64 - . . , 634034, , 004.931 ! " # . $" " ! $ ! # ! #- % %% . & " !$ ! #- " " %" % ! $" #. : #- ", ! #, %" , "% . This paper provides a brief review on contour-based shape signatures. A new algorithm for shape recognition based on Fourier descriptors and multilayer neural network is proposed. The paper also presents an analysis on the capabilities of the Fourier-descriptors as the input data for neural networks in recognition of the complex shapes. Key words: Fourier descriptors, shape recognition, neural networks, multilayer perceptron !"#. ! ! % !% ' !. ( ! ! ) !$ !* # – * ! !. +## " !" # ! #- [1]. / % # " * %% * ' ! ! #. $% &%! '$!%"#( )#*+$ " " ,"%+$. &2 *2 " # $ # *2 !: 5 ", " , ", " , !; #-*2 (IP) #-*2 " (NIP). / ! " "* * # " !* " # #" (one-dimensional function), * (olygonal approximation), !! " ! (spatial interrelation feature), " (moments), " '" (scale-space methods), " ! #" (shape transform domains) [2]. $" # !* " ", # , "% , ! #- - 65 . . ". / 5 ( #- ) " #% #". . , !$ # f(x,y) Pn ( xn , yn ), n [1, N ] – $ ( ) #". / 5 zn=xn+iyn !" % %, * $ ! #" " " #-!. 5 ! # Pn=zn, n=[1,N]. "% !, : "% ! " 2*, ' * 2*. @ " " " zn " " 2*, "* $ ( ): zn=(xn–xg)+i(yn–yg), g=(xg,yg) – $ #". . B Rn Pn=(xn,yn), n=[1,N] " $% C(x0,y0) $% (xn,yn). / " " #" [2]: ( xn x0 )2 ( yn y0 )2 . Rn B $ 2 , " ". . $"% % %, 5 $ %, % $% [2]: Tn § y yn w · arctg ¨ n ¸. © x n xn w ¹ C w – ' !. !, "% 2 " : ' " . " !$ " , # Mn T n T 0 , 0 – "% %% "% . 5 % # # $ . / 2% # ! % # #-!. - . B- " * ! #-! !" "' " # #" [3, 4]. B- !"* " 5## " #-!$. $, ) ! "% % #% c(t), 5 T ak 2 c(t ) cos( kZt )dt , bk T ³0 T 2 c(t ) sin( kZt ) dt , ck T ³0 ak 2 bk 2 (ak – ; bk – ; ck – #- ). B- " %" 2*, ' * 2* ) [2, 3], ! ! #". *$#%& # * $#/0#(. ! " * 5 : . D2 ! . 1. E! " $ 66 !$ ! # 5## " #-! % % # #! ! " (! #") . 1. D2 . 2. E! " %% 20 " "" !$% ) #. D) " *2 ": $ , , , " (. 2). " ' " ! ( (Moore’s neighbors) [5]. ! " " ) 2* ( . 3. /""% Pn = (xn, yn), n = [1, N], N – " . " % . / $% % ! % ( #). # ! [0, 2!). !, " (!% ! 2! 0) $ $ % #% #-!. 5 % " ! #. D # : " % ! ! " . " $ " #-!, # $ " [3]: § L · M* (t ) M ¨ t ¸ t © 2S ¹ (J – #; J* – #; L – ). . 3. /" ! (: – !$; – ) "" 67 . . y y y x * Re(*) t t Im(*) " F t t . 4. ! " #-! $ : – "% ; – #; – #; – #; – #-!; – #-!; " – #- / ! #-! % % % # (. 4,–"): ak 1 S 2S ³M 0 * (t ) cos(kt ) dt , bk 1 S 2S ³ M (t ) sin(kt ) dt , * ck ak2 bk2 . 0 " ! #- " " 2*, ' * 2* " !" " " %% . 5## #-! %% ! "$ " #". + !" , ! $" # 15–20 5## . / % !* 20 5## ( ). ! # % % " ', % ! . 5. / # ! " #. "' * *2 #: (Nguyen – Widrow)-, , [6]. + !" , 40 – 60 % " * '% ! ! ' – . / % !* 50 " " %. 68 /% % – 20 % &" "% % – 50 % /"% % – 4 % . 5. & %% 1+2!"# $/+3%%. , ! !" C# 2008, !$ # !" " ! %% (%"% ), $ "% #% . 5 10 000 5 % '%, % 0,001. 50 ! ! % !" ", 2% ! 18 !$% (. 6). @ ' 0,1 %. 5## " !" !" " (. 7). " ! " !, ! ! $" #", 2 ! " 5 (, 5, . .) "% . 6. " !$ *: ! ", !" . 7, 30 $" ' ( ' – 0,15 %). . 7. ! $" #: – ; – 69 . . !. !, ! ! # ! ! #- %% . !, #- %" % 5## " ' ! ! ) . ! ! $" #" "% *. & " 1. FOLKERS A., SAMET H. Content-based image retrieval using Fourier descriptors on a logo database // Proc. of the 16th Intern. conf. on pattern recognition, Quebec (Canada), 11–15 Aug. 2002. Washington: IEEE Computer Soc., 2002. V. 3. P. 521ದ 524. 2. ZHANG D., LU G. Review of shape representation and description techniques // Pattern Recognition. 2004. V. 37. P. 1–19. 3. NIXON M. Feature extraction and image processing / M. Nixon, A. Aguado. Oxford: Elsevier, 2008. 406 p. 4. PATTERN recognition techniques, technology and applications / Ed. by Peng-Yeng Yin. Croatia: InTech, 2008. 626 p. 5. GHUNEIM A. G. Moore-neighbor tracing // Contour Tracing. 2010. http://www.imageprocessingplace. com/downloads_V3/root_downloads/tutorials/contour_tracing_Abeer_George_Ghuneim/moore.html. 6. FAUSETT L. V. Fundamentals of neural networks-architectures, algorithms, and applications. Upper Saddle River: Prentice Hall, 1993. 461 p. – . $ % ; .: (382-2)70-16-09; e-mail: [email protected] – 02.11.11