IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 The Invariant Moments Based With Wavelet Used To Decide the Authintication and Originality o f Images H.L. Hussein Departme nt of Computer Science, College of Education, Unive rsity of Baghdad Abstract The digital image with the wavelet tools is increasing nowadays with M AT LAB library, by using this method based on invariant moments which are a set of seven moments can be derived from the second and third moments , which can be calculated after converting the image from colored map to gray scale , rescale the image to (512 * 512 ) p ixel , dividing the image in to four equal p ieces (256 * 256 ) for each piece , then for gray scale image ( 512 * 512 ) and the four p ieces (256 * 256 ) calculate wavelet with moment and invariant moment, t hen store the result with the author ,owner for this image to build data base for the original image to decide the authority of these images by using comp arison using M ean Square Error (M SE) as shown below :- The moments value of any image will be comp ared with the original data base images moment. T he exp eriments were performed on a Pentium IV, 1.6 GHz p rocessor, running M icrosoft Windows XP and the programs were imp lemented by MATLAB . Index Terms— wavelet, digital image, moment Introduction Searchin g a digital libr ary having lar ge numbers of digital images or video sequences has become imp ortant in this visual age. Every day, large numbers of p eople are using the Internet for searching and browsin g through d ifferent multimedia databases. Image feature vector indexing has b een d eveloped and imp lemented in several multimedia database sy stems such as the IBM QBIC Sy st em developed at the IBM Almaden Resear ch Center, the Virage Sy st em develop ed by Virage, Inc., and the Phot o book Sy st em developed by the M IT M edia Lab[1]. For each image inserted into the database, a feature vector on the order of 500 elements is generated to rep resent accurately the content of the image. This vector is much smaller in size than the original image. The difficult p art of t he problem is to construct a vector that both p reserves the image content and yet is efficient for search ing. Once the feature vectors are gener ated, they are then stored in p ermanent st orage. To answer a query, the image search engine scans through the previously comp uted vector indexes to 2 1 0 1 0 ),(),( M y N x   1  yxfyx N* M MSE         IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 select t hose with shortest distances to the image query vector. In this p roject, the research develops a new algor ithm to make se mantically -meanin gfu l comp arisons of images efficient and accurate. Fi gure 1 shows the basic structure of the system. To accurately encode semantic features of images we emp loy wavelets based. Using these wavelets and st atistical moments' analysis, the algorithm p roduces feature vectors t hat p rovide much bett er frequency localization than other traditional color lay out coding al- gorithms. The libraries can use the digital ima ge p rocessing to decide the authority of each picture in them by using simple algorithm by extracting the moment of each p icture and st ore that values in term of data base to comp are these values with any unknown p icture. As a result, millions of p ictures flow on the Internet every day. Nowadays, the interchange of ima ges becomes mor e and more frequent. M any techniques op erating on images formats have been p ublished and become p ublicly available. To answer a query, the image se arch engine scans through the p reviously com- p uted vector indexes t o select t hose with short est moment t erms to the image query vector. M any color image formats are currently in use, e.g., GIF, JPEG, PPM and TIFF are the most widely used formats. Because images in the image database can have different formats and different sizes. For t he test database of relatively small images, a rescaled thumbnail consisting of 512 x 512 p ixels in Red-Green-B lue (RGB) color sp ace is adequate for the p urp ose of comp uting the feature vectors, and then convert the inp ut image from color ed image to the gray-scale image. The original gray scale ima ge (512 * 512) will be divid ed into four equal divisions ,each part is ( 256 * 256 ) p ixel as shown in fig. 2 . Wavelet Wavelets are mathematical functions that cut up data into different frequency comp onents, and then study each comp onent with a resolution matched to its scale. Wavelets were develop ed indep endently in the fields of mathematics, quantum p hy sics, electrical engineer ing, and seism ic geology . Interchanges between these fields during the last ten years have led to many new wavelet applications such as image compression, turbulence, hu man v ision, radar, and earthquake p rediction [2]. So that , this p roject use the Haar as a type of wavelet with MATLAB Lan guage as a function of image co mpression. The Haar wavelet is the oldest and simp lest transform and based on the Haar scaling and wavelet functions. The decomp osition and reconst ruction filter for a Haar b ased transform are of len gth 2 and obtained as followes : >> [ Lo_D, Hi_D, Lo_R, Hi_D] = wfilters('Haar') Lo_D = 0.7071 0.7071 Hi_D = -0.7071 0.7071 Lo_R = 0.7071 0.7071 Hi_D = 0.7071 -0.7071 Invariant Moments Invariant moments which ar e a set of sev en moments can be deriv ed from the second and IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 third moments. M oment features used in this p aper can p rovide the p rop erties of invarian ce to scale, p osition, and rotation. We used moment analy sis t o extract invar iant features from tessellated cells in an ROI. This section gives a brief des crip tion of the moment analysis. For a 2-D continuous function f(x, y ), the moment of order (p+q) is defined as [3,4] : ∞ ∞ μpq = ∫ ∫ x p y q f(x,y ) dxdy for p ,q = 0,1,2,……….. (1) -∞ -∞ A uniqueness theorem states that if f(x, y ) is p iecewise continuous and has nonzero values only in a finite p art of the xy -p lane, moment of all ord ers exist, and the moment sequence (μpq) is uniquely determined by f(x, y ). Conversely , (μpq) is uniquely determined by f(x, y ). The central moments are def ined as: ∞ ∞ μpq = ∫ ∫(x - xbar) p (y –y bar) q f(x, y ) dx dy ………………...….(2) -∞ -∞ Where xbar =( µ10 / µ00) and y bar = (µ01/ µ00). i.e. moments where the centre of gravity has been moved to the origin (i.e. µ10 = µ01 = 0). If f(x, y ) is a digital image, then Eq. (2) becomes μpq =∑ ∑ (x – xb ar ) p (y – y bar) q f (x , y ) ……………..(3) x y and the normalized central moments, denoted ŋpq ,are defined as: ŋp q = μp q / μ00 ; where y bar = (p + q) / 2 + 1 for p + q = 2 , 3 , . . . …(4) A set of seven invariant moments can be derived from the second and third mo ments (4), It shows the derivation of exp ressions from algebraic invariants app lied to the moment generating function under a rotation transformation. The moments consist of group s of nonlinear centralized moment e xp ressions. T he result is a set of absolute orthogonal moment invariants that can be used for scale, p osition, and rotation invariant p attern identification, by using the invariant moments which are a set of seven moments can be d erived from the second and third moments as below[5]. Ø1 = ŋ20 +ŋ02 Ø2 = (ŋ20 - ŋ02) 2 + 4ŋ 2 11 Ø3 = (ŋ30 - 3ŋ12) 2 + 3(ŋ 21 + ŋ03 ) 2 Ø4 = (ŋ30 + ŋ1 2) 2 + (ŋ21 + ŋ0 3) 2 Ø5 = (ŋ30-3ŋ12) (ŋ30+ŋ12) [(ŋ3 0+ŋ12) 2 -3(ŋ21+ŋ03) 2 ] + (3ŋ2 1- ŋ03) (ŋ2 1+ŋ03)[3(ŋ3 0+ ŋ12 ) 2 - (ŋ21+ ŋ03 ) 2 ] Ø6 = (ŋ20-ŋ02) [ (ŋ30+ŋ12) 2 - (ŋ21+ŋ03) 2 ] +4ŋ11 (ŋ 30+ŋ12)(ŋ21+ŋ0 3) Ø7 = (3ŋ21-ŋ03)(ŋ30+ŋ12)[(ŋ30+ŋ12) 2 -3(ŋ21+ŋ03) 2 ] +(ŋ30- 3ŋ12) (ŋ21+ŋ03 ) [3(ŋ30 + ŋ12) 2 - (ŋ21+ŋ03) 2 ] Central moments have the advantage of bein g invar iant to translation. It is well known that a small nu mber of moments can characterize an image fairly well; it is equally known that moments can be used to reconstruct t he original image (1). In order to ach iev e invar ian ce to common factors and op erations such as scale, rotation and contrast , rather than using the moments themselves algebraic comb inations there of known as moment invariants are used that are independent of these transformations. IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 Experime ntal Re sults and Discussion The moment invariant descrip tors described above were used to index an image d atabase of many images (10 images as a sample). An example of an image of a flower was used to p erform image retrieval on the whole dataset. The result of this query is given which shows the descendin g similarity from other st ored images data. Unfort unately , due to the lack of enough samples of images, we are in the p rocesses of collecting a lar ge number of images, This documented dataset will then provide a test for the evaluation of our method p rop osed in this p ap er as well as fut ure app roaches. As p ublic databases, were established with the aim of p roviding acquired sy st em by using scanners. Here the p rop osed algorithm was evaluated on image taken fro m the database which contains five distinctive databases: DB1, DB2, DB3, DB4 and DB5. Each d atabase consists of many images data in gr ay scale levels. A series of exp eriments was conducted to evaluate the p erformance of the p rop osed method. Conclusions We have invest igated the app lication of content-based image r etrieval to the domain images. Each image is characterized by a set of moment invariants which are indep endent to translation, scale, rotation and contrast as shown in table (1,2). Retrieval is p erformed by returnin g those images whose moments are most similar to t he ones of a given query image. A moment based object reco gnition sy st em is p rop osed. In a given sc ene, an object may be occlud ed due to various re asons and hence reco gn ition of original ob ject beco mes necessary for machine vision sy st ems. The invariant moments as well as som e of the lower order mo ments are used to authorize of unknown ima ges owner. In this p aper the search for known image is more accurate than the comp arison of two colored images as p ixel to p ixel, because the use of moment and invar iant moment is done by comp aring little values of moments. Re ferences 1- James Z e Wang1, Gio Wiederhold2, Oscar Firsch ein2, Sha Xin Wei3 Content-based image indexing and searching usin g Daub echies' wavelets 1 Dep artment of Comp uter Science and School of M edicine, Stanford University , Stanford, CA 94305, USA 2 Dep artment of Comp uter Science, Stanford University , Stanford, CA 94305, USA 3 Stanford University Libraries, Stanford University , Stanford, CA 94305, USA International journ al on Di gital Libraries , Sp ringer-Verle g 1007 .Int J Digit L ibr(1997) 1: 311-328 2- Asmara Graps , An Introduction To Wavelets. 3- Shao Yin g Zhu and Gerald Schaefer , Thermal med ical image retrieval by moment invariants. 1App lied Comp uting, University of Derby , Derby , U.K., e-mail: S. Y.Zhu@derby.ac.uk 2School of Co mputing and Informatics, Not tingham Trent University , Nottingham,U.K., e-mail: Gerald.Schaef er@ntu.ac.uk 45- Saib al Dut ta and P.K.Nanda , M oment based Object Recogn ition using Art ificial Neural Network .http://dsp ace.nitrk1.ac.in/dsp ace 5- Rafael, C. Gonz ales & Richard, E. (2004), Woods. digital image p rocessing usin g MATLAB, ,by Pearson Education . Inc,Pearson Prentice- Hall. IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 Table( 1): Example of calcul ating the moment of the image Moments Origin first quarter se cond quarter thi rd quarter fourth quarter μ00 0 0 0 0 0 μ10 3.783863e+007 4.938875e+006 5.871984e+006 3.908114e+006 4.200341e+006 μ01 8.913924e+009 2.514108e+008 2.944227e+008 3.014090e+008 3.480867e+008 μ20 9.738164e+009 2.690497e+008 3.935360e+008 2.041220e+008 2.833067e+008 μ02 2.277567e+012 1.214415e+010 2.021076e+010 1.672020e+010 2.333748e+010 μ11 3.204147e+012 1.214415e+010 2.062193e+010 2.905460e+010 3.337624e+010 μ30 3.475306e+012 2.176426e+010 3.441361e+010 1.629083e+010 2.486389e+010 μ12 1.379838e+015 2.060579e+012 3.370046e+012 1.534540e+012 2.446069e+012 μ21 8.146100e+014 9.409422e+011 1.800647e+012 1.354361e+012 2.033085e+012 μ03 8.214088e+014 8.776290e+011 1.437899e+012 1.662394e+012 2.235337e+012 Table( 2):Example of retrieving the set of seven invariant moments of the i mage Fig. (1a) illustrates the overview of the system to build the database . PHI Origin first quarter se cond quarter thi rd quarter fourth quarter Ø1 1.448088e-003 5.644571e-004 4.030901e-004 7.489013e-004 5.829668e-004 Ø2 9.441665e-009 1.652168e-008 4.767174e-009 1.652238e-008 5.077208e-009 Ø3 2.284418e-011 1.643365e-011 4.770410e-013 2.653920e-011 6.309182e-012 Ø4 3.304694e-011 8.909984e-012 1.111096e-012 2.546404e-011 1.096206e-011 Ø5 3.087560e-022 -7.821719e-23 4.962452e-025 -5.997825e-22 8.625016e-023 Ø6 3.191786e-015 -1.032175e-15 -7.380705e-17 -3.010348e-15 -7.610436e-016 Ø7 8.538908e-022 -7.420455e-23 6.388198e-025 2.801038e-022 -2.952706e-023 Read The Image Pre- processing (Convert to Divide the image into fou r equal divisions Wavelet T ransform ation On the divisions of image Extract Moment Store the moments of the image in the database IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 Fig. (1b) illustrates the overview of the comparison syste m of image information with the database . Fig.(2.a) the g ray scale of the origin al image Fig.(2.b) the fou r e qu al di visions Read the image Pre- processing (Convert to grayscale + resize) Divide the image into fou r equal divisions Wavelet trans formation On the divisions of image Extract Moment terms Compare the result with database Final result (f ound or not found) IHJPAS 2010) 2( 32المجلد مجلة ابن الهیثم للعلوم الصرفة والتطبیقیة اللحظات الثابتة الموجي التحویل إستندْت َمع ُیسَتعمُل لَتْقریر عائدیة واصالة الصوِر الرقمیة حسین لفتة حسین جامعة بغداد ،ابن الهیثم -كلیة التربیة ،قسم الحاسبات الخالصة التحویــل المــوجي مــع لغــة مــاتالب تزایــد فــي الوقــت الحاضــر إســتعمال الصــوِر الرقمیــِة وبــأدواِت ة مســتندة علــى اللحظــاِت الثابتــِة وهــي مجموعــة ِمــْن ســبع لحظــاِت ُیْمِكــُن َأْن تُشــَتقَّ ِمـــْن وباســتخدام هــذه التقنیــ ــابها بعــد قــراءة الصـــورة الرقمیــة وتحویلهــا مـــن الصــور الملونــة الـــى اللحظــاِت الثانیــِة والثالثـــِة ، التــي یمكــن حسـ وتقســیم هـذه الصــورة ، ) 512 * 512(ثـم تحجــیم الصـورة وجعلهـا ثابتــة بقیـاس ، الصـور ذي التـدرج الرمــادي 512(التحویل المـوجي للصـورة ثم عمِل ، لكل جزء منها ) 256* 256( على اربعة اجزاء متساویة بقیاس لغـرض ضـغط الصـورة مـع ازالـة ، ) 256* 256( التدرج الرمادي و االجـزاء االربعـة االخـرى يذ) 512* الثالثة وخزن النتیجِة لِبنـاء قاعـدِة البیانـات ) Ø( مشتقتها مع احتساب اللحظات االولى و ، الضوضاء منها .للصوِر األصلیِة لَتْقریر اصالة هذه الصور عند مقارنتها مع صور اخرى حیث تبین ان عملیة المقارنة بین الصور الرقمیة تكون صعبة وتاخذ وقتا كبیرا نتیجة لكمیة البیانات التي تعمل علیها عملیة المقارنة ولكن باسـتخدام هـذه الخوارزمیـة اصـبحت العملیـة اسـرع وادق الن المقارنـة تعتمـد علـى قـیم یـد اقـل نسـبة االخطـاء المقبولـة وكمـا مبـین فــي اللحظـات بعـد ضـغط الصـورة باسـتخدام مربـع معـدل الخطـأ لتحد ) .2و 1(الجدولین IHJPAS