TELK OMNIKA Indonesian Journal of Electrical Engineering V ol. 12, No . 5, Ma y 2014, pp . 3920 3927 DOI: http://dx.doi.org/10.11591/telk omnika.v12.i5.4390 3920 Ima g e Def ormation Based on W a velet Filter and Contr ol Cur ves Hong-an Li 1* , Jie Zhang 2 , and Baosheng Kang 1 1 School of Inf or mation Science and T echnology , Nor thw est Univ ersity , Xi’an 7 10127, China 2 Depar tment of Hematology , T angdu Hospital, F our th Militar y Medical Univ e rsity , Xi’an 710038,China * corresponding author , e-mail: an6860@126.com Abstract W e pro vide an image def or mation metho d based on w a v elet filter using control cur v es and mo ving least squares . The image is preprocessed firstly instead of being directly def or med b y the old w a ys . And the or iginal image will be filtered into a high frequency par t and a lo w fre quency par t b y the w a v elet, and then use the mo ving least squares and the control cur v es only to def or m the lo w frequency par t, b ut not the high frequency par t. The k e y points are set to creat e control cur v es according to shape inf or mation or def or mation requirement, and mo v ed to ne w position to def or m the image using mo ving least square s . The final result of image def or mation is obtained b y adding the def or med lo w frequency par t to the high frequency par t of the or iginal image . Exper iments sho w that the high frequency detail inf or m ation is w ell preser v ed and the image shape and contour are also w ell descr ibed, and so the def or mation results are satisf actor y and realistic. K e yw or ds: Image Def or mation, W a v elet Filter , Mo ving Least Squares , Control Cur v es Cop yright c 2014 Institute of Ad v anced Engineering and Science . All rights reser ve d. 1. Intr oduction The image def or mation technology is widely applied in the fields of tele vision animation [1] and medical image processing [2], etc. The f amiliar image def or mation method is that some con- trol objects are chosen to control the def or mation, which can be control points [3], line segments or polygon meshes [4]. The image def or mation is carr ied out through changing the positions of the control objects . Man y scholars ha v e put f orw ard image def or mation methods , and the main diff erence of those methods is that their def or mation control objects are diff erent. Lee presented the free g r id def or mation technology [5], which achie v es def or mation b y the image par ameter ization based on binar y cubic inter polation spline , and the def ault of this method is that it needs to align the register g r id according to image char acter istics with the control point spline . Beier and Neely impro v ed the free g r id def or mation technology b y using a set of line segments to control the def or mation, which is con v enient f or users [6]. K oba used the impro v ed free g r id def or mation technology in the image surf ace def or mation and achie v ed a good def or mation result [7]. Igar ashi put f orw ard point-based image def or mation method [8], in which the input image is subdivided into tr iangles and to solv e the system of linear equations with the its n umber of unkno wn v ar iab les equal t o the n umber of all tr iangle v er te x es , in order to reduce the distor tion deg ree of the def or med image and k eep image def or mation as r igid as possib le . A common char acter istic of the abo v e def or mation methods is to minimiz e their local scaling and shear ing, b ut these def or mation oper ations are complicated and the realistic eff ect of def or mation is not v er y good. Liter ature [9] proposed an image def or mation method based on Mo ving Least Squares (MLS), in which a def or mation mapping function of f e ature points or segments are estab lished and used to control diff erent image def or mations . The def or mation method has good realistic eff ect and enab les users to f eel lik e manipulating real objects . But it is apt to produce bad results with shear , distor tion and stretch with wrong propor tion, and its def or mation eff ect is often not ideal in some local locations with the same scale , so it has some limitations . W e propose an image method based on w a v elet filter using control cur v es and MLS . Firstly , the image is preprocessed and filtered out the high frequency par t. Then only the lo w Receiv ed October 10, 2013; Re vised December 7, 2013; Accepted J an uar y 2, 2014 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA ISSN: 2302-4046 3921 frequency par t is def or med using the control cur v es and MLS . Finally , the def or med lo w frequency par t is added to the high frequency par t, thus the realistic image def or mation is realiz ed. 2. Ima g e Def ormation Using MLS The MLS def or mation technology regards the image bef ore def or mation as an indepen- dent v ar iab le , the def or med image as target v ar iab le , and the whole process of def or mation al- gor ithm is to find the mapping function f . Fig. ?? is the or iginal image and Fig. ?? is the corre- [Or iginal]                 [Def or med]                       Figure 1. Image def or mation sponding def or med image , which is obtained b y emplo ying def or mation function f . According to MLS theoretical model [8], with set S as the f eature points set of or iginal image and set D as the f eature points set of def or med image , there is a def or mation function f which can mak e the v alue of Eq. (1) minim um. X w i j f ( s i ) d i j 2 : (1) w i = 1 j s i v j 2 : (2) Where , w i is w eight and its v alue v ar ies according to the position of v in the image , and v stops mo ving when corresponding v alue of Eq. (1) is minim um, so the method is called MLS [9]. When v is equal to s i , w eight v alue w i is infinite , so define f ( s i ) = d i ; When f eature point does not v ar y , define f ( s i ) = s i = d i . f ( x ) = xM + T : (3) Where , M represents linear tr ansf or mation, and T represents tr anslation tr ansf or mation. T = X i w i d i = X i w i   X i w i s i = X i w i ! M : (4) With Eq. (4) substituted into Eq. (3), w e obtain: f ( x ) =   x X i w i s i = X i w i ! M + X i w i d i = X i w i : (5) Set 8 > > < > > : ^ s i = s i P i w i s i = P i w i ^ d i = d i P i w i d i = P i w i (6) So Eq. (1) can be re wr itten into: X i w i j ^ s i M ^ d i j 2 : (7) The procedure of the MLS image def or mation algor ithm includes: Step 1 Select f eature points set S = f s 1 ; s 2 ; ; s n g in the or iginal image Fig. ?? . Image Def or mation Based on W a v elet Filter and Control Cur v es (Hong-an Li) Evaluation Warning : The document was created with Spire.PDF for Python.
3922 ISSN: 2302-4046 Step 2 Deter mine the positions of in the def or med image Fig. ?? , which can be denoted as a ne w f eature points set D = f d 1 ; d 2 ; ; d n g . Step 3 Deter mine the mapping function f according to d i = f ( s i ) . Linear tr ansf or mation M can be affine tr ansf or mation, similar ity tr ansf or mation and r igid tr ansf or mation. The def or med image can be obtained b y applying mapping f to the remaining points of or iginal image . F orw ard mapping or re v erse mapping can be used to gener ate a ne w image . F orw ard mapping is prone to produce v oids and o v er lapping phenomena, so re v erse mapping is adopted in this paper . The MLS image def or mation eff ects are sho wn in Fig. 2 [9]. [Or iginal]                                   [Affine]                                                                               [Similar ity]                                                               [Rigid]                                                     Figure 2. Image def or mation based on MLS Where , Fig. ?? is the or iginal image , Fig. ?? is an affine def or med image , Fig. ?? is a similar ity def or med image , and Fig. ?? is a r igid def or med image . There is ser ious wrong shear phenomenon and une v en scaling tr ansf or mation in Fig. ?? . The eff ect of Fig. ?? is better than that of Fig. ?? , b ut there is propor tional distor tion in the r ight par t of image in Fig. ?? . Fig. ?? is pref er ab ly and relativ ely similar to the def or mation eff ect of real object, so r igid tr ansf or mation is adopted in this paper . [Or iginal] [Def or med] [Def or med] Figure 3. Image r igid def or mation The most significant char acter istic of the MLS image def or mation method is simple and easy to realiz e . But it also has se v er al def ects , which are m ainly reflected in f ollo wing aspects . Firstly , it achie v es good def or mation eff ect only when dealing with point-based affine tr ansf or ma- tion. Secondly , in actual oper ation f eature points set S ma y not be completely accur ate mapping to the def or mation f eature points set D . Thirdly , there ma y be stretch phenomenon in def or med image as sho w ed in Fig. ?? and Fig. ?? . Lastly , it does not consider that there e xists a large n umber of unneeded oper ating points in the def or mation process , which could be filtered out ac- cording to the intensity of the frequency v ar iation, so the computation al comple xity of the MLS image def or mation method is large , and there is real-time bottlenec ks when the n umber of f eature points is large . 3. W a velet Filter W a v elet tr ansf or m is considered as a ne w milestone in the de v elopment of F our ier tr ans- f or m, which is regard as mathematical microscope with e xcellent ”z oom” perf or mance . In w a v elet TELK OMNIKA V ol. 12, No . 5, Ma y 2014 : 3920 3927 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA ISSN: 2302-4046 3923 tr ansf or m, signal is repr esented as a w eighted sum of a ser ies of basis functions , and basis func- tions are obtained from a w a v elet mother function b y dilation and tr anslation. W a v elet function is a shor t-ter m shoc k function with compact suppor t and it has local char acter istics in the time domain, also being called as spatial domai n, and frequency domain [10]. The joint a nalysis of spatial domain and frequency domain obtained from w a v elet tr ansf or m mak es it to be a good tool to e xtr act both detail components and appro ximate components of images , where the lo w frequent par t of signal is considered as the appro ximate signal and the high frequent par t is considered as the details of signal. The or iginal image is treated as a signal f ( t ) , which is filtered into diff erent frequency components using Mallat algor ithm [11], [12]: f ( t ) = A j 1 f ( t ) = A j f ( t ) + D j f ( t ) : (8) Where , A j f ( t ) is one component of signal f ( t ) , whose frequency is not past 2 j ; The frequency of D j f ( t ) is betw een 2 j and 2 j +1 . Eq. (8) is re wr itten into a matr ix f or m: C j +1 = H C j ; D j +1 = GC j ( j = 1 ; 2 ; ; J ) : (9) Where , J is the w a v elet decomposition le v el. Eq. (9) is the Mallat p yr amidal decomposition algo- r ithm, whose process is sho wn b y Fig. 4. Where , 2 # is the v alue of only e v en location.           H 2 Ę G 2 Ę j C 1 j C + Figure 4. Decomposition of Mallat p yr amidal algor ithm After f ( t ) is decomposed according to the Mallat algor ithm, the signal is distinguished from noise based on the e xper ient ial inf or mation, and then f ( t ) is filtered to gener ate a ne w sequence C j and D j . The Mallat reconfigur ation algor ithm is: C j = H C j +1 + G D j +1 ( j = J ; J 1 ; ; 1) : (10) Where , the conjugates of H and G are H and G , whose process is sho wn in Fig. 5. Where , " 2 is the liter sample , it means that the n umber of samples is 2 times than the or iginal.           ň 2   1 j C − ň 2 H *   G * C   1 j j D − Figure 5. Reconstr uction of Mallat p yr amidal algor ithm When the signal is reconfigured, the par t is deleted which is relativ e to the high frequency detail signal and corresponding to the noise , and then the filtered signal is obtained: f ( t ) = A j f ( t ) = X k 2 Z C J ;k J ;k ( t ) : (11) Image Def or mation Based on W a v elet Filter and Control Cur v es (Hong-an Li) Evaluation Warning : The document was created with Spire.PDF for Python.
3924 ISSN: 2302-4046 Eq. (11) is a smooth signal e xpression after f ( t ) is fi l tered. It is equiv alent to using a smooth cur v e to fit it [12]. The high and lo w frequency of image are used to measure the changing intensity of                             Figure 6. The process of image def or mation based on w a v elet filter using control cur v es and MLS diff erent locations . W e use w a v elet filter to filter out the high frequency par t of image , and use the control cur v es and MLS to def or m the lo w frequency par t of the image . Then the final result of image def or mation will appear b y adding the def or med lo w frequency par t to the high frequency par t of the or iginal image . The algor ithm process is sho wn in Fig. 6. 4. Contr ol Cur ves In order to control the path of contro l cur v es , w e use cubic spline cur v e fitting method to gener ate the control cur v es [13], [14]. Control points are piece wise fitted b y cubic spline cur v e , and the cur v e can pass the control points accur ately which has second or der contin uity on the connection point. W e can get the control points b y clic king the mouse . Assuming that w e w ant to use n + 1 order ly control points a j ( j = 0 ; 1 ; 2 ; ; n ) to gener ate a cur v e which includes n segments . W e use cubic spline cur v e to gener ate each segm ent, and the free endpoint conditions to gener ate the cubic spline cur v e . Suppose that s i ( i = 0 ; 1 ; 2 ; ; n ) w as the i th control cur v e bef ore def or mation, the d i ( t ) w as the corresponding i th cur v e after the def or mation, its corresponding n + 1 ordered control points w ere b j ( j = 0 ; 1 ; 2 ; ; n ) , a nd t 2 (0 ; 1) . According to Eq. (1) w e can obtain: X i Z 1 0 w i ( t ) j s i ( t ) M + T d i ( t ) j 2 dt: (12) The equation of w eight w i ( t ) is: w i ( t ) = j s 0 i ( t ) j j s i ( t ) v j 2 a . By getting the minim um v alue of Eq. (12) w e can obtain: T = d s M : (13) The equation of s and d are: s = P i R 1 0 w i ( t ) s i ( t ) dt P i R 1 0 w i ( t ) dt d = P i R 1 0 w i ( t ) d i ( t ) dt P i R 1 0 w i ( t ) dt : (14) Eq. (12) can be re wr itten into: X i Z 1 0 w i ( t ) j ^ s i ( t ) M ^ d i ( t ) j 2 dt: (15) Where , ^ s i = s i ( t ) s , ^ d i = d i ( t ) d , s i ( t ) and d i ( t ) are the cur v e segment of cubic spline cur v es respectiv ely bef ore and after image def or mation, and the matr ix e xpression of par ameter v ar iab le equation, which is fitted inter polation b y the cubic spline cur v e , is: s i ( t ) = ( s ix ( t ) s iy ( t )) = ( t 3 t 2 t 1) 2 2 1 1 3 3 2 1 0 0 1 0 1 0 0 0 a i 1 a i a 0 i 1 a 0 i : (16) TELK OMNIKA V ol. 12, No . 5, Ma y 2014 : 3920 3927 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA ISSN: 2302-4046 3925 a i 1 and a i are respectiv ely the star t and end coordinates of the ith cur v e bef ore image def or ma- tion, while a 0 i 1 and a 0 i are respectiv ely the first der iv ativ e v alues of star t and end coordinates , and the v alue can be calculated b y the free endpoints . In the same w a y , b i 1 and are respectiv ely the star t and end coordinates of the i th cur v e after image def or mation, b 0 i 1 and b 0 i are respectiv ely the first der iv ativ e v alues of star t and end coordinates . According to Eq. (16), the e xpression of cubic spline cur v e can be re wr itten into: s i ( t ) = ( s ix ( t ) s iy ( t )) = ( t 3 t 2 t 1) ( m 1 i m 2 i m 3 i m 4 i ) T : (17) d i ( t ) = ( d ix ( t ) d iy ( t )) = ( t 3 t 2 t 1) ( n 1 i n 2 i n 3 i n 4 i ) T : (18) According to Eq. (17) and Eq. (18), w e can gener ate cubic spline cur v e on the fre e end- points , so the control cur v e set S and D are gener ated. Let the points in S match with the points in D , and use them as control points , and def or m the image based on the control points set. 5. Experiments 5.1. Feature points e xtraction According to the def or mation requirement of f ace image in our e xper iment, w e define 68 f ace f eature points which ref er to the definitions of f ace f eature point par ameters in MPEG-4 [15]. The f ace f eature points mainly locate at outside contour of f ace , e y ebro ws , nose and mouth, and relativ ely dense f eature points are set t o the f acial f eatures region, which is the main par t of def or mation and action [16]. F acial f eature point s are divided into organ descr iption f eature points and basic f eature points which are also called contour f eature points . Basic f eature points denoted as hollo w dots in Fig. 7 descr ibe the whole f acial e xter nal char acter istic , and the y divide a whole f ace according to f acial shape f eatures and deter mine the char acter istics of the f ace and the major organs , which is the impor tant ref erence standard f or estab lishing f ace def or mation f eature points .                                                                                                                                       Figure 7. The MPEG-4 definition of the human f ace f eatures Only 13 points are set as the f eature points in this paper , because those points co v er the changing par t of the smiling f ace and the eff ects of image def or mation using the 13 points will be v er ified enough. 5.2. The algorithm of ima g e def ormation based on wa velet filter using contr ol cur ves and MLS Input a image needed to be def or med, and tak e the f ollo wing steps to def or m: Step 1 Set k e y points to create a control cur v e set S , and the contour or shape of the image is represented. Step 2 Mo v e the points and change the position and direction of the spline cur v es to gener ate a control cur v e set D which has been def or med. Image Def or mation Based on W a v elet Filter and Control Cur v es (Hong-an Li) Evaluation Warning : The document was created with Spire.PDF for Python.
3926 ISSN: 2302-4046 Step 3 Through calculation, mak e one-to-one correspondence betw een the control points of S and D to gener ate the control points . Step 4 Filter the or iginal image into a high frequency par t and a lo w fre quency par t ( Using the w a v elet tool kit of the Matlab softw are). Step 5 Def or m the lo w frequency par t of the image using the control points method. Step 6 Add the def or med lo w frequency par t to the high frequency par t of the or iginal image , and then the final result of image def or mation will be obtained. 5.3. Experiment results Matlab 2011b is adopted in the e xper iments , and the e xper iment results are sho wn in Fig. 8. [Or iginal]                                               [MLS]                                                 [MLS]                                       [Our method]                         Figure 8. Image def or mation results The Fig. ?? is or iginal image , the Fig. ?? and the Fig. ?? are the def or med images using MLS , and the Fig. ?? is the def or med image using our method. F rom the eff ect of the def or mation w e can see our met hod is go od enough to k eep the image details , and there is no local distor tion and tension phenomenon as the Fig. ?? and the Fig. ?? , and our def or mation is smooth and realistic. Because the high frequency par t of the image has been filtered out, the diff erences betw een points in the lo w frequency par t ha v e been significantly reduced. Besides , dur ing the def or mation process , w e don’t deal with the high frequency inf or mation and only deal with the edge and contour of the image , retain the high frequency inf or mation completely . The control cur v e set is used to descr ibe the shape topology relations or contour inf or mation, and the diff erent par ts of the contour and edge are def or med in diff erent scales , so the diff erent par ts of the contour and edge can k eep their shapes , and the final def or mation eff ect will be more natur al and smooth, so it can g reatly impro v e the fitting eff ect using our met hod. At the same time it will reduce the n umber of f eature points , so it can g reatly increase the def or mation speed. 6. Conc lusions W e propose an imag e def or mation method based on w a v elet filter using control cur v es and MLS . In the aspects of comple xity , def or mation speed and the eff ect of the def or mation are all impro v ed using our method. Those mainly reflect in the f ollo wing aspects: (1) The speed of algor ithm and precision of calculatio n are impro v ed, because only the lo w frequency par t of the image is processed through the w a v elet filter ing; (2) The shape a nd contour of the image are w ell descr ibed, b ecause diff erent scales are tak en to def or m the diff erent par ts of the contour and edge of the image using control cur v es; (3) The high frequency inf or mation of the image is completely reser v ed, so the detail is clear and the def or mation is smooth. TELK OMNIKA V ol. 12, No . 5, Ma y 2014 : 3920 3927 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA ISSN: 2302-4046 3927 At present, the 3D model has been another impor tant object to be dealt with in the field of visualization technology because of the r apid de v elopment of the computer hardw are [17]. F or the ne xt w or k, the method of the this paper should be applied in the def or mation of the 3D model in order to mak e it more smooth and natur al. Ac kno wledg ement This w or k is suppor ted b y the National Natur al Science F oundation of China ( No .61379010) and ( No .61272286) . Ref erences [1] Sm ythe , D .B . A tw o-pass mesh w ar ping algor ithm f or object tr ansf or mation and image inter- polation. T ech. Rep . 1030, ILM Computer Gr aphics Depar tment, 1990. [2] Bookstein, F . L. Thin-plate splices and the decomposition of def or mations . IEEE T r ansactions on P atter n Analysis and Machine Intelligence , 1989; 11(6): 567-585. [3] McCr ac k en, R and Jo y , K. I. F ree f or m def or mations with lattices of arbitr ar y topology . In Proceedings of A CM SIGGRAPH 1996, A CM Press , 1996; 181-188. [4] Beier , T . and Neely , S . F eature based image metamor phosis . In SIGGRAPH 1992: Proceed- ings of the 19th ann ual conf erence on Computer g r aphics and inter activ e techniques , A CM Press , Ne w Y or k, USA, 1992; 35-42. [5] Lee , S ., Chw a, K. and Shin, S . Image metamor phosis using snak es and free-f or m def or- mations . In SIGGRAPH 1995: Proceedings of the 22nd ann ual conf erence on Computer g r aphics and inter activ e techniques , A CM Press , Ne w Y or k, USA, 1995; 439-448. [6] W arren, J ., Eechele , G., and Thaller , C ., etc. A geometr ic database f or gene e xpression data. A CM SIGGRAPH symposium on Geometr y processing, 2003; 166-176. [7] K oba y ashi, K. and Otsubo , K. F ree f or m def or mation b y using tr iangular mesh. Proceedings of the eighth A CM symposium on Solid modeling and applications , 2003; 226-234. [8] Igar ashi, T ., Mosco vich, T ., and Hughes , J . F . As r igid as possib le shape manipulation. A CM T r ans . Gr aph. 2005; 24(3): 1134-1141. [9] Schaef er , S .McPhail T . and W arren J . Image def or mation using mo ving least squares . A CM T r ansactions on Gr aphics , 2006; 25(3): 533-540. [10] F AN Chunnian, W ANG Shuiping. W a v elet-based illumination nor malization algor ithm f or f ace recognition. Computer Engineer ing and Applications , 2010; 46(6): 174-177. [11] Zhang Xiangw ei, Luo Shaoming, Zhong T ongzi. W a v elet Analysis in T esting Signal. Applied Mathematics and Mechanics , 1998; 19(3): 203-207. [12] Ma P an, Meng Lingkui, W en Hongy an. Kalman Filter ing Model of Dynamic Def or mation Based on W a v elet Analysis . Geomatics and Inf or mation Science of W uhan Univ ersity , 2004; 29(4): 349-353. [13] Hua Shungang, Li Xiao xiao , Li Shaoshuai. Image Def or mation Using Control Cur v es and Mo ving Least Squares . Jour nal of Chinese Computer Systems , 2010; 31(11): 2251-2254. [14] Hua Shungang, Liu Ting. Study on image def or mation based on mo ving least squares . Jour- nal of Computer Applications , 2009; 29(1): 71-73. [15] ISO/IEC JTC1/SC29 Document N3908, MPEG4 Video V er ification Model v ersion 18.0, 2001. [16] Beibei Li, Qiang Zhang, etc. F acial Animation Based on F eature P oints . TELK OMNIKA, March 2013; 11(3): 1697-1706. [17] Guangguo Zhang, Jing Sheng, F eng W ang. A Finite Element Analysis of The Rectangle Spline Broach. TELK OMNIKA, December 2012; 10(8): 2125-2130. Image Def or mation Based on W a v elet Filter and Control Cur v es (Hong-an Li) Evaluation Warning : The document was created with Spire.PDF for Python.