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Diffeomorphometry is the metric study of i … Diffeomorphometry is the metric study of imagery, shape and form in the discipline of computational anatomy (CA) in medical imaging. The study of images in computational anatomy rely on high-dimensional diffeomorphism groups which generate orbits of the form , in which images can be dense scalar magnetic resonance or computed axial tomography images. For deformable shapes these are the collection of manifolds , points, curves and surfaces. The diffeomorphisms move the images and shapes through the orbit according to which are defined as the group actions of computational anatomy. The orbit of shapes and forms is made into a metric space by inducing a metric on the group of diffeomorphisms. The study of metrics on groups of diffeomorphisms and the study of metrics between manifolds and surfaces has been an area of significant investigation. In Computational anatomy, the diffeomorphometry metric measures how close and far two shapes or images are from each other. Informally, the metric is constructed by defining a flow of diffeomorphisms which connect the group elements from one to another, so for then . The metric between two coordinate systems or diffeomorphisms is then the shortest length or geodesic flow connecting them. The metric on the space associated to the geodesics is given by. The metrics on the orbits are inherited from the metric induced on the diffeomorphism group. The group is thusly made into a smooth Riemannian manifold with Riemannian metric associated to the tangent spaces at all . The Riemannian metric satisfies at every point of the manifold there is an inner product inducing the norm on the tangent space that varies smoothly across . Oftentimes, the familiar Euclidean metric is not directly applicable because the patterns of shapes and images don't form a vector space. In the Riemannian orbit model of Computational anatomy, diffeomorphisms acting on the forms don't act linearly. There are many ways to define metrics, and for the sets associated to shapes the Hausdorff metric is another. The method used to induce the Riemannian metric is to induce the metric on the orbit of shapes by defining it in terms of the metric length between diffeomorphic coordinate system transformations of the flows. Measuring the lengths of the geodesic flow between coordinates systems in the orbit of shapes is called diffeomorphometry.bit of shapes is called diffeomorphometry.
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Diffeomorphometry is the metric study of i … Diffeomorphometry is the metric study of imagery, shape and form in the discipline of computational anatomy (CA) in medical imaging. The study of images in computational anatomy rely on high-dimensional diffeomorphism groups which generate orbits of the form , in which images can be dense scalar magnetic resonance or computed axial tomography images. For deformable shapes these are the collection of manifolds , points, curves and surfaces. The diffeomorphisms move the images and shapes through the orbit according to which are defined as the group actions of computational anatomy.he group actions of computational anatomy.
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Diffeomorphometry
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