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

Table 3

Two-stage NEWUOA registration results for three deformation models (thin plate splines, Gaussian elastic body splines, and cubic B-splines). Rigid registration is also given for the reference. Each registration result is presented by the cumulative similarity measure SM, the bending energy 𝐸_𝑇 (nonrigid only), 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.

Transform	Var⧵Blk no.	1	2	3	4	5	6	7	8	∑^81
TPS	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
GEBS	SM	6.040	6.133	5.917	5.843	5.357	5.225	5.713	5.746	45.976
	𝐸𝑇	3.6	2.7	3.5	9.9	8.3	14.1	4.2	4.0	50.2
	𝑇(min)	1.3	9.3	26.0	46.6	45.9	70.3	27.8	1.7	228.8
B-SPL	SM	6.073	6.145	5.953	5.866	5.422	5.278	5.761	5.894	46.392
	𝐸𝑇	2.9	2.3	2.1	9.1	7.5	12.2	4.6	3.9	44.5
	𝑇(min)	13.3	31.0	306.7	189.3	99.1	133.1	166.5	23.5	962.5
Rigid	SM	5.321	5.581	5.265	4.613	4.234	4.188	4.979	4.917	39.098
	𝑇(min)	0.1	0.1	0.1	0.2	0.2	0.2	0.2	0.1	1.2