We introduce "PatchMorph," an new stochastic deep learning algorithm tailored
for unsupervised 3D brain image registration. Unlike other methods, our method
uses compact patches of a constant small size to derive solutions that can
combine global transformations with local deformations. This approach minimizes
the memory footprint of the GPU during training, but also enables us to operate
on numerous amounts of randomly overlapping small patches during inference to
mitigate image and patch boundary problems. PatchMorph adeptly handles world
coordinate transformations between two input images, accommodating variances in
attributes such as spacing, array sizes, and orientations. The spatial
resolution of patches transitions from coarse to fine, addressing both global
and local attributes essential for aligning the images. Each patch offers a
unique perspective, together converging towards a comprehensive solution.
Experiments on human T1 MRI brain images and marmoset brain images from serial
2-photon tomography affirm PatchMorph's superior performance.

PatchMorph 是一种新型的随机深度学习算法，用于无监督的三维脑图像配准。与其他方法不同，我们的方法使用了具有恒定小尺寸的紧凑补丁，以得到既能够结合全局变换又能进行局部变形的解决方案。这种方法在训练过程中最小化了 GPU 的内存占用，同时可以在推理过程中处理大量随机重叠的小补丁，从而减轻图像和补丁边界问题。PatchMorph 能够处理两个输入图像之间的世界坐标变换，适应间距、数组大小和方向等属性的变化。补丁的空间分辨率从粗到细，同时处理全局和局部属性，以实现图像对齐所必需的功能。每个补丁都提供了独特的视角，并一起收敛到一个全面的解决方案。对人类 T1 MRI 脑图像和序列 2-photon 层析成像的 marmoset 脑图像的实验证明了 PatchMorph 的出色性能。

PatchMorph：无监督 3D 脑图像配准的随机深度学习方法

PatchMorph: A Stochastic Deep Learning Approach for Unsupervised 3D  Brain Image Registration with Small Patches

Diffeomorphic registration has become a powerful approach for seeking a
smooth and invertible spatial transformation between two coordinate systems
which have been measured via the template and reference images. While the
pointwise volume-preserving constraint is effective for some problems, it is
too stringent for many other problems especially when the local deformations
are relatively large, because it may lead to a poor large-deformation for
enforcing local matching.In this paper, we propose a novel bi-variant
diffeomorphic image registration model with the soft constraint of Jacobian
equation, which allows local deformations to shrink and grow in a flexible
range.The Jacobian determinant of the transformation is explicitly controlled
by optimizing the relaxation function. To prevent deformation folding and
enhance the smoothness of deformation, we not only impose a positivity
constraint in optimizing the relaxation function, but also employ a regularizer
to ensure the smoothness of the relaxation function.Furthermore, the positivity
constraint ensures that is as close to one as possible, which helps to obtain a
volume-preserving transformation on average.We further analyze the existence of
the minimizer for the variational model and propose a penalty splitting method
with a multilevel strategy to solve this model. Numerical experiments show that
the proposed algorithm is convergent, and the positivity constraint can control
the range of relative volume and not compromise registration accuracy.
Moreover, the proposed model produces diffeomorphic maps for large deformation,
and achieves better performance compared to the several existing registration
models.

本文提出了一种具有雅可比方程软约束的新型双变量微分同胚图像配准模型，该模型允许局部变形在一个灵活的范围内收缩和扩大，通过优化松弛函数来明确控制变换的雅可比行列式，并采用正则化器来确保松弛函数的平滑性。数值实验表明，所提出的算法收敛性强，正性约束能控制相对体积的范围而不影响配准准确性。此外，相对于其他几种现有的配准模型，该模型在大变形下产生了微分同胚映射并取得了更好的性能。