Question

multiplying each pixel by the average blurring mask *(1/9) but the result is totally different.

PImage toAverageBlur(PImage a)
{
   PImage aBlur = new PImage(a.width, a.height);

   aBlur.loadPixels();

   for(int i = 0; i < a.width; i++)
   {
      for(int j = 0; j < a.height; j++)
      {
        int pixelPosition = i*a.width + j;
        int aPixel = ((a.pixels[pixelPosition] /9));

        aBlur.pixels[pixelPosition] = color(aPixel);
      }
   }
   aBlur.updatePixels();

   return aBlur;
}

Answer 1

Currently, you are not applying an average filter, you are only scaling the image by a factor of 1/9, which would make it darker. Your terminology is good, you are trying to apply a 3×3 moving average (or neighbourhood average), also known as a boxcar filter.

For each pixel i,j, you need to take the sum of (i-1,j-1), (i-1,j), (i-1,j+1), (i,j-1), (i,j),(i,j+1),(i+1,j-1),(i+1,j),(i+1,j+1), then divide by 9 (for a 3×3 average). For this to work, you need to not consider the pixels on the image edge, which do not have 9 neighbours (so you start at pixel (1,1), for example). The output image will be a pixel smaller on each side. Alternatively, you can mirror values out to add an extra line to your input image which will make the output image the same size as the original.

There are more efficient ways of doing this, for example using FFT based convolution; these methods are faster because they don’t require looping.