{"id":1990,"date":"2014-02-05T17:32:40","date_gmt":"2014-02-05T17:32:40","guid":{"rendered":"https:\/\/www.anagram.at\/en\/diplomarbeit\/stereo-geometry\/"},"modified":"2014-02-05T17:32:40","modified_gmt":"2014-02-05T17:32:40","slug":"stereo-geometry","status":"publish","type":"page","link":"https:\/\/www.anagram.at\/en\/diplomarbeit\/stereo-geometry\/","title":{"rendered":"Stereo Geometry"},"content":{"rendered":"


\n
\n Next:<\/b> Epipolar Geometry<\/a>
\n Up:<\/b> Stereo Vision<\/a>
\n Previous:<\/b> Camera Calibration<\/a>
\n<\/p>\n

<\/p>\n

Stereo Geometry
\n<\/h1>\n

The geometry of a monocular camera system can easily be extended to a stereo camera system. Let us assume that two cameras with an
\nidentical effective focal length \"$ are used (Figure 2.6<\/a>). The distance between their centers of projection is the baseline \"$. A point \"$ in space is projected onto both sensor chips as \"$ and \"$. As one can see, the projected points are slightly translated in x-direction. If camera axes are parallel, there are only horizontal disparities to deal with. This lets us distinguish between two different stereo geometries.<\/p>\n

\n
parallel camera-axes:<\/strong><\/dt>\n
only horizontal disparities, no
\npoints without disparity<\/p>\n<\/dd>\n
converge camera-axes:<\/strong><\/dt>\n
vertical, horizontal and points
\nwithout disparity can occur. The set of points without disparities
\nis called the theoretical horopter. Rectification<\/i> is used to transform
\nthe image so that only horizontal disparities appear. See Section 2.3.3<\/a> for more information.\n<\/dd>\n<\/dl>\n
<\/p>\n\n\n
Figure 2.6:<\/strong>
\nStereo Geometry with parallel optical axes<\/caption>\n
\n
\n \"Image<\/div>\n<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

The disparity \"$ and the depth or z-coordinate in a camera oriented coordinate system are indirectly proportionally related. This coherence is shown in Equation 2.14<\/a>. <\/p>\n\n

<\/p>\n\n\n
\"$displaystyle<\/td>\n\n(2.14)<\/td>\n<\/tr>\n<\/table>\n<\/div>\n


<\/p>\n\nwhere
\n\"$. As mentioned above, \"$ is only one-dimensional if the camera axes are parallel. Otherwise \"$ can be two-dimensional, i.e. vertical and horizontal disparities occur.<\/p>\n\n

Subsections<\/strong><\/a><\/p>\n