Hausdorff Distance

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This node computes the (symmetric) Hausdorff distance between the boundary (TRUE) voxels of two masks. The Hausdorff distance measures the greatest of all distances from any point on one surface to the closest point on the other surface. Formally, for two sets of surface points (A) and (B):

\[ H(A, B) = \max\bigl\{\sup_{a \in A} d(a, B),\; \sup_{b \in B} d(b, A)\bigr\}, \]

where

\[ d(a, B) = \inf_{b \in B} \|a - b\| \]

is the minimum Euclidean distance from point (a) to the set (B).

Haussdorf

A smaller Hausdorff distance indicates that the two masks’ boundaries are closer, i.e., more geometrically similar. Because it captures the worst-case boundary deviation, it is especially sensitive to outlier mismatches.

Inputs

Reference

Reference mask(s).

Type: Mask, List, Required, Single

Inputs

Input mask(s).

Type: Mask, List, Required, Single

Outputs

Output

Table(s) containing the results.

Type: Table, List

Settings

Slice-wise Boolean

Calculate the 2D Hausdorff distance per slice.

Slice Plane Selection

Select the slice plane for slicewise calculation.

Values: i-j, i-k, j-k

Compare Input List Selection

If Pairwise is selected, each element in the Reference list is compared to the corresponding element in the Input list. The two lists must be the same lenght. Output is a list of tables, one for each pair. If you want to have the information as a single table, use Merge Tables.

If Against each Ref element is selected, the filter compares each reference volume to all volumes in the input list. If the reference input is a list, each element in that list will be compared to all elements in the input list, and the output will be a list of tables.

Values: Pairwise, Against each Ref element

Merge Tables Boolean

If output produces a list, merge the list into one table.

See also

Keywords:

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