Table 2 Comparison test of AD-SVFD with seven alternative registration methods

	Method	Multi shape	DL	Max. errors (in cm)
				Direct		Inverse
				FLD	BLD	FLD	BLD
P#090	CPD	✗	✗	1.4321	2.0983	1.3985	2.9714
	TPS	✗	✗	0.2918	0.2615	0.4305	0.3674
	LDDMM	✗	✗	0.1813	0.1227	0.2625	0.3332
	ResNet	✗	✓	0.2470	0.2806	0.4393	0.6520
	I-ResNet	✗	✓	0.1948	0.2269	0.2139	0.2466
	SVFD	✗	✓	0.1339	0.1479	0.1674	0.1659
	SDF4CHD	✓	✓	0.3861	1.7831	0.6250	0.4207
	AD-SVFD	✓	✓	0.1693	0.1923	0.2071	0.1719
P#278	CPD	✗	✗	1.5265	1.1772	1.3802	2.0471
	TPS	✗	✗	0.5092	0.3521	0.7974	0.7104
	LDDMM	✗	✗	0.1281	0.1681	0.5160	0.5441
	ResNet	✗	✓	0.3085	0.2720	0.3546	0.3594
	I-ResNet	✗	✓	0.2805	0.2498	0.2986	0.3367
	SVFD	✗	✓	0.1343	0.1614	0.2248	0.2259
	SDF4CHD	✓	✓	0.2598	1.2918	1.0277	0.2754
	AD-SVFD	✓	✓	0.2166	0.1807	0.2817	0.2933

In particular, we report the maximal pointwise errors on patients P#090 and P#278, obtained considering CPD⁴⁰, TPS⁵⁴, LDDMM⁹, ResNet-LDDMM ²⁸ (optionally endowed with a penalty of the inverse deformation, I-ResNet-LDDMM), SVFD (i.e., our model without auto-decoder structure), SDF4CHD³³, and AD-SVFD. The errors are quantified through the forward and backward local distances (FLD and BLD), expressed in cm. The column Multi Shape identifies methods that allow for the simultaneous registration of multiple shapes; the column DL identifies deep learning models. The best results for single-shape approaches are shown in bold; the best results for multi-shape approaches are underlined. For reference, the inlet diameters are: 1.31 cm for P#091 (template); 1.22 cm for P#090; 1.52 cm for P#278.

Quick links

Search