Given the RGB components of a 4 ×4 color image with intensity values varying from 0 to 255 , fin

First, we need to convert the given RGB components to the intensity component of the HSI model.

Given the RGB components of a 4 ×4 color image with...

Given the RGB components of a $4 \times 4$ color image with intensity values varying from 0 to 255 , find the histogram-equalized version of its intensity component of its HSI model. $*$ (i) $$ \left[\begin{array}{rrrr} 81 & 80 & 81 & 90 \\ 78 & 73 & 84 & 100 \\ 75 & 79 & 93 & 93 \\ 74 & 84 & 102 & 91 \end{array}\right]\left[\begin{array}{rrrr} 108 & 107 & 107 & 116 \\ 105 & 99 & 110 & 129 \\ 101 & 106 & 120 & 122 \\ 100 & 110 & 130 & 120 \end{array}\right]\left[\begin{array}{llll} 38 & 36 & 37 & 45 \\ 37 & 31 & 41 & 55 \\ 35 & 38 & 50 & 49 \\ 34 & 43 & 59 & 49 \end{array}\right] $$ (ii) $$ \left[\begin{array}{rrrr} 58 & 110 & 89 & 25 \\ 61 & 106 & 89 & 81 \\ 64 & 83 & 130 & 157 \\ 62 & 88 & 173 & 162 \end{array}\right]\left[\begin{array}{rrrr} 79 & 129 & 112 & 39 \\ 82 & 124 & 111 & 83 \\ 86 & 100 & 130 & 139 \\ 85 & 92 & 149 & 134 \end{array}\right]\left[\begin{array}{rrrr} 30 & 73 & 45 & 7 \\ 29 & 66 & 49 & 45 \\ 27 & 43 & 70 & 90 \\ 27 & 39 & 97 & 94 \end{array}\right] $$ (iii) $$ \left[\begin{array}{rrrr} 114 & 127 & 144 & 114 \\ 129 & 136 & 131 & 84 \\ 144 & 137 & 124 & 76 \\ 143 & 139 & 145 & 120 \end{array}\right]\left[\begin{array}{rrrr} 84 & 99 & 139 & 128 \\ 106 & 120 & 135 & 95 \\ 127 & 135 & 133 & 86 \\ 143 & 148 & 155 & 130 \end{array}\right]\left[\begin{array}{rrrr} 69 & 68 & 71 & 55 \\ 98 & 71 & 57 & 39 \\ 111 & 80 & 64 & 34 \\ 89 & 90 & 96 & 76 \end{array}\right] $$

Given the RGB components of a $4 \times 4$ color image with intensity values varying from 0 to 255 , find the histogram-equalized version of its intensity component of its HSI model.
$*$ (i)
$$
\left[\begin{array}{rrrr}
81 & 80 & 81 & 90 \\
78 & 73 & 84 & 100 \\
75 & 79 & 93 & 93 \\
74 & 84 & 102 & 91
\end{array}\right]\left[\begin{array}{rrrr}
108 & 107 & 107 & 116 \\
105 & 99 & 110 & 129 \\
101 & 106 & 120 & 122 \\
100 & 110 & 130 & 120
\end{array}\right]\left[\begin{array}{llll}
38 & 36 & 37 & 45 \\
37 & 31 & 41 & 55 \\
35 & 38 & 50 & 49 \\
34 & 43 & 59 & 49
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{rrrr}
58 & 110 & 89 & 25 \\
61 & 106 & 89 & 81 \\
64 & 83 & 130 & 157 \\
62 & 88 & 173 & 162
\end{array}\right]\left[\begin{array}{rrrr}
79 & 129 & 112 & 39 \\
82 & 124 & 111 & 83 \\
86 & 100 & 130 & 139 \\
85 & 92 & 149 & 134
\end{array}\right]\left[\begin{array}{rrrr}
30 & 73 & 45 & 7 \\
29 & 66 & 49 & 45 \\
27 & 43 & 70 & 90 \\
27 & 39 & 97 & 94
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{rrrr}
114 & 127 & 144 & 114 \\
129 & 136 & 131 & 84 \\
144 & 137 & 124 & 76 \\
143 & 139 & 145 & 120
\end{array}\right]\left[\begin{array}{rrrr}
84 & 99 & 139 & 128 \\
106 & 120 & 135 & 95 \\
127 & 135 & 133 & 86 \\
143 & 148 & 155 & 130
\end{array}\right]\left[\begin{array}{rrrr}
69 & 68 & 71 & 55 \\
98 & 71 & 57 & 39 \\
111 & 80 & 64 & 34 \\
89 & 90 & 96 & 76
\end{array}\right]
$$

Key Concepts

Cumulative Distribution Function (CDF)

The cumulative distribution function (CDF) of an image histogram is a running total of the histogram values and is used in histogram equalization to map original intensity values to new ones. The CDF provides a measure of the cumulative probability distribution, which, when scaled appropriately, ensures that the intensity levels are evenly distributed across the desired range.

Histogram Equalization

Histogram equalization is a contrast enhancement technique that redistributes the luminance values of an image. By spreading out the most frequent intensity values, it improves the overall contrast of the image. This process uses the image's histogram to inform the remapping of the original intensity levels, resulting in an image with a more uniform histogram and enhanced visual clarity.

Histogram

An image histogram is a graphical representation of the distribution of pixel intensity values within an image. It counts how many pixels have a certain brightness level and serves as the starting point for many image processing techniques, including contrast enhancement methods like histogram equalization.

Intensity Component

The intensity component in the HSI model represents the brightness levels of the image. It is essentially a grayscale representation that contains crucial information about the lightness and contrast of the image. By focusing on this component, techniques such as histogram equalization can effectively enhance image contrast while preserving hue and saturation.

HSI Model

The HSI (Hue, Saturation, Intensity) model separates the color information (hue and saturation) from the brightness (intensity), making it particularly useful for tasks like image enhancement. In the context of histogram equalization, working with the intensity component allows for contrast adjustments without altering the inherent color attributes of the image.

RGB Color Model

The RGB color model represents images through combinations of red, green, and blue channels. It is a basis for digital image processing and is widely used in devices like cameras and displays. Understanding this model is crucial because any transformation such as converting to other color spaces fundamentally starts with these components.

Please give Ace some feedback