Image Processing for Dummies with C# and GDI+ Part 4 - Bilinear Filters and Resizing

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Here we go again...

Well, this is the fourth installment in the series, and I thank you for sticking around this long.  I am wanting to do some groundwork for a future article, which will be involved enough that I didn't want to add bilinear filtering to the mix at that stage, so I'm covering it here.  In a nutshell, bilinear filtering is a method of increasing the accuracy with which we can select pixels, by allowing the selection of pixels in between the ones we draw.  Honest!!! To illustrate it's effect, we are going to write a resize filter first, then we are going to add a bilinear filter to see the effect it has on the final result.

A resize filter.

If you want to resize an image arbitrarily, the easiest way to do it is to calculate a factor for the difference between the source and destination in both x and y axes, then use that factor to figure out which pixel on the source image maps to the colour being placed on the destination image.  Note for this filter I step through the destination image and calculate the source pixels from there, this ensures that no pixels in the destination image are not filled.

SetPixel ?

Before I show you the code, you'll notice that I've chosen to use Set/GetPixel this time around instead of getting a pointer to my bitmap data.  This does two things for me, firstly it means my code is not 'unsafe', and secondly, it makes the code a lot simpler, which will help when we add the bilinear filter, which does enough work without my sample being cluttered by all the pointer lookup code that would also be required, as you will see.

The code

Here then is my code for a function that resizes a bitmap, fills it with data from a copy that was made prior, and then returns it.  Note that unlike my other functions, I found I had to return the new Bitmap because when I create one of a new size, it is no longer the same bitmap that is referred to by the 'in' parameter, and therefore I am unable to return a bool to indicate success.

public static Bitmap Resize(Bitmap b, int nWidth, int nHeight, bool bBilinear)
{
    Bitmap bTemp = (Bitmap)b.Clone();
    b = new Bitmap(nWidth, nHeight, bTemp.PixelFormat);

    double nXFactor = (double)bTemp.Width/(double)nWidth;
    double nYFactor = (double)bTemp.Height/(double)nHeight;

    if (bBilinear)
    {
        // Not yet 80)
    }
    else
    {
        for (int x = 0; x < b.Width; ++x)
            for (int y = 0; y < b.Height; ++y)
                b.SetPixel(x, y, bTemp.GetPixel((int)(Math.Floor(x * nXFactor)),
                          (int)(Math.Floor(y * nYFactor))));
    }

    return b;
}

In order to highlight the artifacts we get from such a filter, I have taken an image of Calvin and increased the width while decreasing the height ( both by 10 pixels ) several times, to get the following:

As you can see, things start to deteriorate fairly rapidly.

Bilinear Filtering

The problem we are having above is that we are not grabbing the pixels we want a lot of the time.  If we resize an image of 100 x 100 to 160 x 110, for example, then our X scale is 100/160, or .625.  In other words, to fill column 43, we need to look up column (43 * .625), or 26.875.  Obviously, we are not able to look up such a value, we will end up with column 27.  In this case, the difference is slight, but we can obviously end up with decimal values including .5, right in the middle between two existing pixels.  The image above shows how such small rounding of values can accumulate to cause image quality to deteriorate.  The solution is obviously to look up the values without rounding.  How do we look up a pixel that does not exist ? We interpolate it from the values we can look up.  By reading the values of all the surrounding pixels, and then weighting those values according to the decimal part of the pixel value, we can construct the value of the sub pixel.  For example, in the above example, we would multiply the values of column 26 by .875, and the values of column 27 by .125 to find the exact value required.

In order to make the example clearer, I have used GetPixel to read the four pixels in the area surrounding the subpixel we want to find.  In a future example I will use direct pixel access, which will be faster, but also a lot more complex.  The variable names have been chosen to help clarify what is going on.  Here is the missing code from above, the code which is executed when bBilinear = true.

if (bBilinear)
{
    double fraction_x, fraction_y, one_minus_x, one_minus_y;
    int ceil_x, ceil_y, floor_x, floor_y;
    Color c1 = new Color();
    Color c2 = new Color();
    Color c3 = new Color();
    Color c4 = new Color();
    byte red, green, blue;

    byte b1, b2;

    for (int x = 0; x < b.Width; ++x)
        for (int y = 0; y < b.Height; ++y)
        {
            // Setup

            floor_x = (int)Math.Floor(x * nXFactor);
            floor_y = (int)Math.Floor(y * nYFactor);
            ceil_x = floor_x + 1;
            if (ceil_x >= bTemp.Width) ceil_x = floor_x;
            ceil_y = floor_y + 1;
            if (ceil_y >= bTemp.Height) ceil_y = floor_y;
            fraction_x = x * nXFactor - floor_x;
            fraction_y = y * nYFactor - floor_y;
            one_minus_x = 1.0 - fraction_x;
            one_minus_y = 1.0 - fraction_y;

            c1 = bTemp.GetPixel(floor_x, floor_y);
            c2 = bTemp.GetPixel(ceil_x, floor_y);
            c3 = bTemp.GetPixel(floor_x, ceil_y);
            c4 = bTemp.GetPixel(ceil_x, ceil_y);

            // Blue
            b1 = (byte)(one_minus_x * c1.B + fraction_x * c2.B);

            b2 = (byte)(one_minus_x * c3.B + fraction_x * c4.B);
            
            blue = (byte)(one_minus_y * (double)(b1) + fraction_y * (double)(b2));

            // Green
            b1 = (byte)(one_minus_x * c1.G + fraction_x * c2.G);

            b2 = (byte)(one_minus_x * c3.G + fraction_x * c4.G);
            
            green = (byte)(one_minus_y * (double)(b1) + fraction_y * (double)(b2));

            // Red
            b1 = (byte)(one_minus_x * c1.R + fraction_x * c2.R);

            b2 = (byte)(one_minus_x * c3.R + fraction_x * c4.R);
            
            red = (byte)(one_minus_y * (double)(b1) + fraction_y * (double)(b2));

            b.SetPixel(x,y, System.Drawing.Color.FromArgb(255, red, green, blue));
        }
}

The result is as follows:

As you can see, this is a much better result.  It looks like it has gone through a softening filter, but it looks much better than the one above.  It is possible to get a slightly better code by going through a much more complex process called bicubic filtering, but I do not intend to cover it, simply because I've never done it.

What's Next

As I said above, the whole point of this article was to illustrate how bilinear filtering works.  A bilinear filter will be employed in my next article, which will talk about the process of writing a filter from scratch to be optimised for a particular process instead of through the sort of generic processes we've used so far.  At that point we will reimpliment the bilinear filter to be more optimised, but hopefully this version has helped you to understand that part of the process, so we can focus on other aspects in the next article.