Multi-dimensional array edge/border conditions

Question

I'm iterating over a 3 dimensional array (which is an image with 3 values for each pixel) to apply a 3x3 filter to each pixel as follows:

//For each value on the image    
for (i=0;i<3*width*height;i++){
    //For each filter value
    for (j=0;j<9;j++){
        if (notOutsideEdgesCondition){
            *(**(outArray)+i)+= *(**(pixelArray)+i-1+(j%3)) * (*(filter+j));
        } 
    }
}

I'm using pointer arithmetic because if I used array notation I'd have 4 loops and I'm trying to have the least possible number of loops. My problem is my notOutsideEdgesCondition is getting quite out of hands because I have to consider 8 border cases. I have the following handled conditions

• Left Column: ((i%width)==0) && (j%3==0)
• Right Column: ((i-1)%width ==0) && (i>1) && (j%3==2)
• Upper Row: (i<width) && (j<2)
• Lower Row: (i>(width*height-width)) && (j>5)

and still have to consider the 4 corner cases which will have longer expressions. At this point I've stopped and asked myself if this is the best way to go because If I have a 5 line long conditional evaluation it'll not only be truly painful to debug but will slow the inner loop. That's why I come to you to ask if there's a known algorithm to handle this cases or if there's a better approach for my problem. Thanks a lot.

Answer 1

Yes, there's a much better way. Write a fast loop to handle the cases where there is guaranteed to be no boundary problems. This will consist of the region from the second to the next-to-last columns and the second to next-to-last rows. Then you can write four routines to handle each of the sides (row 0, column 0, row N and column N) and you can hand code the last four points.

That said, there are also a heck of a lot faster ways of doing the addressing calculations you're doing.

Answer 2

A nice tip is to add an additional row at the top of the array, and another at the end (do the same for the columns).

These additionals rows/columns won't contain any information but they will ease the computation (no border cases). At the price of consuming more memory...

Just an idea :)