Table 2.

Description of notation used throughout this paper.

Notation	Description	Notation	Description
𝒞M	3D MRI image scene.	Pi(FT(c))	Probability of FT (c) belonging to class i.
CM	3D grid of pixels on 𝒞M.	ℳT	3D TRUS prostate segmentation.
fM(c)	MRI image intensity function for c ∈ CM.	gT(c)	TRUS segmentation function for c ∈ CT.
ℳM	3D MRI prostate segmentation.	ΩT,i	Collection of pixels in CT that belong to class i.
Pi(c)	TRUS segmentation function for c ∈ CT.	μF,i	Mean vector of FT (c) for ΩT,i.
gM(c)	MRI segmentation function for c ∈ CM.	ΣF,i	Covariance matrix of FT (c) for ΩT,i.
𝒞T	3D TRUS image scene.	ℳ̂T	Estimated TRUS prostate segmentation.
CT	3D grid of pixels on 𝒞T.	gT(c)	Estimated TRUS segmentation function for c ∈ CT.
fT(c)	TRUS image intensity function for c ∈ CT.	T	Transformation function.
𝒞P,i	3D probabilistic model for class i.	S(T(ℳM), 𝒞T)	Similarity metric for T(ℳM) and CT.
Pi(c)	Probability of belonging to class i for c ∈ CT.	R(T)	Regularization metric for T.
FT(c)	Set of intensity and texture based features for c ∈ CT.	ΩM,i	Collection of pixels in CM that belong to class i.
(r,θ, z)	Corresponding polar coordinates for c ∈ CT.	p	Control point location defined on CT.
f̃T(c)	TRUS image intensity function with out signal attenuation for c ∈ CT.	E[p]	Expected location of control point p.
Pi(c)	Spatial prior for c ∈ CT.	𝒩(p)	Set of control points with neighbor p.