Binary erosion checks a neighborhood against the foreground support. Its result depends on the structuring element and defined boundary treatment.
Specify the binary neighborhood
With a flat binary structuring element, erosion retains foreground where the required neighborhood is foreground; the local minimum gives the binary result. The structuring-element support and reference position define that requirement. It is an image operation, not a direct subtraction of a physical length from every object. Primary reference: MathWorks erosion and flat-neighborhood minimum.
For an original worksheet, name which value is foreground and list the required offsets. Keep a horizontal three-position element distinct from a square three-by-three element. They test different sample sets even when both are called size three.
Trace a fictional foreground run
Consider an invented binary row [0,1,1,1,0] with foreground 1. Use horizontal offsets −1,0,+1, centered at each tested sample. The middle foreground sample has neighborhood [1,1,1] and survives. Its adjacent foreground samples each see a zero and do not survive.
The result is [0,0,1,0,0] under this stated setup. The example’s acquired zeros determine the relevant failures; outside-row extension is not needed to justify them. This tiny row is a teaching mask and does not describe physical container dimensions.
Review the required feature support
Prepare an original mask and mark each tested offset at a narrow feature. Retain the element orientation, reference and output boundary convention in the record. If the element changes, review the feature-support question again rather than describing the two masks as equivalently cleaned.
Erosion can remove desired foreground structure as well as another selected pattern. No result here certifies a defect or an HM inspection capability. The decision is which foreground samples meet the stated neighborhood requirement, before a derived mask is used for subsequent counting or geometry.
Customer Questions
Which foreground sample survives in the fictional row?
Only the middle one, whose full required neighborhood is foreground.
Is a horizontal element the same as a square element?
No. They test different offsets.
Does the result establish physical shrinkage?
No. Physical interpretation needs additional geometry and calibration.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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