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 intensi

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.
$$
\left[\begin{array}{llll}
4 & 0 & 2 & 6 \\
3 & 6 & 5 & 6 \\
6 & 1 & 7 & 6 \\
5 & 2 & 6 & 5
\end{array}\right]
$$

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Key Concepts

Separability Index

The Separability Index is a quantitative measure used to assess how effectively a threshold divides an image into distinct classes. It is often defined as the ratio of the between-class variance to the total variance, and a higher value indicates a more pronounced separation between the classes, reflecting better segmentation performance.

Image Thresholding

Image Thresholding is a fundamental step in image segmentation where pixel intensities are divided into classes such as object and background. The method involves selecting a threshold value that best partitions the pixels so that the resulting regions are homogeneous, facilitating further analysis or processing.

Otsu's Method

Otsu's Method is an automatic thresholding technique used in image processing to separate an image into foreground and background classes by maximizing the between-class variance. It works by iterating through possible thresholds to find the one that minimizes the intra-class variance and maximizes the inter-class variance, thereby achieving the best separation based on the image histogram.

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