Find the co-occurrence matrix of the 8 ×83-bit image. [ 5 4 4 5 5 2

step 1 For this exercise, we have 8, 5, 1, 4, 2, negative 2, negative 1, negative 1, negative 2. This i

Find the co-occurrence matrix of the 8 ×83-bit image. [ ...

Find the co-occurrence matrix of the $8 \times 83$-bit image. $$ \left[\begin{array}{llllllll} 5 & 4 & 4 & 5 & 5 & 2 & 2 & 2 \\ 5 & 2 & 4 & 5 & 5 & 2 & 2 & 2 \\ 3 & 2 & 5 & 5 & 6 & 3 & 2 & 2 \\ 2 & 4 & 4 & 5 & 5 & 4 & 2 & 2 \\ 4 & 5 & 5 & 5 & 6 & 4 & 2 & 2 \\ 5 & 5 & 5 & 5 & 4 & 4 & 2 & 2 \\ 5 & 5 & 5 & 3 & 3 & 4 & 2 & 2 \\ 5 & 5 & 4 & 3 & 4 & 5 & 2 & 2 \end{array}\right] $$ Let the spatial relationship of a pair of pixels be $x(m, n)$ and $x(m, n+1)$. That is, a pixel and its immediate right neighbor form the pair. Find the contrast, correlation, energy, and homogeneity.

Find the co-occurrence matrix of the $8 \times 83$-bit image.
$$
\left[\begin{array}{llllllll}
5 & 4 & 4 & 5 & 5 & 2 & 2 & 2 \\
5 & 2 & 4 & 5 & 5 & 2 & 2 & 2 \\
3 & 2 & 5 & 5 & 6 & 3 & 2 & 2 \\
2 & 4 & 4 & 5 & 5 & 4 & 2 & 2 \\
4 & 5 & 5 & 5 & 6 & 4 & 2 & 2 \\
5 & 5 & 5 & 5 & 4 & 4 & 2 & 2 \\
5 & 5 & 5 & 3 & 3 & 4 & 2 & 2 \\
5 & 5 & 4 & 3 & 4 & 5 & 2 & 2
\end{array}\right]
$$
Let the spatial relationship of a pair of pixels be $x(m, n)$ and $x(m, n+1)$. That is, a pixel and its immediate right neighbor form the pair. Find the contrast, correlation, energy, and homogeneity.

Key Concepts

Co-occurrence Matrix

A co-occurrence matrix is a statistical tool that tabulates how frequently different combinations of pixel intensity values occur in an image, given a specific spatial relationship between the pixels. It is especially useful for analyzing the texture of an image by capturing the spatial dependencies of gray levels.

Spatial Relationship in GLCM

The spatial relationship in a co-occurrence matrix defines how pixel pairs are selected from the image, such as choosing a pixel and its immediate right neighbor. This relationship determines the orientation and distance between the pixel pairs, significantly influencing the computed texture features.

Contrast

Contrast, in the context of a co-occurrence matrix, measures the intensity difference between a pixel and its neighboring pixel. It quantifies how much the gray levels differ in regions of the image, with higher values indicating larger contrasts and a coarser texture.

Correlation

Correlation in a co-occurrence matrix captures the statistical correlation between pixel intensities at a given offset. It assesses the degree to which the intensity of one pixel can be predicted by the intensity of its neighbor, indicating the level of linear dependency between the pixel values.

Energy

Energy, also known as angular second moment, is a measure of the uniformity of an image texture. It is calculated from the co-occurrence matrix and reflects the sum of squared elements; higher energy values suggest a more homogeneous and orderly texture, while lower values indicate more variability.

Homogeneity

Homogeneity evaluates how close the elements of the co-occurrence matrix are to the main diagonal, meaning it measures the similarity between neighboring pixel values. High homogeneity values indicate that the pixel pairs have similar intensities, reflecting a smoother texture with fewer abrupt changes.

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