min_max_filter.jl

# ---
# title: Max min filters
# cover: assets/max_min.gif
# author: Deeptendu Santra
# date: 2020-10-08
# ---

# In this tutorial we see how can we can effectively use max and min filter to distinguish
# between smooth and texture edges  in grayscale images.

# We will use the [`mapwindow`](@ref) function in `ImageFiltering.jl` which provides a general
# functionality to apply any function to the window around each pixel.

using ImageCore, ImageShow, ImageFiltering
using TestImages

img = Gray.(testimage("house");)      # Original Image

# We can use the `minimum` function to compute the minimum of the grayscale values in the given
# matrix or array. For example: 
minimum([Gray(0.7),Gray(0.5),Gray(0.0)]) # Should return Gray(0.0) i.e black.
# 
filter_size = (15, 15)
## Using the `mapwindow` function, we create an image of the local minimum.
## `mapwindow` maps the given function over a moving window of given size.
img_min = mapwindow(minimum, img, filter_size)
## Similarly for maximum
img_max = mapwindow(maximum, img, filter_size)
## The max(min) filter
img_max_min = mapwindow(maximum, img_min, filter_size)
## The min(max) filter
img_min_max = mapwindow(minimum, img_max, filter_size)
mosaicview(img_min, img_max, img_max_min, img_min_max; nrow=1)

# Now that we are done with the basic filtered images, we proceed to the next part
# which is edge detection using these filters.

# For edge detection, we need to define thresholds for our image. The threshold is an important tool
# to binarize a grayscale image. The threshold value for a given pixel practically
# decides if the pixel visible or not in the output image. However, appyling a global threshold might not consider the
# variation of colors/brightness within the image. Thus we consider an adaptive type theresholding method
# here using max/min results.

# The max(min) and min(max) filter effectively follows the smooth edges of the image. Therefore,
# their average also follows the smooth parts of the image. If we use this image as a threshold for the original
# image, the smooth parts of the original image will get filtered out, leaving only the texture and/or noise behind.
# So we can use the average of `img_max_min` and `img_min_max` as the texture threshold.

# The average of min and max filters also gives us the smooth edges, but it also includes the noise in the image.
# So using average of `img_min` and `img_max` as a threshold will yeild only texture.

img_texture_noise_threshold = (img_max_min + img_max_min) ./ 2
img_texture_threshold = (img_max + img_min) ./ 2
mosaicview(img_texture_noise_threshold, img_texture_threshold; nrow=1)
#
## The Dynamic Gist is obtained by subtracting the img_texture_threshold from the original image.
## The filtered image gives us the texture of the image.
img_dynamic_gist = img - img_texture_threshold
## The Texture Gist is obtained by subtracting img_texture_noise_threshold from the original image.
## The filtered image gives us the texture along with the noise of the image.
img_texture_gist = img - img_texture_noise_threshold
mosaicview(img_dynamic_gist, img_texture_gist; nrow=1)
#
## We extract out the smooth/ramp parts of the image.
## The darker section of the image consist of the ramp edges. The brighter pixels are mostly noise.
ramp = img_dynamic_gist - img_texture_gist
## Filtered-out edges
edge = img_max - img_min
## Smoothed-out version of edge
edge_smoothed = img_min_max - img_max_min
mosaicview(img, ramp, edge, edge_smoothed; nrow=2)

# # References

# Verbeek, P. W., Vrooman, H. A., & Van Vliet, L. J. (1988). [Low-level image processing by max-min filters](https://core.ac.uk/download/pdf/194053536.pdf). Signal Processing, 15(3), 249-258.

## save covers #src
using ImageMagick #src
mkpath("assets")  #src
ImageMagick.save("assets/max_min.gif", cat(img, edge, edge_smoothed, map(clamp01nan, ramp);dims=3);fps=1) #src