bv_cvxbook_extra_exercises

# bn and a int a explain how to solve the problem

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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 ˆ lies in); we are guaranteed that vi − vi ∞ ≤ ρi /2, ˆ 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 ˆ 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....
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