As the reader may recall, the motivation for computing the projection matrices, was to visualise three-dimensional models. In this application the models are stored as a sequence of segmented images. Each segment is assigned to a planar surface and each surface is assigned a vector normal.
A new viewpoint is generated by first projecting the known segmentations into the new viewpoint. If the camera matrix of the reference image is P=[I | 0] , and the camera matrix of the new image P'=[A | a4] , the plane [d1 d2 d3 n] is transfered using the homography Faugeras93b :
The visualisation algorithm requires an image segmentation for each reference image, and the plane vector of each surface. This information is specified once for each surface. A closed contour is drawn using a mouse and three points along the contour are matched with corresponding points in any of the other reference images. The linear solution to the plane vector is computed:
This equation can be easily solved using the SVD from three point matches, provided that the image co-ordinates are correctly normalised. For stable solutions it, is essential that the corresponding points obey the epipolar constraint.
An example of surface matching is shown in figure \ref{fig_create_model} and the rendered output is shown in figure \ref{fig_view_model}.
