Question

Given a list of x,y coordinates and a known width & height how can the NUMBER of the enclosed areas be determined (in C#)?

For Example:

In this image 5 ENCLOSED AREAS are defined:

1. Face (1)
2. Eyes (2)
3. Nose (1)
4. Right of face (1)

The list of x,y points would be any pixel in black, including the mouth.

Answer 1

You can use this simple algorithm, based on idea of flood fill with helper bitmap:

// backColor is an INT representation of color at fillPoint in the beginning.
// result in pixels of enclosed shape.
private int GetFillSize(Bitmap b, Point fillPoint)
{
   int count = 0;
   Point p;
   Stack pixels = new Stack();
   var backColor = b.GetPixel(fillPoint.X, fillPoint.Y);
   pixels.Push(fillPoint);
   while (pixels.Count != 0)
   {
       count++;

       p = (Point)pixels.Pop();
       b.SetPixel(p.X, p.Y, backColor);

       if (b.GetPixel(p.X - 1, p.Y).ToArgb() == backColor)
           pixels.Push(new Point(p.X - 1, p.Y));

       if (b.GetPixel(p.X, p.Y - 1).ToArgb() == backColor)
           pixels.Push(new Point(p.X, p.Y - 1));

       if (b.GetPixel(p.X + 1, p.Y).ToArgb() == backColor)
           pixels.Push(new Point(p.X + 1, p.Y));

       if (b.GetPixel(p.X, p.Y + 1).ToArgb() == backColor)
           pixels.Push(new Point(p.X, p.Y + 1));
   }

   return count;
}

UPDATE

The code above works only this quadruply-linked enclosed areas. The following code works with octuply-linked enclosed areas.

// offset points initialization.
Point[] Offsets = new Point[]
{
    new Point(-1, -1),
    new Point(-0, -1),
    new Point(+1, -1),
    new Point(+1, -0),
    new Point(+1, +1),
    new Point(+0, +1),
    new Point(-1, +1),
    new Point(-1, +0),
};

...

private int Fill(Bitmap b, Point fillPoint)
{
    int count = 0;
    Point p;
    Stack<Point> pixels = new Stack<Point>();
    var backColor = b.GetPixel(fillPoint.X, fillPoint.Y).ToArgb();
    pixels.Push(fillPoint);
    while (pixels.Count != 0)
    {
        count++;

        p = (Point)pixels.Pop();
        b.SetPixel(p.X, p.Y, Color.FromArgb(backColor));

        foreach (var offset in Offsets)
            if (b.GetPixel(p.X + offset.X, p.Y + offset.Y).ToArgb() == backColor)
                pixels.Push(new Point(p.X + offset.X, p.Y + offset.Y));
    }

    return count;
}

The picture below clearly demonstates what I mean. Also one could add more far points to offset array in order to able to fill areas with gaps.