Joint registration of a stack of 2D histological sections to recover 3D structure (“3D histology reconstruction”) finds application in areas such as atlas building and validation of in vivo imaging. Straightforward pairwise registration of neighbouring sections yields smooth reconstructions but has well-known problems such as “banana effect” (straightening of curved structures) and “z-shift” (drift). While these problems can be alleviated with an external, linearly aligned reference (e.g., Magnetic Resonance (MR) images), registration is often inaccurate due to contrast differences and the strong nonlinear distortion of the tissue, including artefacts such as folds and tears. In this paper, we present a probabilistic model of spatial deformation that yields reconstructions for multiple histological stains that that are jointly smooth, robust to outliers, and follow the reference shape. The model relies on a spanning tree of latent transforms connecting all the sections and slices of the reference volume, and assumes that the registration between any pair of images can be see as a noisy version of the composition of (possibly inverted) latent transforms connecting the two images. Bayesian inference is used to compute the most likely latent transforms given a set of pairwise registrations between image pairs within and across modalities. We consider two likelihood models: Gaussian (${\ell }_2$ norm, which can be minimised in closed form) and Laplacian (${\ell }_1$ norm, minimised with linear programming). Results on synthetic deformations on multiple MR modalities, show that our method can accurately and robustly register multiple contrasts even in the presence of outliers. The framework is used for accurate 3D reconstruction of two stains (Nissl and parvalbumin) from the Allen human brain atlas, showing its benefits on real data with severe distortions. Moreover, we also provide the registration of the reconstructed volume to MNI space, bridging the gaps between two of the most widely used atlases in histology and MRI. The 3D reconstructed volumes and atlas registration can be downloaded from https://openneuro.org/datasets/ds003590. The code is freely available at https://github.com/acasamitjana/3dhirest.

联合配准一堆 2D 组织学切片以恢复 3D 结构（“3D 组织学重建”）可应用于图谱构建和体内成像验证等领域。相邻部分的直接成对配准可产生平滑的重建，但存在众所周知的问题，例如“香蕉效应”（弯曲结构的拉直）和“z 偏移”（漂移）。虽然可以通过外部线性对齐参考（例如磁共振（MR）图像）来缓解这些问题，但由于对比度差异和组织的强烈非线性失真（包括折叠和撕裂等伪影），配准通常不准确。在本文中，我们提出了一种空间变形的概率模型，该模型可以对多个组织学染色进行重建，这些染色共同平滑，对异常值具有鲁棒性，并且遵循参考形状。该模型依赖于连接参考体积的所有部分和切片的潜在变换的生成树，并假设任何图像对之间的配准可以被视为连接参考体积的潜在变换（可能是反向的）组合的噪声版本。两个图像。贝叶斯推理用于计算给定模态内和跨模态的图像对之间的一组成对配准的最可能的潜在变换。我们考虑两种似然模型：高斯（${\mathrm{<span\; data-immersive-translate-walked="fa60125c-758d-4f2a-be48-e72cbb02d755">\ell </span>}}_{\mathrm{<span\; data-immersive-translate-walked="fa60125c-758d-4f2a-be48-e72cbb02d755">2</span>}}$范数，可以以封闭形式最小化）和拉普拉斯（${\mathrm{<span\; data-immersive-translate-walked="fa60125c-758d-4f2a-be48-e72cbb02d755">\ell </span>}}_{\mathrm{<span\; data-immersive-translate-walked="fa60125c-758d-4f2a-be48-e72cbb02d755">1</span>}}$范数，通过线性规划最小化）。 多种 MR 模态的合成变形结果表明，即使存在异常值，我们的方法也能准确、稳健地记录多种对比度。该框架用于对 Allen 人脑图谱中的两种染色剂（尼氏染色和小清蛋白）进行精确 3D 重建，显示了其对严重扭曲的真实数据的优势。此外，我们还提供重建体积到 MNI 空间的配准，弥合组织学和 MRI 中两个最广泛使用的图册之间的差距。 3D 重建体积和图集注册可以从 https://openneuro.org/datasets/ds003590 下载。该代码可在 https://github.com/acasamitjana/3dhirest 上免费获取。