Computational Anatomy (CA) is the mathematical study of anatomy
, an
orbit under groups of diffeomorphisms (i.e., smooth invertible mappings)
of
anatomical exemplars
.
The observable images are the output of medical imaging
devices. There are three components that CA examines: (i) constructions of the
anatomical submanifolds, (ii) comparison of the anatomical manifolds via
estimation of
the underlying diffeomorphisms
defining the shape or geometry of the anatomical
manifolds, and (iii) generation of probability laws of anatomical variation
on the
images
for inference and disease testing within the anatomical models. We review
recent advances principally in the area of metric comparison of anatomical
coordinates.
The Euler equations are reviewed for the static metric matching problem as well
as the
growth problem. Recent results on the normal equations of motion for the
momentum
are described, summarizing the relationship between the conservation of momentum
law, geodesic shooting based on the initial vector field at the identity and
growth and
photometric variation representation.
Growth of the murine hippocampal surface measured using Large
Deformation
Diffeomorphic Metric Mapping (LDDMM) methods. Surface displacements are color
coded and the direction of growth visualized by 3D glyphs. Although these
results
contain not only the effects of growth, but the effects of landmark placement
variations
as well, it suggests that the hippocampal growth is not spatially uniform. In
the ventral
part of the hippocampus there is greater tissue displacement during development
than in
the dorsal part.
Copyright. All Rights Reserved.