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Unformatted text preview: s work on sets of points extracted from analysed surfaces and such points should be uniformly sampled from the whole surface in order to avoid that local characteristics override the global behaviour. For instance, sampling a part of a sphere provides an axial surface overriding the global spherical behaviour. Another interesting consideration invests the role of sampling noise. The symmetries of the underlying surface are retained in the set of sampled points if and only if the sampling noise does not introduce distortions. A measured point P∈ℜ3 is a noisy version of some unknown point Q belonging to the surface S; this is mathematically 174 P. Chiabert and M. De Maddis translated in the convolution of p n (P | Q ) , the conditional PDF that accounts for the noise, and p S (Q ) , the probabilistic version of the indicator function on S:
ˆ It can be demonstrated [Costa et al., 2001] that p S (P ) shows the same symmetries of ˆ ∀P ∈ ℜ 3 , p S (P ) = ∫ 3 p n (P | Q ) p S (Q )d 3 Q
ℜ (4) the underlying surface p S (Q ) if p n (P | Q ) is actua...
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This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.
- Spring '10
- The Land