Erosion shrinks a shape by removing material from its border. Geometrically, it is an inward offset: voxel models lose volume, while a true signed distance function (SDF) receives a positive offset. section 10.2.3 section 12.3.6
Use erosion in practical modeling workflows to:
- Remove small isolated artifacts and smooth noisy borders before restoring the remaining shape with dilation. section 12.3.3
- Create a hollow shell by eroding, removing the SDF sign, and dilating the resulting border. section 10.2.4
- Expose features thinner than a selected wall threshold for early 3D-printing checks. section 12.3.5
- Patch thin cracks or test spacing by reversing the sequence: dilate first, then erode. section 12.3.5
SDF_dilated = SDF - offset SDF_eroded = SDF + offset
For a true SDF, erosion is implemented by adding the offset to the function; dilation uses subtraction. section 10.2.3
Binary-image erosion
A reusable implementation inverts a binary image, dilates the inverted image, and inverts it again: erode(img, depth) = invert(dilate(invert(img), depth)). Applying erosion and then proportionate dilation removes a small noisy component while retaining thicker features. section 12.3.2 section 12.3.3
The representation matters. Voxel erosion is fast and reliable when operands share a grid, whereas SDF offsets are correct only while the function remains a true distance function. Boolean operations destroy that property, so post-Boolean erosion can preserve incorrect sharp features. section 10.2.3 section 12.3.6
