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Unformatted text preview: r’s distance is used to compare, for example, 2D images, with Cij equal to the
distance between pixels i and j . If x and y represent two photographs of the same scene, from
slightly diﬀerent viewpoints and with an oﬀset in camera position (say), d(x, y ) will be small, but
the distance between x and y measured by most common norms (e.g., x − y 1 ) will be large.
(a) Show that d satisﬁes the following. Symmetry : d(x, y ) = d(y, x); Nonnegativity : d(x, y ) ≥ 0;
Deﬁniteness : d(x, x) = 0, and d(x, y ) > 0 for x = y .
(b) Show that d(x, y ) is the optimal value of the problem
maximize ν T x + µT y
subject to νi + µj ≤ Cij , i, j = 1, . . . , n, with variables ν, µ ∈ Rn .
17.2 Radiation treatment planning. In radiation treatment, radiation is delivered to a patient, with the
goal of killing or damaging the cells in a tumor, while carrying out minimal damage to other tissue.
The radiation is delivered in beams, each of which has a known pattern; the level of each beam can
be adjusted. (In most cases multiple beams ar...
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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
- The Aeneid