Table 1 Registration results of AD-SVFD considering different data attachment measures

From: Deformable registration and generative modelling of aortic anatomies by auto-decoders and neural ODEs

 

Train errors (in cm)

Test errors (in cm)

 

Direct

Inverse

Direct

Inverse

Loss

FLD

BLD

FLD

BLD

FLD

BLD

FLD

BLD

\({{\bf{{\mathcal{D}}}}}_{{\rm {CD}}}\)

0.2162

0.2175

0.2686

0.2297

0.2777

0.2253

0.2562

0.2642

\({{\bf{{\mathcal{D}}}}}_{{\rm {CD}}}^{{\rm {W}}}\)

0.2412

0.2497

0.2869

0.2564

0.4088

0.2479

0.2952

0.4283

\({{\bf{{\mathcal{D}}}}}_{{\rm {PCD}}}\)

0.3195

0.2165

0.3225

0.2611

0.3138

0.2516

0.2749

0.3540

\({{\bf{{\mathcal{D}}}}}_{\rm {{PCD}}}^{{\rm {W}}}\)

0.2515

0.2510

0.2958

0.2579

0.3489

0.2439

0.3043

0.3686

\({{\bf{{\mathcal{D}}}}}_{{\rm {NCD}}}\)

0.2033

0.2166

0.2628

0.2396

0.2965

0.2260

0.2497

0.3090

\({{\bf{{\mathcal{D}}}}}_{{\rm {SD}}}\)

0.4887

0.3795

0.5355

0.3923

0.4519

0.4695

1.1094

0.4384

\({{\bf{{\mathcal{D}}}}}_{{\rm {SD}}}^{{\rm {W}}}\)

0.5866

0.3861

0.5155

0.3917

0.4156

0.4155

0.8275

0.4420

  1. In particular, we report the maximal pointwise errors on training and testing datapoints, obtained for six different data adherence metrics. The errors are quantified through the forward and backward local distances (FLD and BLD), expressed in cm. The best value for each performance metric is shown in bold. For reference, the template shape inlet diameter is 1.31 cm, while the average inlet diameter in the dataset is 1.45 cm. CD: Chamfer distance; PCD: point-to-surface Chamfer distance48; NCD: Chamfer distance with normals penalization; SD: debiased Sinkhorn divergence49. Notation: the W superscript denotes the use of a weighted measure.
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