erode

The dilation operator erode is essentially a min filter. This is a basic term in mathematical morphology – many operations are built on top of erode and the dilate operator.

using ImageMorphology
using TestImages
using ImageBase
using ImageShow

img = restrict(testimage_dip3e("fig1005")) # wirebond mask

For each pixel, dilation is the minimum of the pixels in the neighborhood. In mathematics, erode(A, Ω) is defined as $\delta_A[p] = \inf\{A[p+o] | o \in \Omega\}$ where Ω is the structuring element.

The simplest usage is erode(img; [dims], [r]), where dims and r controls the neighborhood shape.

out1 = erode(img) # default: all spatial dimensions, r=1, a box-shape SE
out2 = erode(img; dims=(2,)) # only apply to the second dimension
out3 = erode(img; r=5) # half-size r=5
mosaic(out1, out2, out3; nrow=1)

It uses the strel_box to create a box-shaped structuring element. You can also provide a custom SE via the erode(img, se) interface.

out1 = erode(img, strel_box((3, 3))) # default se for`erode(img)`
se = centered(Bool[1 1 1; 1 1 0; 0 0 0]) # match top-left region
out2 = erode(img, se)
mosaic(out1, out2; nrow=1)

An in-place version erode! is also provided, for instance

out1 = similar(img)
erode!(out1, img)

out2 = similar(img)
erode!(out2, img, strel_diamond((3, 3)))

See also

erode is the dual operator of dilate in the following sense:

complement.(erode(img)) == erode(complement.(img))

false

For bool arrays and symmetric SEs, erosion becomes equivalent to the minkowski difference on sets: $A \ominus B = \{ a-b | a \in A, b \in B \}$.

For a comprehensive and more accurate documentation, please check the erode reference page.

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