Zisserman - 9 
Figure 3: Accuracy of the computed infinite homography. The stereopair shows (in 
white) image lines corresponding to the parallel sides of the table, and intersecting 
at a vanishing point for that direction. For the right images, the square is the result 
of transferring the vanishing point from the left image using the computed infinite 
homography (see text). The agreement between the transferred and constructed 
vanishing points is excellent, indicating the accuracy of Hoc,. Figure courtesy of Paul 
Beardsley 
2. Metric structure can be recovered under two general (unknown) motions (three 
images) of a camera with unchanging (but unknown) internal parameters. 
The fundamental matrix between each pair of images generates two quadratic 
constraints on K via the Kruppa equations [6, 17]. K is a solution of this system 
of polynomial equations. 
3. From a single general motion of a fixed stereo rig (i.e. two stereo pairs of views, 
each with fixed — though different — internal parameters for the left and 
right cameras, and a fixed relation between the cameras): affine structure can 
be computed uniquely using only linear methods (eigenvectors); and, metric 
structure can be computed up to a one parameter family, again using linear 
methods, and reduced to a two fold ambiguity using a quadratic constraint [30]. 
Figure 3 shows an example of the computed Hoo using this method. 
3 Model Based Object Recognition 
Object recognition systems draw on a library of geometric models, which usually 
contain information about the shape and appearance of a set of known objects, to 
determine which, if any, of those objects appear in a given image or image sequence. 
Recognition is considered successful if the geometric configuration in an image can 
be explained as a perspective projection of a geometric model of the object. Here we 
concentrate on recognition from a single uncalibrated perspective image of a scene. 
For a small number of models, for example two or three, it is reasonable simply 
to try to find image feature support for each model. Typically recognition proceeds 
by hypothesising an association between a group of image features and a group of 
model features (usually a small subset of all the model features). This association is