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Digital Image Processing

D. Sundararajan

Chapter 14

Color Image Processing - all with Video Answers

Educators

Chapter Questions

Problem 1

Given the RGB components of a $4 \times 4$ color image, find the CMY components of its CMY model.
(i)
$$
\left[\begin{array}{llll}
229 & 226 & 238 & 214 \\
239 & 238 & 225 & 233 \\
252 & 247 & 222 & 242 \\
214 & 213 & 240 & 224
\end{array}\right]\left[\begin{array}{llll}
215 & 212 & 231 & 213 \\
222 & 225 & 214 & 224 \\
242 & 235 & 209 & 229 \\
201 & 196 & 225 & 211
\end{array}\right]\left[\begin{array}{llll}
71 & 41 & 73 & 72 \\
90 & 70 & 74 & 93 \\
91 & 76 & 53 & 89 \\
50 & 33 & 69 & 79
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{llll}
171 & 228 & 231 & 229 \\
180 & 225 & 231 & 221 \\
192 & 225 & 229 & 213 \\
204 & 221 & 229 & 216
\end{array}\right]\left[\begin{array}{rrrr}
133 & 54 & 64 & 44 \\
130 & 51 & 63 & 42 \\
99 & 48 & 63 & 40 \\
71 & 50 & 65 & 44
\end{array}\right]\left[\begin{array}{llll}
125 & 120 & 130 & 113 \\
125 & 115 & 129 & 105 \\
119 & 114 & 127 & 102 \\
116 & 114 & 128 & 109
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{llll}
64 & 68 & 67 & 66 \\
61 & 59 & 65 & 65 \\
68 & 64 & 66 & 69 \\
74 & 71 & 68 & 69
\end{array}\right]\left[\begin{array}{rrrr}
102 & 107 & 108 & 108 \\
93 & 100 & 106 & 104 \\
107 & 102 & 102 & 106 \\
115 & 110 & 103 & 107
\end{array}\right]\left[\begin{array}{llll}
55 & 64 & 63 & 54 \\
55 & 56 & 63 & 59 \\
65 & 59 & 58 & 62 \\
69 & 66 & 60 & 56
\end{array}\right]
$$

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Problem 2

Given the RGB components of a $4 \times 4$ color image, find the HSI components of its HSI model.
*(i)
$$
\left[\begin{array}{llll}
232 & 234 & 235 & 235 \\
235 & 235 & 237 & 235 \\
236 & 236 & 234 & 234 \\
236 & 237 & 234 & 236
\end{array}\right]\left[\begin{array}{llll}
49 & 48 & 57 & 71 \\
52 & 55 & 61 & 78 \\
53 & 61 & 61 & 84 \\
57 & 64 & 69 & 92
\end{array}\right]\left[\begin{array}{llll}
162 & 169 & 174 & 188 \\
166 & 175 & 181 & 194 \\
169 & 180 & 185 & 200 \\
172 & 184 & 191 & 206
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{llll}
210 & 148 & 149 & 155 \\
201 & 152 & 146 & 150 \\
190 & 152 & 140 & 144 \\
180 & 157 & 134 & 137
\end{array}\right]\left[\begin{array}{rrrr}
103 & 37 & 29 & 34 \\
64 & 37 & 28 & 34 \\
48 & 35 & 27 & 34 \\
37 & 34 & 28 & 31
\end{array}\right]\left[\begin{array}{llll}
137 & 111 & 120 & 125 \\
113 & 115 & 119 & 124 \\
125 & 120 & 115 & 122 \\
135 & 131 & 110 & 115
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{llll}
98 & 94 & 86 & 82 \\
94 & 90 & 83 & 80 \\
88 & 85 & 80 & 78 \\
80 & 79 & 76 & 74
\end{array}\right]\left[\begin{array}{llll}
131 & 127 & 120 & 116 \\
124 & 122 & 116 & 112 \\
116 & 115 & 111 & 108 \\
109 & 106 & 103 & 103
\end{array}\right]\left[\begin{array}{llll}
82 & 80 & 77 & 74 \\
80 & 80 & 78 & 74 \\
75 & 75 & 74 & 71 \\
69 & 70 & 69 & 67
\end{array}\right]
$$

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Problem 3

Given the RGB components of a $4 \times 4$ color image, find the YIQ components of its NTSC model.
(i)
$$
\left[\begin{array}{llll}
236 & 239 & 242 & 247 \\
236 & 239 & 244 & 249 \\
235 & 240 & 245 & 250 \\
236 & 241 & 245 & 249
\end{array}\right]\left[\begin{array}{llll}
193 & 190 & 187 & 186 \\
190 & 187 & 185 & 184 \\
189 & 185 & 184 & 182 \\
188 & 184 & 182 & 180
\end{array}\right]\left[\begin{array}{llll}
1 & 0 & 0 & 0 \\
0 & 1 & 2 & 2 \\
0 & 3 & 6 & 6 \\
2 & 6 & 9 & 9
\end{array}\right]
$$
*(ii)
$$
\left[\begin{array}{llll}
209 & 210 & 232 & 250 \\
206 & 212 & 235 & 248 \\
208 & 213 & 233 & 238 \\
212 & 212 & 220 & 219
\end{array}\right]\left[\begin{array}{llll}
32 & 28 & 37 & 43 \\
29 & 29 & 40 & 42 \\
31 & 33 & 43 & 39 \\
35 & 38 & 39 & 32
\end{array}\right]\left[\begin{array}{llll}
51 & 54 & 66 & 76 \\
46 & 51 & 65 & 69 \\
47 & 49 & 61 & 61 \\
50 & 49 & 53 & 48
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{llll}
222 & 223 & 227 & 231 \\
226 & 227 & 232 & 235 \\
233 & 234 & 235 & 237 \\
238 & 239 & 238 & 238
\end{array}\right]\left[\begin{array}{llll}
185 & 185 & 186 & 189 \\
183 & 183 & 183 & 186 \\
179 & 179 & 179 & 180 \\
175 & 174 & 174 & 174
\end{array}\right]\left[\begin{array}{llll}
3 & 1 & 2 & 5 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0
\end{array}\right]
$$

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Problem 4

Given the RGB components of a $4 \times 4$ color image, find the $\mathrm{YCbCr}$ components of its YCbCr model. *(i)
$$
\left[\begin{array}{llll}
142 & 142 & 150 & 149 \\
144 & 144 & 143 & 163 \\
145 & 144 & 152 & 157 \\
147 & 153 & 155 & 126
\end{array}\right]\left[\begin{array}{llll}
15 & 15 & 24 & 24 \\
17 & 17 & 12 & 35 \\
18 & 18 & 16 & 24 \\
18 & 21 & 20 & 18
\end{array}\right]\left[\begin{array}{llll}
44 & 44 & 49 & 48 \\
46 & 47 & 37 & 59 \\
47 & 46 & 43 & 51 \\
48 & 49 & 42 & 28
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{llll}
227 & 230 & 230 & 229 \\
224 & 215 & 214 & 215 \\
208 & 207 & 208 & 209 \\
191 & 197 & 198 & 195
\end{array}\right]\left[\begin{array}{llll}
0 & 6 & 5 & 3 \\
4 & 0 & 0 & 0 \\
2 & 2 & 2 & 1 \\
0 & 6 & 6 & 3
\end{array}\right]\left[\begin{array}{llll}
27 & 32 & 32 & 32 \\
30 & 20 & 19 & 22 \\
19 & 15 & 14 & 16 \\
13 & 15 & 14 & 13
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{llll}
226 & 226 & 226 & 225 \\
226 & 226 & 225 & 223 \\
226 & 226 & 225 & 222 \\
226 & 226 & 225 & 223
\end{array}\right]\left[\begin{array}{llll}
239 & 239 & 238 & 235 \\
239 & 239 & 238 & 235 \\
239 & 239 & 238 & 235 \\
239 & 239 & 238 & 236
\end{array}\right]\left[\begin{array}{llll}
219 & 221 & 221 & 220 \\
219 & 221 & 220 & 218 \\
219 & 221 & 220 & 218 \\
219 & 221 & 221 & 219
\end{array}\right]
$$

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02:56

Problem 5

A 8-bit gray level image is to be converted to a color image by pseudocoloring. What is the color map for the given color assignment.
(i)
(FIGURE CAN'T COPY)
(ii)
(FIGURE CAN'T COPY)
(iii)
(FIGURE CAN'T COPY)

Willis James
Willis James
Numerade Educator

Problem 6

Given the RGB components of a $4 \times 4$ color image, find its complement.
(i)
$$
\left[\begin{array}{rrrr}
76 & 69 & 93 & 147 \\
129 & 88 & 77 & 163 \\
67 & 114 & 142 & 163 \\
100 & 92 & 160 & 165
\end{array}\right]\left[\begin{array}{rrrr}
96 & 90 & 121 & 179 \\
153 & 113 & 102 & 180 \\
99 & 142 & 169 & 191 \\
132 & 122 & 188 & 186
\end{array}\right]\left[\begin{array}{rrrr}
50 & 47 & 58 & 82 \\
78 & 59 & 49 & 100 \\
34 & 69 & 96 & 111 \\
57 & 54 & 109 & 104
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{rrrr}
69 & 114 & 59 & 41 \\
78 & 82 & 141 & 56 \\
138 & 47 & 81 & 106 \\
128 & 131 & 52 & 79
\end{array}\right]\left[\begin{array}{rrrr}
81 & 131 & 82 & 65 \\
90 & 99 & 167 & 82 \\
157 & 61 & 104 & 136 \\
153 & 150 & 70 & 106
\end{array}\right]\left[\begin{array}{llll}
42 & 73 & 40 & 27 \\
49 & 48 & 93 & 37 \\
93 & 30 & 53 & 68 \\
83 & 88 & 35 & 51
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{llll}
128 & 164 & 139 & 142 \\
174 & 199 & 178 & 163 \\
179 & 204 & 204 & 169 \\
101 & 174 & 202 & 149
\end{array}\right]\left[\begin{array}{llll}
160 & 190 & 169 & 171 \\
197 & 215 & 199 & 189 \\
200 & 217 & 218 & 193 \\
124 & 189 & 216 & 175
\end{array}\right]\left[\begin{array}{rrrr}
74 & 93 & 71 & 88 \\
102 & 105 & 99 & 105 \\
90 & 100 & 109 & 100 \\
42 & 70 & 104 & 82
\end{array}\right]
$$

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Problem 7

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)
$$
\left[\begin{array}{rrrr}
114 & 127 & 144 & 114 \\
129 & 136 & 131 & 84 \\
144 & 137 & 124 & 76 \\
143 & 139 & 145 & 120
\end{array}\right]\left[\begin{array}{rrrr}
84 & 99 & 139 & 128 \\
106 & 120 & 135 & 95 \\
127 & 135 & 133 & 86 \\
143 & 148 & 155 & 130
\end{array}\right]\left[\begin{array}{rrrr}
69 & 68 & 71 & 55 \\
98 & 71 & 57 & 39 \\
111 & 80 & 64 & 34 \\
89 & 90 & 96 & 76
\end{array}\right]
$$

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