Constrained distance transforms for spatial atlas registration

BMC Bioinformatics

Table 4 3D Displacement errors

N	\({\frac {1}{\sqrt [3]{N}}}\)	l _RBF	l _MESH	ε
7963	0.050	65.7 ±78.5	65.4 ±78.1	0.0134 ±0.0268
13899	0.042	61.1 ±75.0	60.9 ±74.5	0.0095 ±0.0235
40255	0.029	62.2 ±75.4	62.0 ±74.5	0.0061 ±0.0278
117537	0.020	58.9 ±75.0	58.8 ±75.0	0.0046 ±0.0325
1294844	0.009	67.1 ±84.2	67.0 ±82.9	0.0023 ±0.0259

Variation in the length of the mesh element centroid displacement error vector with the number of nodes in the mesh; where N is the number of nodes in the mesh, l _RBF is the length of the RBF displacement vector, l _MESH is the length of the interpolated displacement vector and ε=(l _RBF −l _MESH )/l _RBF. There is an approximate linear relationship between the displacement error (ε) and \(\boldsymbol {\frac {1}{\sqrt [3]{N}}}\), with a correlation coefficient of 0.98.

ISSN: 1471-2105