The Image Points dialog allows you to set the object origin (the point of rotation) and image points (arbitrary points that can be accessed by events) on an image. It is accessed via the Image and Animations editor.
The Origin is a special kind of image point defining the center of the object, or its point of rotation. It has a different icon, colored red. The term image point usually means "image points including the origin". Image points have a zero based index, and the first image point (number 0) is always the origin. The origin cannot be renamed.
Image points are useful to create spawn points for other objects. Since you can create objects at image points in events, it is often useful to place an image point in places like the end of the player's gun in the image. Image points can also be given a name, and referred to in events by this name.
Below, an image point is placed at the end of the player graphic's gun. Notice the indicator there.
Select an image point in the list and a corresponding point should appear on the image. Left click to place the point under the mouse. The arrow keys can also nudge it 1 pixel in each direction.
An image point can be quickly placed using the num pad, e.g. 1 for the top-left corner or 5 for centered. Alternatively the image point can be right clicked in the Image Points dialog and an option chosen from the quick assign menu.
Right clicking an image point in the Image Points dialog also provides an Apply to whole animation option. This sets the image point in the same relative place in all frames in an animation. If an image point does not exist in all frames in the animation, this option also creates it. Holding shift while placing the image point is a shortcut for this.