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 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 Image-Varifold LDDMM,extending the family of large deformation diffeomorphic metric mapping (LDDMM) algorithms to accommodate the "copy and paste" varifold action of particles which extends consistently to the tissue scales. We represent the brain data as geometric measures, termed as {\em image varifolds} supported by a large number of unstructured points, % (i.e., not aligned on a 2D or 3D grid), each point representing a small volume in space % (which may be incompletely described) and carrying a list of densities of {\em features} elements of a high-dimensional feature space. The shape of image varifold brain spaces is measured by transforming them by diffeomorphisms. The metric between image varifolds is obtained after embedding these objects in a linear space equipped with the norm, yielding a so-called "chordal metric."
翻译:基本上自动化的显微镜学方法(如MERFISH)的开发进展,如用于鼠脑成像细胞结构的MERFISIS等,正在提供微分解基因表达的空间探测。虽然在实地计算解剖基因(CA)方面已经取得巨大进展,以便在组织规模上应用异光绘图技术,以便在共同坐标上进行先进的神经信息学研究,通过共同坐标将分子和细胞规模人口通过平均统计法进行整合,但还有待完成。本文描述了计算多种非结构化点(即,不与2D或3D网格相匹配)的第一套计算大地学的算法,我们称之为图像-Varifyle LDDMMM,将大规模变异成的变异性指标(LDDDMMM)的组合扩展为组织规模一致扩展的粒子的“复制和糊状”变动动作。我们把大脑数据作为几何测度衡量尺度,称为 缩图变形数%(即不统一在2D或3D网格上),每个点代表着空间结构的缩缩成型图状图状图状的缩图状。