Center of Imaging Science and Department of Biomedical Engineering, Johns Hopkins University, United States of America.
Centre Giovanni Borelli (UMR 9010), Ecole Normale Supérieure Paris-Saclay, Université Paris-Saclay, France.
Med Image Anal. 2024 Apr;93:103068. doi: 10.1016/j.media.2023.103068. Epub 2023 Dec 23.
Advances in the development of largely automated microscopy methods such as MERFISH for imaging cellular structures in mouse brains are providing spatial detection of micron resolution gene expression. While there has been tremendous progress made in the field of Computational Anatomy (CA) to perform diffeomorphic mapping technologies at the tissue scales for advanced neuroinformatic studies in common coordinates, integration of molecular- and cellular-scale populations through statistical averaging via common coordinates remains yet unattained. This paper describes the first set of algorithms for calculating geodesics in the space of diffeomorphisms, what we term space-feature-measure LDDMM, extending the family of large deformation diffeomorphic metric mapping (LDDMM) algorithms to accommodate a space-feature action on marked particles which extends consistently to the tissue scales. It leads to the derivation of a cross-modality alignment algorithm of transcriptomic data to common coordinate systems attached to standard atlases. We represent the brain data as geometric measures, termed as space-feature measures supported by a large number of unstructured points, each point representing a small volume in space and carrying a list of densities of features elements of a high-dimensional feature space. The shape of space-feature measure brain spaces is measured by transforming them by diffeomorphisms. The metric between these measures is obtained after embedding these objects in a linear space equipped with the norm, yielding a so-called "chordal metric".
广泛应用于成像鼠脑细胞结构的全自动显微镜方法（如 MERFISH）的发展为基因表达的微米分辨率的空间检测提供了可能。尽管在计算解剖学（CA）领域已经取得了巨大的进展，可以在组织尺度上进行变形映射技术，以在共同坐标下进行高级神经信息学研究，但通过共同坐标进行分子和细胞尺度群体的统计平均的整合仍未实现。本文描述了在变形空间中计算测地线的第一组算法，我们称之为空间特征度量 LDDMM，将大变形变形度量映射（LDDMM）算法家族扩展到可以适应标记粒子的空间特征操作，该操作可以一致地扩展到组织尺度。这导致了转录组数据到附着在标准图谱上的共同坐标系的跨模态配准算法的推导。我们将大脑数据表示为几何度量，称为空间特征度量，由大量非结构化点支持，每个点代表空间中的一个小体积，并携带高维特征空间的特征元素的密度列表。通过变形来测量空间特征度量脑空间的形状。在将这些对象嵌入配备范数的线性空间后，获得这些度量之间的度量，从而得到所谓的“弦测度”。
