Where an arbitrary point on an image is designated in the field of a medical image, it is generally designated on a sectional image, and an arbitrary point on a three-dimensional image cannot be designated. According to the invention the orientation of the three-dimensional image is controlled in a first direction corresponding to the operation of the user. When an arbitrary point of the three-dimensional image is designated by the user, a plane passing through that point and normal to a display screen is created and stored. Next, the three-dimensional image is oriented in a second direction, and an arbitrary point is designated in the second direction by the user. Then, there is created a straight line which passes through that point and which is normal to the display screen. Then, the coordinates of the intersection the stored screen and the straight line are determined, and the point having the coordinates of the intersection point is displayed on the three-dimensional image. As a result, an arbitrary point on the three-dimensional image can be designated by a simple operation.