This preview shows page 1. Sign up to view the full content.
Unformatted text preview: square) pixel that it lies in.
In other words, the camera gives us a measurement vi (the center of the pixel that the image point
lies in); we are guaranteed that
vi − vi ∞ ≤ ρi /2,
where ρi is the pixel width (and height) of camera i. (We know nothing else about vi ; it could be
any point in this pixel.)
Given the data Ai , bi , ci , di , vi , ρi , we are to ﬁnd the smallest box B (i.e., ﬁnd the vectors l and
u) that is guaranteed to contain x. In other words, ﬁnd the smallest box in R3 that contains all
points consistent with the observations from the camera.
(a) Explain how to solve this using convex or quasiconvex optimization. You must explain any
transformations you use, any new variables you introduce, etc. If the convexity or quasiconvexity of any function in your formulation isn’t obvious, be sure justify it.
(b) Solve the speciﬁc problem instance given in the ﬁle camera_data.m. Be sure that your ﬁnal
numerical answer (i.e., l and u) stands out....
View Full Document
- Fall '13
- The Aeneid