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.

翻译：图像配准是医学成像应用中的一项关键任务，它能够将医学图像表示在共同的空间参考框架中。当前的图像配准方法通常基于一个假设：图像内容通常可以以明文形式访问，进而从中估计空间变换。然而，这一常见假设在实际应用中可能无法满足，因为医学图像的敏感性最终可能要求在其分析过程中遵守隐私约束，从而防止图像内容的公开共享。在本文中，我们提出了隐私保护机制下的图像配准问题，其中图像被视为机密信息，不得以明文形式披露。我们通过扩展经典配准范式，引入先进密码学工具（如安全多方计算和同态加密），推导出隐私保护图像配准框架，这些工具能够在不泄露底层数据的情况下执行操作。为了克服密码学工具在高维场景中的性能和可扩展性问题，我们提出了多种技术来优化图像配准操作，包括使用梯度近似以及重新审视通过打包技术使用同态加密的方法，从而实现对大型矩阵的高效加密和乘法。我们在线性与非线性配准问题中验证了所提出的隐私保护框架，并评估了其相对于标准非隐私对应方法的准确性和可扩展性。我们的结果表明，隐私保护图像配准是可行的，并且可以应用于敏感的医学成像任务中。