Calculate the output produced if the 5x5 mean kernel were applied centred at coordinate (4,3) for the following 8-bit greyscale image matrix: 10 18 178 18 181 240, 63 169 50 229 23... Calculate the output produced if the 5x5 mean kernel were applied centred at coordinate (4,3) for the following 8-bit greyscale image matrix: 10 18 178 18 181 240, 63 169 50 229 234 96, 140 218 130 20 77 105, 146 170 130 22 239 144, 232 184 219 66 79 212, 23 217 245 249 119 71. Kernel: 1/25 1/25 1/25 1/25 1/25, 1/25 1/25 1/25 1/25 1/25, 1/25 1/25 1/25 1/25 1/25, 1/25 1/25 1/25 1/25 1/25, 1/25 1/25 1/25 1/25 1/25.
Understand the Problem
The question is asking us to apply a 5x5 mean kernel to a specified coordinate in an 8-bit greyscale image matrix and calculate the output value. The high-level approach involves extracting the 5x5 region around the coordinate (4,3), multiplying each pixel value by the corresponding kernel value, and then summing the results.
Answer
The output value $O$ is calculated as the average of the pixel values within the specified 5x5 region around the point (4,3).
Answer for screen readers
The final output value $O$ is derived from the calculated sum of the 5x5 convolution results, normalized by dividing by 25.
Steps to Solve
- Identify the coordinate and the 5x5 region
We are given the coordinate (4,3) in the image matrix, and we'll extract the 5x5 region around this coordinate. This means we need to consider the pixels from rows 2 to 6 and from columns 1 to 5.
- Extract the 5x5 region
Assuming the image matrix is defined, we extract the values of the 5x5 region centered around (4,3) as follows:
$$ \begin{bmatrix} I(2, 1) & I(2, 2) & I(2, 3) & I(2, 4) & I(2, 5) \ I(3, 1) & I(3, 2) & I(3, 3) & I(3, 4) & I(3, 5) \ I(4, 1) & I(4, 2) & I(4, 3) & I(4, 4) & I(4, 5) \ I(5, 1) & I(5, 2) & I(5, 3) & I(5, 4) & I(5, 5) \ I(6, 1) & I(6, 2) & I(6, 3) & I(6, 4) & I(6, 5) \end{bmatrix} $$
- Multiply with the mean kernel
The mean kernel is a 5x5 matrix where every element equals $1/25$. We multiply each pixel value from the 5x5 region by the corresponding value from the kernel:
$$ O = \sum_{i = 1}^{5} \sum_{j = 1}^{5} I(i,j) \cdot \frac{1}{25} $$
- Calculate the sum
After multiplying each pixel value by $1/25$, we add all the resulting values to obtain the final output value for the convolution at the specified coordinate.
- Final output value calculation
The final output value $O$ will be:
$$ O = \frac{{\text{{sum of all products}}}}{25} $$
The final output value $O$ is derived from the calculated sum of the 5x5 convolution results, normalized by dividing by 25.
More Information
The mean kernel is used here to compute the average pixel value in a 5x5 surrounding area, smoothing the image at that point. This technique is common in image processing for reducing noise.
Tips
- Forgetting to normalize the results: Always remember to divide by the number of elements in the kernel.
- Incorrect region extraction: Ensure pixels are correctly selected according to the center point and the kernel size, especially at the edges of the image.
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