Table 3.

The mathematical notation for pointwise surface distance calculation.

Notation	Definition
A	All pixels that have non-zero intensity on the MRA image.
B	All pixels that have non-zero intensity on the PSM reconstruction.
S(A)	Set of all pixels on the boundary of the binary mask A.
S(B)	Set of all pixels on the boundary of the binary mask B.
||a, S(B)||	Set of Euclidian distances for a point from a a ∈ S(A), to all the points of S(B).
d(a, S(B))	Minimum distance from a a ∈ S(A) to the closest point of S(B).
h(S(A), S(B))	One-sided Hausdorff distance from S(A) to S(B).
H(S(A), S(B))	Two-sided Hausdorff distance between S(A) and S(B).
g(S(A), S(B))	One-sided pointwise surface distance from S(A) to S(B).
G(S(A), S(B))	Two-sided pointwise surface distance (PSD) between S(A) and S(B)