2010) 2( 23مجلة ابن الهیثم للعلوم الصرفة والتطبیقیة المجلد الجیب تمام الرقميتحویل لواصف ال بوساطةفسیفساء الصور الفضائیة عبد الجبار حمید مجید ، كلیة التربیة ابن الھیثم، جامعة بغداد قسم الفیزیاء الخالصة معدلـة عـن بوسـاطة الواصـف لتحویـل الجیـب تمـام الرقمـي الصـور الفضـائیة طریقـة لفسیفسـاء قّدمت في هذا البحث النتـائج المستحصــلة مــن قورنــت. تسـریع عملیــة الفسیفسـاءلطرائـق جدیــدة اذ قــّدمت، للتشـابه ]1[معیـار الباحــث عبـد الكــریم ــابه جــذر معـــدل مربــع الخطـــاء تطبیــق الواصــف لتحویـــل الجیــب تمـــام الرقمــي مـــع طریقــة الفسیفســاء باســـتخدام معیــار التشـ RM SEاثبت طریقة الفسیفساء المعدلة بوساطة الواصف لتحویل الجیب تمام الرقمي هي طریقة سریعة ودقیقة ، اذ. IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 Satellite Image Mosaics Using Digital Cosine Transform (DCT) Descriptor H. M. Abdul Jabar Departme nt of Physics,College of Education I bn Al-Haitham, Unive rsity of Baghdad Abstract In this research work, a modified DCT descrip tor are p resented to mosaics the satellite images based on Abdul Kareem [1] similarity criterion are p resented, new method which is p rop osed to sp eed up the mosaics p rocess is p resented. The results of app lying the modified DCT descrip tor are comp ared with the mosaics method using RM SE similarity criterion which prove that the modified DCT descrip tor to be fast and accurate mosaics method. Introduction Satellite image mosaics is essential p reprocessing st ep to obtain a large view of the interest location from number of scenes that t aken from one or different satellites, where each scene cover fragment of the complete view. T he main obstacle in such task is to find criterion that can find the match locations in the different scenes in order to mosaics them, using the regular distance metric (like M SE, M AE, …) will not detect t he similar location if any change happ ened in either locations, since the regular distance metric is variant for scaling, transition, flip p ing and rotation operations or if some kind of noise is p resent in the scenes, and it utilizes huge computation to find the matched location between two scenes. M any researchers t ry to use other distance metrics that invariant to scaling, transition, flip p ing and rotation op erations, where metrics that work in sp aces other than the sp atial domain are suggested such as Zhang and Lu [2], they try to use Fourier coefficients as descrip tor shap e-based image retrieval, they suggested to use the p olar form of the Fourier transform and use the new domain coefficients as descrip tors and use rational matching criterion to find the matching locations, where the matching criterion will be invariant to scaling, rotation and transition, The main obst acle in this criterion is that it is variant to flip p ing and every image should be convert to p olar form before app lying Fourier transform on it and it uses 36 features to decide if the two location matches or not, therefore it needs a huge computations. While Poly akov et al. [3] uses Fouri er descrip tor to identify the objects boundary to classify the human sign atures. Folkers and Samet [4] use the same Poly akov techniques but with one difference, they decompose the target shape to simp le elementary shap es (rectangle, p oly gon, ellipse, and B-sp line) then use its boundary . These algorithms can't be used for raster since it ori ginally design ed for boundary vector. DCT De scriptor Like other transforms, the Discrete Cosine Transform (DCT ) att emp ts to decorrelate the image data. Aft er decorrelation each transform coefficient can be encod ed indep endently without losing comp ression efficiency. [5] Nearly all forms of invariants, whether p rojective or not, involve ratios. By constructing ratios, even if one quantity changes und er a transformation, as long as another quantity changes p rop ortionally under the same transformation, their ratio stay s the same. [6] IHJPAS ),( ),( dcCoff baCoff F  ………………..………………… (1) IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 Where a, b, c, and d are the coefficient location, Abdul Kareem [1] in his thesis p resents a new method to find the similarity between two slid windows using DCT coefficients as descrip tors, he uses the following rational equation to achieve the similarity metric invariant for scaling, translation, rotation, flipp ing and noise addition. 22 22 , ),(),( ),(),( ijDCTjiDCT ijDCTjiDCT F ji    ………………..…… (2) the coefficients p airs [DCT (0,1), DCT (1,0)], [DCT (0,2),DCT (2,0)], and [DCT (1,2),DCT (2,1)] are used individually , and comp are the time that each p air need to find the match slide window for fractal compression p urp ose. New DCT Descriptor One of the DCT p rop erties is the energy comp actness; it has t he ability to p ack input data into as few coefficients as p ossible near the DC coefficient (left top corner). Using coefficients p airs with high energy comp actness in the Abdul Kareem DCT descrip tor equation (eq. 2) will give bett er results in the match p rocess. In this research work, a developed DCT descrip tor criterion had been made based on the Abdul Kareem method, where in the new DCT descrip tor equation more than one DCT coefficient p air are involved, but with maintaining the p rop erty that t he coefficient that closer to the DC coefficient has higher energy , this has been done by giving each F factor exp onent increase with its distance from the DC coefficient. Using more than four F factors (DCT coefficient p airs) is not recommended since the value of the F factor will be very small when the exp onent is larger than four as illust rated by .    4 1i i iFF …..……………………………………. (3) Research Procedures The images that view the International Airp ort, Baghdad, Iraq used to mosaics and form the fall view; the images were collected multisp ectral image using IKONOS figure (1), four p airs of the DCT coefficients are used in eq. 3 which are [DCT (0,1), DCT (1,0)], [DCT (0,2),DCT (2,0)], [DCT (0,3),DCT (3,0)], and [DCT (1,2),DCT (2,1)] therefore eq. [3] become in the following form: 4 2,1 3 3,0 2 2,01,0 FFFFF  ………………………………. (4) To sp eed up the matching p rocess, the F factor for the two images is calculated in advance for each slide window and taking the lowest difference between the F factors of the two images as the matched windows. Beside that, the effects of calculating the DCT transform using the waveform method [5] which calculates the DCT transform faster than the regular way , this method is called in this research the fast new F factor method. Re sults and Discussions Scenes that cover the Baghdad International Airp ort, Baghdad, Iraq cap tured using IKONOS satellite figure (1), are used to evaluate the new F factor method (the regular and fast way ) it is comp ared with the root mean square method (RM SE) by calculating the total time needed to find the matched slide window between the two images to mosaics the comp lete view using different sizes for the slide window, figure (2). The RM SE record the highest comp utational time comp ared with the other methods and it has inverse relationship with the slide window size because it will reduce the number of windows that are needed to exam, while the new F factor records comp utational time less than the RM SE method but it has forward relationship with the window size because when window size increases the IHJPAS comp utation time to calculate the DCT transform is increased exp onentially, the two method intersect at window size equals to 25 p ixel. The fast new F factor, as shown in the figure (2), IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 does notnave any effect with the changing of the size of the slide window and records the lowest comp utational time for all methods. Since the total comp utational time to find the match window is vary from set image to mosaics to another, therefore another criterion used to show the results which is invariant to changing the images set and it is illustrated in figure (3). The new criterion is time needed to comp lete the search for one slide window (time p er window) and it is calculated by dividing the total comp utational time by the number of the examined windows until finding the matched window. The behavior for the new F factor (the regular and the fast way ) is the same, but for the RM S mosaics method the behavior is changed where the computational time p er window has foreword relationship with the size of the slide window instead of the inverse relationship for the tot al comp utation time. Conclusions From the results that obtained by app lying the new F factor methods, the following conclusions are driven:  The F factor method is invariant to the scaling, translation, rotating and flip p ing op erations, which will be more accurate to calculate the similarity to mosaics different images.  Participating the F factors of other DCT coefficients in the calculation of the final F factor and giving each of them weight according to its energy p ickiness ability (equation 3) is more reliability than using F factor for one p air with regarding to its energy p ickiness ability .  Using the new F factor criterion with satellite images as similarity measurement is recommended because it is fast er than the other criteria and more accurate.  The computational time for the F factor (the regular way ), is very sensitive to the size of the slide window after 25 p ixels.  The fast way is recommended to be used to mosaics the satellite images because it is very fast and invariant t o the size of the slide window. Re ferences 1. Abdul-Kareem, A. S.(2006), Phd. Thesis, Baghdad University , College of Education Ibn Al-Haitham, Phy sics Dep artment. 2. Zhang, D, Lu G.(2002), ICM E, p roceedin gs, 1, 425-428. 3. Poly akov, et al,( 2000), United States Patent, Patent Number 6,144,171. 4. Folkers, A. and Samet ,H. (2002), Proc of the 16th Int. Conf. on Pattern Recognition, III, 521-524, Quebec City , Canada. 5. Khay am, S. A. (2003), Department of Electrical & Computer Engineering, M ichigan State University , p 4. 6. M orse, B. S.(2000), Brigham Youn g University , P7. IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 0 500 1000 1500 2000 2500 3000 4 6 8 10 15 20 25 30 Window Siz e C o m p u ta ti o n a l T im e ( s e c *E -6 ) RMS New F Factor Fast New F Factor 0 20 40 60 80 100 120 140 160 4 6 8 10 15 20 25 30 Window Size C o m p u ta ti o n a l T im e ( s e c *E -6 ) RMS New F Factor Fast New F Factor c Fig. (1) The scene of Baghdad Inte rnationals airport a) first view b) se cond view c) the merged complete view a b Fig. (2) The total computati onal time to find the match window for the three methods IHJPAS Fig. (3) The computati onal time needed to complete search one window for the three methods IHJPAS