extreme_filter

The extreme_filter function is the core operation in ImageMorphology. Many other morphological operations such as dilate and erode are direct usages of it. The cover image shows a pixel jitter using random select function.

This page gives an overview of the extreme_filter function as a tutorial. It might not exactly show every details. For a comprehensive and more accurate documentation, please check the extreme_filter page.

using ImageMorphology
using ImageFiltering
using TestImages
using ImageBase
using ImageShow

Definition

Below is the basic interface for this function

extreme_filter(f, A, se)

For each pixel p in A, a select function f(x, y) will be applied iteratively to the its neighborhood. The neighborhood is defined by the structuring element se. In plain Julia codes, this is as simple as:

# For illustration purposes only; you should use `extreme_filter` in practice
function simple_extreme_filter(f, A, se)
    se = strel(CartesianIndex, se)
    R = CartesianIndices(A)
    for p in R
        x = A[p]
        for o in se
            q = p + o
            q in R || continue
            x = f(x, A[q])
        end
        A[p] = x
    end
end

The name "extreme" comes from the fact that max and min are typical examples of the select function f.

Examples

To illustrate how it works, let's load the wirebond mask image and apply the extreme filter to it.

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

se = strel_diamond((3, 3)) # a dimond shape structuring element

3×3 ImageMorphology.StructuringElements.SEDiamondArray{2, 2, UnitRange{Int64}, 0} with indices -1:1×-1:1:
 0  1  0
 1  1  1
 0  1  0

We use max as the select function – applying max gives the dilation operation:

extreme_filter(max, img, se)

with the SE size controls the degree of dilation:

imgs = [extreme_filter(max, img, strel_diamond((n, n))) for n in 3:2:13]
mosaic(imgs; nrow=1)

and dims controls the dimension to be dilated:

img_d1 = extreme_filter(max, img, strel_diamond((13, 13), (1,)))
img_d2 = extreme_filter(max, img, strel_diamond((13, 13), (2,)))
img_d12 = extreme_filter(max, img, strel_diamond((13, 13))) # (1, 2)
mosaic(img, img_d1, img_d2, img_d12; nrow=1)

The extreme_filter can be used to build many operations, including the basic dilation, erosion, and some other operators. Here we just list a few for inspiration:

se = strel_diamond((7, 7))
img_1 = extreme_filter(max, img, se) # dilate
img_2 = extreme_filter(min, img, se) # erode
img_3 = extreme_filter((x, y) -> rand() > 0.5 ? x : y, img, se) # jitter
# or pipe the filters
img_4 = extreme_filter(max, extreme_filter(min, img), se) # opening
img_5 = extreme_filter(min, extreme_filter(max, img), se) # closing
mosaic(img, img_1, img_2, img_3, img_4, img_5; nrow=1)

Many of the above operations are already implemented in ImageMorphology.

# the `mapwindow` function

There is a very similar function to extreme_filter called mapwindow(f, img, window) from ImageFiltering.jl. The main difference is that f in mapwindow applies to the entire neighborhood instead of two points in extreme_filter.

# currently, mapwindow only supports the box-shaped neighborhood
img1 = extreme_filter(max, img, strel_box((7, 7)))
img2 = mapwindow(maximum, img, (7, 7))
img1 == img2

true

This page was generated using DemoCards.jl and Literate.jl.