The Emerging Field of Computational Anatomy

Michael Miller
Johns Hopkins University
Center for Imaging Science

Computational Anatomy (CA) is the mathematical study of anatomy

, an

orbit under groups of diffeomorphisms (i.e., smooth invertible mappings)


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


for inference and disease testing within the anatomical models. We review

recent advances principally in the area of metric comparison of anatomical

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

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

Diffeomorphic Metric Mapping (LDDMM) methods. Surface displacements are color

coded and the direction of growth visualized by 3D glyphs. Although these

contain not only the effects of growth, but the effects of landmark placement

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.

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