Implementation of oil-painting filter for images
Just my few cents...
There is no reason to treat distance == 1 differently:
    public static int findNumberOfPixels(int distance)
    {
        int numberOfPixels = 0;
        int increment = 4;
        for (int i = 1; i &lt;= distance; i++)
        {
            numberOfPixels += increment;
            increment += 4;
        }
        return numberOfPixels;
    }

Furthermore, this method returns the same output for the same input every time. But you are calling it once for every pixel. It might be better to compute this value only once.