Slice-to-Volume Nonrigid Registration of Histological Sections to MR Images of the Human Brain

Table 2

Two-stage NEWUOA registration results for six cost functions (correlation coefficient, correlation ratio, local correlation, rank correlation, Maes’ normalized mutual information with 64 bins, and sum of squared differences). Each registration result is presented by the cumulative similarity measure SM, the bending energy 𝐸_𝑇, and the running time 𝑇 in minutes. Columns 1–8 are for eight slices from eight distinct blocks of the brain sample. The last column is the sum of 1–8. Values referenced in the text are in boldface.

CostFunc	Var∖Blk no.	1	2	3	4	5	6	7	8	∑^81
CC	SM	6.056	6.124	5.941	5.814	5.349	5.261	5.688	5.876	46.109
	𝐸𝑇	3.1	2.3	2.4	9.5	6.7	12.2	3.5	4.7	44.3
	𝑇 (min)	0.7	4.5	12.1	9.0	10.4	22.0	6.9	3.5	69.2
CR	SM	6.029	6.125	5.941	5.421	5.397	5.249	5.773	5.871	45.808
	𝐸𝑇	4.3	2.3	4.4	18.7	11.6	24.2	8.9	9.2	83.6
	𝑇 (min)	0.5	5.5	15.9	21.8	11.2	22.1	15.8	3.3	96.1
LC	SM	5.215	6.150	5.250	5.806	5.306	5.217	5.713	5.681	44.338
	𝐸𝑇	23.6	3.9	19.7	10.5	6.6	14.8	5.1	6.3	90.5
	𝑇 (min)	3.6	16.4	69.4	43.2	56.0	60.7	47.4	10.9	307.6
RC	SM	5.958	6.064	5.379	5.806	5.389	5.221	5.687	5.71	45.215
	𝐸𝑇	3.3	4.2	12.7	8.1	7.4	11.4	3.4	6.5	56.9
	𝑇 (min)	0.3	9.7	42.8	14.0	24.2	30.1	31.4	3.3	155.8
NMI	SM	5.570	5.778	5.810	5.304	4.938	4.540	5.544	5.418	42.901
	𝐸𝑇	6.9	5.7	7.1	8.6	6.7	5.5	6.0	5.1	51.7
	𝑇 (min)	0.3	4.6	19.3	10.8	15.9	14.2	15.9	2.4	83.4
SSD	SM	6.075	6.079	5.925	5.882	5.392	5.309	5.778	5.712	46.152
	𝐸𝑇	4.1	6.2	4.3	12.2	10.6	19.7	7.7	10.3	75.1
	𝑇 (min)	0.8	6.8	13.5	16.9	15.3	24.0S	16.6	2.6	96.5