3D Galatea: Entry of three-dimensional moving points from multiple perspective views

We describe an interactive graphics system for the entry of three-dimensional moving points from multiple perspective views. This work represents a major extension of Galatea, our system for graphics-assisted 2D motion analysis. 3D Galatea permits reconstruction of 3D time-dependent positions from 2D entries in two or more perspective views. The system supports a general approach for calibrating perspective views. This method, based on work of Sutherland, uses a known 3D reference object to calibrate completely arbitrary perspective projections. A somewhat restricted class of perspective views may be calibrated without an explicit calibration object using another approach developed from photogrammety. In 2D Galatea, we have used an animated graphics overlay onto the source image to give the analyst feedback regarding current and previous data entries. This capability is extended in 3D Galatea by overlaying auxiliary lines, which are the backprojections of previous 2D entries from one view into other views. This concept amounts to a fourth interpretation of the well-known Roberts homogeneous matrix equation describing perspective projections of 3D space into a 2D image. The auxiliary line is useful in locating a point which is obscured in one of the images, or in determining the correspondence of projected points as seen in different views, which may be ambiguous or easily confused.