of the application of transforms $T^{-1}_{\alpha_k}$ and $T_{\alpha_k}$, and related domains.
  • ...and 2 more figures