Phương pháp xây dựng các mô tả Fourier cho từng phần hình dạng và một số tính chất

In this paper, a description method for partial shapes is introduced with the use of Fourier transformation. The proposed method allows to easily get a partial Fourier set which is invariant with respect to translation, rotation and scaling, to minimize the required parameter numbers for describing partial shapes. | Tl;l-p chi Tin hoc va Dieu khi€n hQC, , $.4 (2007), 334-345 PHlfONG PHAp XAY DlfNG cAc MO TA FOURIER 'A. .,. K, ,,/ "'r D~ \ ' III ~ Hinh 2. Tao tuyen dong tir tuyeri mo (~_ ,g! !I~lOoI'l1C:'"I,.,"" /" r>; ;,/ . i I' '~I = -l. OO[ "'i // -I '.":0 1.~ -'" .a • : I' I . • . I, :I: i la don vi phirc, i2 = 0, 2N - 1, · 1 :1 2N. M I "I +l = "l- - - -----~ : "~7 -' • J .I .~ neu k 909N •.•• ---11 !/'--I -L, . --v:~~, 0~ ~-. -, "'-,_;; - ! ••. PHUONG PHAp XAy DVNG cAc MO 337 TA FOURIER CHO TUNG PHAN HINH DANG f)~t Z = {ZO, zl, . Z2N-l}, ta goi Z la the hien phirc cua tuyen G va G la tuyen tirong irng veri z. Thirc hien phep bien doi Fourier len cac thanh phan cua z ta thu diroc cac he so Fourier tinh toan nlnr sau 2N-l Fm = zke-i27rkm/2N, m = 0,1, . , 2N - 1. (3) k=O L Ta noi (3) la phep bien doi Fourier tung phan len tuyen mo T = (gOgl . g N)' Khi do, tuyen dong G hoan toan co the diroc mo ta boi t~p cac he so Fourier F = {Fo, Fl, F2, . , F2N-l}. (4) Cac thanh phan cua z co the nhan 19-idiroc tir F bang each SITdung phep bien doi Fourier ngiroc 2N-l Zk = 2~ Fmei27rkm/2N, k = 0, 1, . , 2N - 1. (5) L m=O Ky hieu F = Jt(z), thirc (3) va (5). Ky hieu Real(A), chat sau. z = Jel Imag(A) (F), trong do cac phan tIT cua z va F lien h~ nhau theo cong ttrong irng la phan thirc va phan ao cua so plnrc A. Ta co tinh 'I'inh chat 1. ss« gOgN ndm tren true hoiuih. thi Imag(Fm) = 0, '11m = 0, 2N - 1. Tucrng tv, neu gOgN ruim. tren true tung thi Real(Fm) = 0, '11m= 0, 2N - 1. Chung minh: Gia SITgOgN narn tren true hoanh, khi do, g2N-k va Y2N-k = -Yk, k = 0, N. Do do, doi xirng gk ¢:? = Xk X2N-k Fm = Zo + ZN cos(1Tm)+ ?; N-l [Zk (cos 2;~m Suy ra, Imag(Fm) ~ Z:: k=l 2N + Z2N-k (cos 21T(2~;; k)m _ i sin 21T(2~;; k)m) ] . = [ (21Tkm Yk cos -2N ,21Tkm VI . _ i sin 2;~m)+ - cos 21T(2N - k)m 2N 21T(2N- k)m) 2N . - Xk (. = 21Tm. V~y, .