page_title: Computational anatomy
section_title: The random orbit model of computational anatomy
hierarchical_section_title: Computational anatomy / The random orbit model of computational anatomy
caption_attribution_description: English: Showing randomly generated subcortical structures in two-dimensional space
context_page_description: Computational anatomy is an interdisciplinary field of biology focused on quantitative investigation and modelling of anatomical shapes variability. It involves the development and application of mathematical, statistical and data-analytical methods for modelling and simulation of biological structures.
  The field is broadly defined and includes foundations in anatomy, applied mathematics and pure mathematics, machine learning, computational mechanics, computational science, biological imaging, neuroscience, physics, probability, and statistics; it also has strong connections with fluid mechanics and geometric mechanics. Additionally, it complements newer, interdisciplinary fields like bioinformatics and neuroinformatics in the sense that its interpretation uses metadata derived from the original sensor imaging modalities. It focuses on the anatomical structures being imaged, rather than the medical imaging devices. It is similar in spirit to the history of Computational linguistics, a discipline that focuses on the linguistic structures rather than the sensor acting as the transmission and communication media.
context_section_description: The random orbit model  of computational anatomy first appeared in modelling the change in coordinates associated to the randomness of the group acting on the templates, which induces the randomness on the source of images in the anatomical orbit of shapes and forms and resulting observations through the medical imaging devices. Such a random orbit model in which randomness on the group induces randomness on the images was examined for the Special Euclidean Group for object recognition in.
  Depicted in the figure is a depiction of the random orbits around each exemplar, , generated by randomizing the flow by generating the initial tangent space vector field at the identity , and then generating random object .
  The random orbit model induces the prior on shapes and images  conditioned on a particular atlas . For this the generative model generates the mean field  as a random change in coordinates of the template according to , where the diffeomorphic change in coordinates is generated randomly via the geodesic flows. The prior on random transformations  on  is induced by the flow , with  constructed as a Gaussian random field prior . The density on the random observables at the output of the sensor  are given by
  Shown in the Figure on the right the cartoon orbit, are a random spray of the subcortical manifolds generated by randomizing the vector fields  supported over the submanifolds.
caption: Figure showing the random spray of synthesized subcortical structures laid out in the two-dimensional grid representing the variance of the eigenfunction used for the momentum for synthesis.
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