Morphological Operations

Binary and grayscale morphological filters: erosion, dilation, opening, closing, top-hat transforms, hit-or-miss, and morphological reconstruction.

Design

All morphological operations operate on flat host buffers via substrate-agnostic pure functions. Binary operations use safe-border padding (zero padding at boundaries); grayscale operations preserve spatial metadata.

Binary Morphology

• BinaryErodeFilter, BinaryDilateFilter — flat rectangular structuring elements with one voxel radius per axis
• BinaryFillholeFilter — flood-fill based hole filling
• BinaryMorphologicalClosing, BinaryMorphologicalOpening — dilation followed by erosion (closing) or erosion followed by dilation (opening)

For anisotropic volumes, a voxel radius does not represent one physical distance. voxel_radii_for_physical_radius converts a millimetre radius to independent [z, y, x] radii using floor(radius / spacing_i). Pass the result to with_axis_radii; for 3.0 mm slices and 0.4 mm in-plane spacing, a 3.2 mm support becomes [1, 8, 8] rather than [8, 8, 8]. The latter would span 24 mm through-plane and can corrupt registration masks even though its axial view looks plausible.

Grayscale Morphology

• GrayscaleErosion, GrayscaleDilation — min/max filter with safe-border padding
• GrayscaleClosingFilter, GrayscaleOpeningFilter — extensive and anti-extensive operations, respectively
• WhiteTopHatFilter, BlackTopHatFilter — residue of opening/closing
• GrayscaleGradientFilter — erosion minus dilation

Reconstruction

• GrayscaleGeodesicErosion, GrayscaleGeodesicDilation — geodesic operations using reconstruction

Verification

Each operation is differentially tested against its Coeus-generic counterpart via assert_coeus_matches_coeus. Analytical oracles verify:

• Radius 0 is identity
• All-foreground/all-background edge cases
• Opening is anti-extensive; closing is extensive away from the finite-image boundary where the documented zero-background padding applies

The binary opening and closing example constructs a mask with both removable foreground artifacts and fillable background holes, then renders explicit red removal and green fill maps from the native filter outputs.