Continuous Wavelet Transform on the Hyperboloid - Université de ...
Continuous Wavelet Transform on the Hyperboloid - Université de ... Continuous Wavelet Transform on the Hyperboloid - Université de ...
a=0.5, χ=0, φ=0 a=1, χ=0, φ=0 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 −0.2 1 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 −0.1 1 0.5 1 0.5 1 0 0.5 0 0.5 −0.5 −0.5 0 −0.5 −0.5 0 −1 −1 −1 −1 a=0.5, χ=1, φ=π/2 a=0.5, χ=1, φ=3π/4 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 −0.2 1 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 −0.2 1 0.5 1 0.5 1 0 0.5 0 0.5 −0.5 −0.5 0 −0.5 −0.5 0 −1 −1 −1 −1 a=0.5, χ=0.75, φ=π a=0.5, χ=2.75, φ=π 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 −0.2 1 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 −0.2 1 0.5 1 0.5 1 0 0.5 0 0.5 −0.5 −0.5 0 −0.5 −0.5 0 −1 −1 −1 −1 Fig. 10. The hyperbolic DOG wavelet fψ ϑ ,forϑ = 2 at different scales a and positions (χ, ϕ), viewed on the unit disk in 3-D perspective. any ρ [Alonso et al., 2002]: ( ) − 1 E ρ ν,ξ (x) = x0 2 − ˆn⃗x −iνρ , (83) ρ for x ∈ H 2 +ρ , (x2 = ρ 2 ). The Inönü-Wigner contraction limit of the Lorentz to the Euclidean group SO(2, 1) + → ISO(2) + is the limit at ρ →∞for (83) 26
Fig. 11. The hyperbolic DOG wavelet fψ ϑ in the disk, for ϑ = 2 at different scales a and positions (χ, ϕ). with x 0 ≈ ρ, ⃗x 2 ≪ ρ 2 , i.e 27
- Page 1 and 2: Continuous <strong
- Page 3 and 4: and on the sphere, it is natural to
- Page 5 and 6: 0 x 0 C 2 + H 2 + r 0 x 2 x 1 Fig.
- Page 7 and 8: The action of a motion on a point x
- Page 9 and 10: 4 p=0.5 4 p=1 3.5 3.5 3 3 2.5 2.5 2
- Page 11 and 12: x 0 H 2 + a N x 1 a S x 2 H 2 - Fig
- Page 13 and 14: E ν,ξ (x)=(ξ · x) − 1 2 −i
- Page 15 and 16: get the more elaborate expression
- Page 17 and 18: We now have all the basic ingredien
- Page 19 and 20: that 0
- Page 21 and 22: By performing the change of variabl
- Page 23 and 24: and so α(a) should behave at least
- Page 25: Fig. 9. The hyperbolic DOG wavelet
- Page 29 and 30: lim ˆψ ρ (ν, ξ)= 1 ∫ ψ(⃗x
- Page 31: April 2004. I. Tosic, I. Bogdanova,
Fig. 11. The hyperbolic DOG wavelet fψ ϑ in <strong>the</strong> disk, for ϑ = 2 at different scales a<br />
and positi<strong>on</strong>s (χ, ϕ).<br />
with x 0 ≈ ρ, ⃗x 2 ≪ ρ 2 , i.e<br />
27
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