Table 1.

Glossary of symbols and parameters in the XDD registration process. Nominal values for excision segmentation given for phantom images reconstructed in units of attenuation coefficient (mm⁻¹).

Process	Symbol	Description [nominal value]
Demons registration	Niter	Number of iterations [15 (DS8), 25 (DS4), 25 (DS2), 15 (DS1)]
	σ	Size of smoothing kernel [1.0 voxel]
	$\stackrel{\rightharpoonup }{u}$	Update field
	$\stackrel{\rightharpoonup }{D}$	Deformation field
Excision segmentation	T	Air/tissue intensity threshold [0.003 mm−1]
	α	Steepness of threshold probability function [1000]
	$P_{\mathrm{moving}}^{\mathrm{tissue}}$	Probability that voxel in moving image is tissue
	$P_{\mathrm{fixed}}^{\mathrm{air}}$	Probability that voxel in fixed image is air
	Pplan	Prior information (surgical plan) probabilistic weighing of voxel for excision
	Pexcision	Probability of excision for given voxel
XDD registration	kforce	Excision force proportionality constant [1.0]
	khorizon	Excision “horizon” proportionality constant [1.0]
	${\stackrel{\rightharpoonup }{u}}_{1:3}$	Update field deformation components
	${\stackrel{\rightharpoonup }{u}}_4$	Update field excision component
	${\stackrel{\rightharpoonup }{D}}_{1:3}$	Deformation field deformation component
	${\stackrel{\rightharpoonup }{D}}_4$	Deformation field excision component