Example: Binary Opening and Closing

Binary opening and closing are dual compositions with visibly different purposes:

• open_B(A) = (A ⊖ B) ⊕ B removes structures that cannot contain the structuring element;
• close_B(A) = (A ⊕ B) ⊖ B fills gaps that cannot contain the reflected structuring element.

Opening is anti-extensive: it removes foreground structures that cannot contain the structuring element. Closing is extensive: it fills background gaps that cannot contain the reflected element.

The runnable example uses one deterministic 3-D mask containing both defect classes. The isolated speck and one-voxel spur give opening something to remove; the small internal holes give closing something to fill. The red and green change maps make those distinct effects explicit:

Source and command

Source: crates/ritk-filter/examples/book_binary_morphology.rs

cargo run -p ritk-filter --example book_binary_morphology -- \
  docs/book/figures/binary_morphology.svg

The example executes BinaryMorphologicalOpening::apply_native and BinaryMorphologicalClosing::apply_native with radius one. It fails unless:

• opening preserves geometry and every displayed interior output voxel is less than or equal to its input voxel;
• closing preserves geometry and every displayed interior output voxel is greater than or equal to its input voxel;
• opening removes at least one foreground voxel;
• closing fills at least one background voxel; and
• the opening and closing outputs differ.

The contract is checked on the center slice because RITK’s documented zero-background boundary condition can remove foreground at the outermost volume planes during the erosion stage of closing.

The complete processing pipeline shows the same operations in a longer filter chain. Tests additionally cover radius-zero identity, border behavior, foreground values, and native/generic parity.