Box Blur

Implement a box blur, also known as a mean filter, to an image by averaging neighboring pixels. This technique is a fundamental concept in Linear Filtering for image processing.

The box blur operates by convolving an image with a kernel, a small matrix that slides over the entire image, computing a weighted average of neighboring pixels at each position. For a given kernel size, the kernel is typically a square matrix with all elements being equal, resulting in a uniform average of the neighboring pixels.

Here are the steps to apply the box blur:

Define the kernel size and compute the kernel elements as $1 / (kernel\_size^2)$ .
Slide the kernel over the image, computing the average of neighboring pixels at each position.
Assign the computed average to the corresponding pixel in the output image.

K = \frac{1}{kernel\_size^2}\begin{pmatrix} 1 & 1 &... & 1 \\ 1 & 1 &... & 1 \\... &... &... &... \\ 1 & 1 &... & 1 \end{pmatrix}

This technique is widely used in image processing applications to reduce noise.

Example:

Input:

image = [[1, 2, 3],
        [4, 5, 6],
        [7, 8, 9]]
kernel_size = 3

Output:

[[5.0]]

Reasoning:

Box blur (mean filter) averages all pixels in a neighborhood.

For a $3 \times 3$ box filter on a $3 \times 3$ image:

$\text{output}[i,j] = \frac{1}{k^2} \sum_{m,n} \text{input}[i+m, j+n]$

Valid convolution produces 1×1 output:
- Output size: $(3 - 3 + 1) \times (3 - 3 + 1) = 1 \times 1$
Calculate the average of all 9 pixels: $\text{mean} = \frac{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9}{9}$
Sum the values: $\text{sum} = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45$
Compute mean: $\text{mean} = \frac{45}{9} = 5.0$
Result: $[[5.0]]$

The box blur smooths the image by replacing each pixel with the average of its neighborhood.

Constraints:

kernel_size is odd (3, 5, 7, etc.)
Round output to nearest integer
Use zero-padding

Example:

Constraints:

Test Results