Implementation summary
Do all calculations for red, green and blue components of the image separately, that is, new red values are computed from old red values etc.
Represent pixels as floats: the results of filtering can be negative or ouside 0..255 range; truncate only the final result to this range and convert it to integer.
If you need a pixel value that falls outside the image, use zero. Write a function that returns a value for any integer pair of arguments (i,j). If (i,j) is inside the image it returns the image value, otherwise a zero. Always access the image using this function.