Count Number of Unique Colors in an Image

Just a few minor improvements to readability and such...

• The catch/throw isn't needed here, since you are just throwing it without doing anything in the catch block. A try/finally could have been used on its own.
• The try/finally isn't necessary because a using statement can achieve the same result without the extra code.

public static int CountImageColors(string fileName)
{
    HashSet<Color> colors = new HashSet<Color>();
 
    if (File.Exists(fileName))
    {
        using (Bitmap bmp = new Bitmap(fileName))
        {
            for (int x = 0; x < bmp.Width; ++x)
            {
                for (int y = 0; y < bmp.Height; ++y)
                {
                    colors.Add(bmp.GetPixel(x, y));
                }
            }
        }
    }

    return colors.Count;
}

In addition to the above, you could also use unsafe code to read out the pixels even faster, an example can be found here[^].