Demo: GLCM matrix

docs/examples/image_features/glcm.jl

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+# ---
+# cover: assets/glcm.gif
+# title: Gray Level Co-occurrence Matrix
+# description: This demo shows GLCM(Gray Level Co-occurrence Matrix)
+# author: Ashwani Rathee
+# date: 2021-08-9
+# ---
+
+# Gray Level Co-occurrence Matrix (GLCM) is used for texture analysis. 
+# We consider two pixels at a time, called the reference and the neighbour pixel.
+# We define a particular spatial relationship between the reference and neighbour 
+# pixel before calculating the GLCM. For eg, we may define the neighbour to be 1 
+# pixel to the right of the current pixel, or it can be 3 pixels above, or 2 pixels
+# diagonally (one of NE, NW, SE, SW) from the reference.
+
+# Once a spatial relationship is defined, we create a GLCM of size (Range of
+# Intensities x Range of Intensities) all initialised to 0. For eg, a 8 bit single
+# channel Image will have a 256x256 GLCM. We then traverse through the image and for
+# every pair of intensities we find for the defined spatial relationship, we increment
+# that cell of the matrix.
+
+# ## Gray Level Co-occurence Matrix
+
+# Each entry of the GLCM[i,j] holds the count of the number of times that pair of 
+# intensities appears in the image with the defined spatial relationship.
+
+# ![](assets/glcm.png)
+
+# The matrix may be made symmetrical by adding it to its transpose and normalised to 
+# that each cell expresses the probability of that pair of intensities occurring in the image.
+
+# Once the GLCM is calculated, we can find texture properties from the matrix to represent
+# the textures in the image.
+
+# ## GLCM Properties
+
+# The properties can be calculated over the entire matrix or by considering a window
+# which is moved along the matrix.
+
+# - Mean
+# - Variance
+# - Correlation
+# - Contrast
+# - IDM (Inverse Difference Moment)
+# - ASM (Angular Second Moment)
+# - Entropy
+# - Max Probability
+# - Energy
+# - Dissimilarity
+
+# ImageFeatures.jl provide methods for GLCM matrix calculation(with symmetric and normalized versions)
+
+using Images, TestImages
+using ImageFeatures
+
+img_src = testimage("coffee")
+
+# In this section, we will see how glcm could be calculated and how results are 
+# different for different types of textures. We will be using 4 `10x10` pixels 
+# patches as shown below.
+
+img_patch1 = img_src[170:180, 20:30] # Patch 1 & Patch 2 are from table with unidirectional texture
+img_patch2 = img_src[190:200, 20:30]
+img_patch3 = img_src[40:50, 310:320] # Patch 3 & Patch 4 are from coffe inside cup
+img_patch4 = img_src[60:70, 320:330]
+img_patches = [img_patch1, img_patch2, img_patch3, img_patch4]
+mosaicview(img_patches; nrow=1, npad=1, fillvalue=1)
+
+# As we can already take a guess, patch 1 and patch 2 are very similiar(unidirectional texture) and 
+# that's also true for patch 3 and patch 4 which are very similiar(smooth texture).
+
+glcm_results = [];
+glcm_sym_results = [];
+glcm_norm_results = [];
+
+# The `distances` and `angles` arguments may be a single integer or a vector of 
+# integers if multiple GLCMs need to be calculated. The `mat_size` argument is used
+# to define the granularity of the GLCM. 
+
+distance = 5
+angle = 0
+mat_size = 4
+
+for patch in img_patches
+    glcm_output = glcm(patch, distance, angle, mat_size)
+    glcm_sym_output = glcm_symmetric(patch, distance, angle, mat_size)
+    glcm_norm_output = glcm_norm(patch, distance, angle, mat_size)
+    push!(glcm_results, glcm_output)
+    push!(glcm_sym_results, glcm_sym_output)
+    push!(glcm_norm_results, glcm_norm_output)
+end
+
+glcm_results # GLCM matrix
+
+# GLCM symmetrical is basically `glcm_output .+ transpose(glcm_output)`
+
+glcm_sym_results # GLCM Symmetrical matrix
+
+# GLCM normalised is basically `glcm_output ./ sum(glcm_output)`
+
+glcm_norm_results # GLCM normalised matrix
+
+# In next part, we will see how the GLCM matrix calculation can be used to 
+# differentiate textures based on statistics. `glcm_prop` is used to calculate
+# various properties. 
+# Various properties can be calculated like `mean`, `variance`, `correlation`,
+# `contrast`, `IDM` (Inverse Difference Moment),`ASM` (Angular Second Moment),
+# `entropy`, `max_prob` (Max Probability), `energy` and `dissimilarity`.
+
+property = [correlation,dissimilarity]
+x = []
+y = [] 
+
+for i in glcm_results
+    point = []
+    for j in property
+        glcm_pro = glcm_prop(i, j)
+        push!(point,glcm_pro)
+    end
+    push!(x,point[1])
+    push!(y,point[2])
+end
+x,y
+
+# These properties can be directly calculated too using syntax `property(glcm_matrix)`.
+# For example: To calculate correlation, we can do `correlation(glcm(img_patch1))``
+
+# We can create graph between correlation and dissimilarity properties of particular
+# GLCM matrices. It's easy to notice that the Patch 1 & Patch 2 are closer in the properties
+# and similiarly for Patch 3 and Patch 4.
+
+# ![](assets/scatter.png)
+
+# Graph can be made using GLCM symmetric and normalised version, which produces very similiar outputs to give
+# us a hint at how similiar textures have similiar properties.
+
+# References:
+# - https://en.wikipedia.org/wiki/Co-occurrence_matrix
+# - Scikit GLCM example