Okay, a quick tutorial on what you're doing.
First up, the Graphics object? All it's doing is modifying the raw image/bitmap that you're pointing it to. In this case, you're modifying the raw image/bitmap that is contained in your postureImg. That's why you're not having to 'reimport' the picture back into that pictureBox - because the graphics is modifying it in-place.
That means that, afterwards, all you have to do is save that raw image/bitmap to file - so what you're really asking is: "How do I save a bitmap that's in a PictureBox to a file?"
In which case, the answer's pretty straight-forward:
postureImg.Image.Save(@"C:\someplace.jpg", ImageFormat.Jpeg);
EDIT: Ah, I forgot that VS does some wonky stuff with PicBoxes - it has an 'actual' image and a 'displayed' image. What you've been editing is the 'displayed' image, which isn't persistent (it'll go away if the form refreshes.)
To be honest, you'll probably be better off if you never go straight from the image in the picture box. For instance, here's code that doesn't work:
Graphics g = Graphics.FromHwnd(pictureBox1.Handle);
SolidBrush brush_Grey = new SolidBrush(Color.Green);
SolidBrush brush_Gold = new SolidBrush(Color.Red);
Rectangle rect = new Rectangle(new Point(100, 100), new Size(10, 10));
g.FillEllipse(brush_Gold, rect);
g.Dispose();
pictureBox1.Image.Save(@"C:\tmpSO1.jpg", System.Drawing.Imaging.ImageFormat.Jpeg);
... a good clue that it won't work is, if you perform this on form load it won't display the red circle; and if the form has to refresh due to clipping or such, the red circle will go away.
Anyway, here's code that does work:
Bitmap bmp = new Bitmap(pictureBox1.Image);
Graphics g = Graphics.FromImage(bmp);
SolidBrush brush_Grey = new SolidBrush(Color.Green);
SolidBrush brush_Gold = new SolidBrush(Color.Red);
Rectangle rect = new Rectangle(new Point(100, 100), new Size(10, 10));
g.FillEllipse(brush_Gold, rect);
g.Dispose();
pictureBox1.Image = bmp;
pictureBox1.Image.Save(@"C:\tmpSO2.jpg", System.Drawing.Imaging.ImageFormat.Jpeg);
Instead of modifying the PictureBox in-place, a separate BMP is loaded from it, and back into it.