next up previous contents
Next: Transferring information back Up: Rectification method Previous: Determining the distance between   Contents

Constructing the rectified image

The rectified images are built up row by row. Each row corresponds to a certain angular sector. The length along the epipolar line is preserved. Figure 7.7 clarifies these concepts. The coordinates of every epipolar line are saved in a list for later reference (i.e. transformation back to original images). The distance of the first and the last pixels are remembered for every epipolar line. This information allows a simple inverse transformation through the constructed look-up table.

Figure 7.7: The image is transformed from (x,y)-space to (r,$\theta $)-space. Note that the $\theta $-axis is non-uniform so that every epipolar line has an optimal width (this width is determined over the two images).
\begin{figure}\centerline{\psfig{figure=stereo/imrectim.ps,width=8cm}}\end{figure}

Note that an upper bound for the image size is easily obtained. The height is bound by the contour of the image $ 2 \times (W + H)$. The width is bound by the diagonal $\sqrt{W^2+H^2} $. Note that the image size is uniquely determined with our procedure and that it is the minimum that can be achieved without pixel compression.


next up previous contents
Next: Transferring information back Up: Rectification method Previous: Determining the distance between   Contents
Marc Pollefeys 2002-11-22