Biomedical Engineering Reference
In-Depth Information
Figure 1.
Using a shape transformation for morphometric measurements: (a) Top left: a
template of the cross-section of the corpus callosum, a brain structure connecting the two
hemispheres. Top middle and right: two individual shapes. Bottom: respective color-coded
maps of the determinant of the Jacobian of the shape transformation mapping the template
to the two shapes. Contraction is colored green and expansion red. Voxel-wise comparison
of these images reveals local shape differences of the respective shapes. (b) Seminal work
by D'Arcy Thompson in 1917 using shape transformations to make comparisons among
species. See attached CD for color version.
Although this approach has gained widespread attention only within the past
decade, it has its roots in the seminal work by D'Arcy Thompson [39], who studied
differences among species by measuring deformations of coordinate grids from
images of one species to images of another (see Figure 1b). At that time, very
limited manual drawing methods were available to D'Arcy Thompson, which
imposed limits on the spatial specificity of this approach. The approach was
later adopted by Bookstein in the landmark-based morphometrics literature [23]
and further extended by Grenander's pattern theory [40] and Miller's work on
