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Consider a 3 × 3 spatial mask that averages the intensity of all neighbours of a pixel (x, y) in this 3 × 3 neighbourhood, but excluding the point itself.

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Image Analyst
Image Analyst on 8 Sep 2021
Make a kernel that has all 1's except for the center, then divide by 8:
kernel = ones(3,3) / 8;
kernel(2, 2) = 0;
blurredImage = conv2(double(grayImage), kernel, 'same');
There will be some slight errors in the very top, left, top, and bottom row. If you need to correct those you can use two calls to conv2() - one to count pixels and one to sum up values, then divide those two images pixel-by-pixel.
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Image Analyst
Image Analyst on 9 Sep 2021
Ben:
For your original question where you wanted the pixel to be replaced by the average of the 8 surrounding neighbors, you'd divide by 8.
For your edited question, which does not specify which pixels to include in the average (Why did you change your question???) you should divide by the number of pixels in the averaging window. If it's a 3x3 window and includes the central pixel, that's 9 pixels so you should divide the sum by 9. For a 5x5 using all pixels, divide by 5x5 = 25.

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