Privacy Preserving Image Registration

TL;DR

This paper introduces Privacy Preserving Image Registration (PPIR), a framework enabling image alignment without exposing sensitive medical data by leveraging Secure Multi-Party Computation (MPC) and Fully Homomorphic Encryption (FHE). It analyzes how classical IR losses—SSD, Mutual Information, and ANTs CC—translate under privacy constraints and develops PPIR variants: PPIR(MPC) and PPIR(FHE) for SSD, plus MPC-focused solutions for MI and CC. To tackle cryptographic overhead, it proposes gradient sampling and matrix partitioning (v1/v2) to reduce communication and computation while preserving accuracy. Experimental results across 2D and 3D datasets show PPIR can achieve comparable registration quality to clear data with substantial privacy guarantees, though FHE-based approaches face scalability limits that are mitigated by proposed optimizations. The work lays a foundation for secure, privacy-compliant medical image analysis and points to future enhancements in loss functions and hardware acceleration for real-time deployment.

Abstract

Image registration is a key task in medical imaging applications, allowing to represent medical images in a common spatial reference frame. Current approaches to image registration are generally based on the assumption that the content of the images is usually accessible in clear form, from which the spatial transformation is subsequently estimated. This common assumption may not be met in practical applications, since the sensitive nature of medical images may ultimately require their analysis under privacy constraints, preventing to openly share the image content.In this work, we formulate the problem of image registration under a privacy preserving regime, where images are assumed to be confidential and cannot be disclosed in clear. We derive our privacy preserving image registration framework by extending classical registration paradigms to account for advanced cryptographic tools, such as secure multi-party computation and homomorphic encryption, that enable the execution of operations without leaking the underlying data. To overcome the problem of performance and scalability of cryptographic tools in high dimensions, we propose several techniques to optimize the image registration operations by using gradient approximations, and by revisiting the use of homomorphic encryption trough packing, to allow the efficient encryption and multiplication of large matrices. We demonstrate our privacy preserving framework in linear and non-linear registration problems, evaluating its accuracy and scalability with respect to standard, non-private counterparts. Our results show that privacy preserving image registration is feasible and can be adopted in sensitive medical imaging applications.

Figures (10)

• Figure 1: Optimization of SSD loss: proposed framework to compute matrix-vector multiplication $S^T \cdot J$ based on PPIR(MPC) and PPIR(FHE)-v1.
• Figure 2: Qualitative results for affine registration with MI over 3D medical images using ADNI dataset mueller2005alzheimer. The images are presented in a $3 \times 4$ grid, with the first row representing the axial axis, the second row the coronal axis, and the third row the sagittal axis. In the first column of each row, the moving image obtained using PET modality is shown, while in the second column, the fixed image obtained using MRI modality is displayed. The third column shows the checkerboard alignment result using Clear, while the fourth column shows the result using PPIR(MPC). The different protocols are highlighted by red and green frames, respectively.
• Figure 3: Qualitative results for diffeomorphic registration with CC between 3D medical images from the AbdomenMRCT dataset hering2022learn2reg. The images are presented in a $3 \times 4$ grid, with the first row representing the axial axis, the second row the coronal axis, and the third row the sagittal axis. First and second column show respectively MRI and CT images. The third column shows the MRI transformed using Clear, while the fourth column shows the MRI transformed using PPIR(MPC). The transformed images are highlighted by red and green frames, respectively.
• Figure A1: Optimization of MI loss: proposed framework to calculate matrix multiplication $P = \frac{1}{N_{{\bm{x}}}} \cdot (A_I^3)^T \cdot B_J^0$ and $P'= - \frac{1}{N_{{\bm{x}}}} \cdot (B_J^0)^T \cdot C_I^3$ based on PPIR(MPC).
• Figure A2: Optimization of ANTS NCC loss: proposed framework to calculate $\frac{2D}{EF}$ and $(\bar{J} - \frac{D}{E} \bar{I} )$ based on PPIR(MPC).