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Box Blur

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Apply a box blur filter to a grayscale image by averaging pixels in a square neighborhood:

O_{ij} = \frac{1}{N} \sum_{u=-k}^{k} \sum_{v=-k}^{k} I_{(i + u)\,(j + v)}

where $k = \lfloor \text{kernel\_size}/2 \rfloor$ and $N$ is the number of valid pixels in the kernel.

This creates a blurring effect by smoothing out pixel values. The larger the kernel size, the more blurred the result!

Input

input_image - grayscale image of shape [width][height] containing floating-point pixel intensities in the range $[0, 255]$ .
width - the number of columns in the image.
height - the number of rows in the image.
kernel_size - the side length of the square blur kernel.

Output

output_image - blurred grayscale image of shape [width][height].

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