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Unformatted text preview: small object is located at unknown position
x ∈ R3 , and viewed by a set of m cameras. Our goal is to ﬁnd a box in R3 ,
B = {z ∈ R3  l z u}, for which we can guarantee x ∈ B . We want the smallest possible such bounding box. (Although
it doesn’t matter, we can use volume to judge ‘smallest’ among boxes.)
Now we describe the cameras. The object at location x ∈ R3 creates an image on the image plane
of camera i at location
1
(Ai x + bi ) ∈ R2 .
vi = T
c i x + di 64 The matrices Ai ∈ R2×3 , vectors bi ∈ R2 and ci ∈ R3 , and real numbers di ∈ R are known, and
depend on the camera positions and orientations. We assume that cT x + di > 0. The 3 × 4 matrix
i
Pi = Ai bi
c T di
i is called the camera matrix (for camera i). It is often (but not always) the case the that the ﬁrst 3
columns of Pi (i.e., Ai stacked above cT ) form an orthogonal matrix, in which case the camera is
i
called orthographic.
We do not have direct access to the image point vi ; we only know the (...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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