Using Otsu's method, find the threshold of the 4 ×4 3-bit image. Find the separability index. [

Step 1: Calculate the histogram of the image The histogram counts the frequency of each pixel va

Using Otsu's method, find the threshold of the 4 ×4 3-bit...

Using Otsu's method, find the threshold of the $4 \times 4$ 3-bit image. Find the separability index.
$$
\left[\begin{array}{llll}
5 & 6 & 5 & 5 \\
6 & 5 & 5 & 6 \\
7 & 6 & 4 & 5 \\
5 & 5 & 5 & 5
\end{array}\right]
$$

Key Concepts

Otsu's Method

Otsu's method is an automatic threshold selection technique used in image processing. It determines the optimal threshold by maximizing the between-class variance or, equivalently, minimizing the within-class variance, thereby achieving the best possible separation between foreground and background classes in a grayscale image.

Image Histogram Analysis

The image histogram represents the frequency distribution of pixel intensities in an image. In thresholding techniques like Otsu's method, the histogram is used to calculate the probabilities of each intensity level, which are essential for computing means and variances for the different classes (foreground and background).

Between-Class Variance

Between-class variance is a statistical measure that quantifies the difference between the mean intensities of the foreground and background classes. In Otsu's method, maximizing this variance ensures that the two classes are as distinct as possible, leading to effective thresholding.

Within-Class Variance

Within-class variance measures the spread or dispersion of pixel intensities within each class (foreground or background). Otsu's method seeks to minimize this variance, which indicates that the pixels within each group are consistent in intensity, thus achieving a clearer segmentation.

Separability Index

The separability index, in the context of Otsu's method, is a metric defined as the ratio of the between-class variance to the total variance of the image. It provides an indication of how well the chosen threshold separates the two classes, with higher values representing better separation between the foreground and background.

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