Exterior orientation of a single image based on line measurements of a rectangle

Objective:

Development of an efficient direct solution for the determination of the exterior orientation (pose) parameters of a single image using the line measurements of a parallelogram or a rectangle in object space. This method can be benificially applied in applications where parallel and coplanar object edges are common like in most buildings.

Approach:

The procedure consists of two steps.

First, the distance ratios of the distances from the projection center to the corner points of the parallelogram are computed using image line measurements and parallelism information only. From the distance ratios model coordinates of the parallelogram are computed (arbitrary scale).

Second, a linear three-dimensional similarity transformation is applied, transforming the model coordinates (and thereby the camera system) into the object coordinate system represented by (at least 7 of) the coordinates of the corner points.

In case of a rectangle, a non-linear condition equation enforcing rectangularity is applied on the measurements first.

Examples:

Parallelograms
The method is applied to determine the orientations (in the camera system) of all the windows and the two facades of the building shown here. Remark: the position of the windows in the 3D-model is "arbitrary".

Click on the image for the VRML-model
Rectangles
The application of rectangularity conditions improves the orientations of the windows; see the VRML-model.

Publication:

F.A. van den Heuvel, 1997:
Exterior Orientation using Coplanar Parallel Lines
Proceedings of the 10th Scandinavian Conference on Image Analysis, Lappeenranta, ISBN 951-764-145-1, pp.71-78
(download the pdf file; 0.1Mb)