? et al. ? images naturelles et al. speckle ? isoline isolines isolines isoline n P_{n−1}

?? a = n− 1 iso- line P_{5} P_{5} =

(0, 1)(0, 2)(0, 3)(0, 4)(0, 5) (0, 1)(0, 2)(−1, 3)(−1, 4)(−1, 5) (0, 1)(−1, 2)(−1, 3)(−2, 4)(−2, 5) (−1, 1)(−1, 2)(−2, 3)(−3, 4)(−3, 5) (−1, 1)(−2, 2)(−3, 3)(−4, 4)(−5, 5) (−1, 1)(−2, 1)(−3, 2)(−4, 3)(−5, 3) (−1, 0)(−2, 1)(−3, 1)(−4, 2)(−5, 2)

(−1, 0)(−2, 0)(−3, 1)(−4, 1)(−5, 1) . . . . . . . . . . . . . . . P_{5} a = 5 (i, j)

P_{n−1} ω (i, j)

(2n− 1 ω S^{n}) / (\overline{S^{n}} S^{n} n) (i_{q}, j_{q}) q ∈

[0..n[

?? a = 5 p_{5,3}

mv.jpgExempledelarpartitiondespixelsdanslargionω n = 6 a = 5 S^{n} μ_{S^{n}} σ S^{n} Z ω \{μ_{ij}\}\overline{S^{n}}

\overline{S^{n}} P [Z|S^{n}, μ_{S^{n}}, {μ_{ij}}_{S^{n}}, σ]

(S^{n}) / (\overline{S^{n}})

∏_{(i,j)∈S^{n}} P [z(i, j)|μ_{S^{n}}, σ] ∏_{(i,j)∈\overline{S^{n}}} P [z(i, j)| \{μ_{ij}\}\overline{S^{n}} , σ] (1)

S^{n} S^{n} z(i, j)

μ̂_{ij} μ_{ij}

∏_{(i,j)∈\overline{S^{n}}} P [z(i, j)| \left\{{ \atop μ_{ij}}\right\}\overline{S^{n}} , σ] = 1. (2)

∏_{(i,j)∈S^{n}} P [z(i, j)|μ_{S^{n}}, σ] (3)

∏_{(i,j)∈S^{n}} \frac{1}{\sqrt{2πσ^{2}}} e^{− \frac{(z(i,j)−μ_{S^{n}})^{2}}{2σ^{2}}} (4)

logvraisemblance

−\frac{n}{2}log (2π) − \frac{n}{2}log (σ^{2}) − \frac{n}{2} (5)

(μ_{S^{n}}, σ)

(\begin{matrix}μ_{S^{n}} = \frac{1}{n} ∑_{(i,j)∈S^{n}} z(i, j) \\ σ̂^{2} = \frac{1}{n} ∑_{(i,j)∈S^{n}} (z(i, j) − μ_{S^{n}})^{2} \end{matrix}

iso- line extension_{1}.jpgAllongementdusegment^{n}

S^{p′} S^{p′′}

S^{p′′} S^{n} S^{p} S^{n}