IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3 ) 2010 Image Improvement Using The Combination of Wavelet and Multiwavelet Transform B.J. AL-Khafaji Departme nt of Computer ,College of Education Ibn-Al-Haitham Unive rsity of Baghdad Abstract This p aper introduces method of image enhancement using the combination of both wavelet and M ultiwavelet t ransformation. New t echnique is p rop osed for image enhancement using one smoothing filter. A critically- Samp led Scheme of p reprocessing method is used for comp uting the M ultiwavelet.It is the 2 nd norm ap p roximation used to sp eed the p rocedures needed for such comp utation. An imp rovement was achieved with the p rop osed method in comp arison with the conventional method. The performance of this t echnique has been done by comp uter using Visual Baisec.6 p ackage. Introduction Image imp rovement is a technique which reduces image noise, removes artifacts, and p reser details. In this p aper, wavelet transform is used as a sub-step of this technique. The wavelet transform [1] has a long and successful history as an efficient image p rocessing tool. However, as a result of a sep arable extension from 1-D bases, wavelets in higher dimensions can only cap ture very limited directional information. Different directions are mixed in certain wavelet sub-bands. For instance, 2-D wavelets only p rovide three directional comp onents, namely horizont al, vertical, and diagonal. Furt hermore, the 45◦ and 135◦ directions are mixed in diagonal sub-bands. With the directional extension for wavelets p rop osed in [2] that mixing p roblem can be imp roved, but not totally resolved. However, the wavelet transforms is st ill very att ractive for image p rocessing app lications. M ultiwavelets are a relatively new addition to the wavelet theory, and have received considerable att ention since their introduction [3]. Contrary to ordinary wavelets, M ultiwavelet offers simultaneous orthogonal, sy mmetry , and short sup p ort. Similar to p erforming wavelet decomposition with filters, M ultiwavelet decomposition can be realized with filter-banks. The filter coefficients in this case are, however, matrices instead of scalars. Therefore, two or more input st reams to the M ultiwavelet filter-bank are required to p erform the decomp osition. Several methods have been developed for obtaining multiple input st reams from a given single input st ream [3]. This p aper uses A Critically Samp led Scheme of Prep rocessing 2 nd norm ap p roximation with its inverse as one ap p roach of M ultiwavelet. Discrete Wavelet Transform The transformation is a process that translates one object from a given do main to another in order to have some imp ortant imp licit information, which can be used for its recognition [4]. One of the conventional transformations is the Fourier transform which usually transforms the signal from its time domain to the frequency domain [5]. The next form of the Fourier transform develop ed to an efficient t ransform is called the Wav elet T ransform (WT) [6]. The IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3 ) 2010 Wavelet can be regarded as the most efficient transform that deals with image, sound, or any other pattern since it p rovides a p owerful time-sp ace (time-frequen cy) representation [7]. The effect of the wavelet transform on image is defined as” it abstracts the image in universal sp ace, this contains all information into an app roximately orthogonal (st atist ical indep endent) sp aces (represent p rojection of the subject) contained in this universal sp ace. By chan ging the scale in each p rojection, the algebraic sum of all these p rojections gives the original subj ect before abstraction process” [8,9]. This ty p e of transformation can be app lied on one as well as on two dimensional signals by using a sp ecial Transformation matrix which is known as a filter denoted by D4 wavelets. D4 wavelet or (transformation matrix) can be reconstructed by using four coefficients:- C 0 = (1+√3) /4√2 C 1 = (3+√3) /4√2 C 2 = (3 -√3) /4√2 C 3 = (1-√3) /4√2 Dep ending on the p revious four coefficients D4 the transformation matrix must be a square matrix NN and depends on the dimension of the input signal which must be also a square matrix NN).[6] Multiwavelet transform M ultiwavelet filter banks require a vector-valued inp ut signal. There is a number of ways to p roduce such a signal for 2-D signal image data. One of the methods is to sp lit first each row or column into two half-length signals, and then use these two half signals as the channel inputs into the multi-filter. A native app roach is to simply take the odd samples for one signal and the even samples for the second signal. As Strela points out (Strela, 1996), [4]. This app roach does not work well because it destroy s the assumed characterist ics of the input signal. It is generally p resumed that image data will be locally well-app roximated by low-order polynomials, usually constant, linear or quadratic. The high p ass filters are Designed to give a uniformly zero outp ut when the input has this form. Taking alternative data p oints as the filter input alters the character of the input signal. Hence the filter outp ut will no longer be forced to zero, reducing comp ression p erformance. Around this p roblem: one may first p re-filter the two-half length signals before p assing them into t he multi-filter. Discrete Multiwavelet Transform using a Critically- Sampled Scheme of preprocessing 2 nd norm Approximation) By using this method of p reprocessing (App roximation-based sch eme of p reprocessing), the DM WT matrix has the same dimensions of the input image which should be a squar e matrix NN where N must be power of 2.[2][8] Transformation matrix dimensions which should be equal to image dimensions after p reprocessing will be NN for a Critically- Sampled Scheme of Preprocessing. A Computer Test: A general comp uter p rogram comp uting a single-level DM WT using a Critical-Samp led Scheme of Prep rocessing (2 nd norm app roximation) are written using Visual Basic V.6.0 for a general NN image as shown in figure (1). IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3 ) 2010 Mean filter :M ean filterin g is a simp le, intuitive and easy to imp lement method of smoothing images, i.e. reducin g the amount of intensity variation between one pixel and the next. It is often used to reduce noise in images.[11] How It Work s :The idea of mean filterin g is simply to replace each pixel value in an image with t he mean (` average') value of its neighbors, includ ing itself. This has the effect of eliminatin g p ixel values which are unrepresentative of their surroundings. M ean filtering is usually thought of as a convolution filter. Like other convolutions it is based around a kernel, which rep resents the shape and size of the neighborhood to be samp led when calculating the mean. Often a 3×3 square kernel is used, as shown in Figur e 1, althou gh lar ger kernels (e.g. 5×5 squares) can be used for more sev ere smoothing. (Not e that a small kernel can be app lied more than once in ord er to p roduce a similar but not identical effect as a sin gle pass with a lar ge kern el.)[12] 3×3 averaging kernel often used in mean filtering Computing the straightforward convolution of an image with t his kernel carries out the mean filterin g p rocess. M ean filterin g is most commonly used as a simp le method for reducing noise in an image. In general the mean filter acts as a low p ass frequency filter and, therefore, reduces t he sp atial intensity derivatives p resent in the image.[12] A Technique for Image Enhancement using DMWT and DW T with Smoothing In this section, a new t echnique is p rop osed for image enhan cement using one smoothin g filter of typ e mean filter which is app lied two times on some parts of the p rocessed image with a combination between DM WT and DWT, as shown in the figure (3).The st eps of the p rop osed method are as follows:- 1. Ap p ly M ultiwavelet t ransformation on the input image, as shown in figure (3-a). 2. Ap p ly mean filter on sp ecific p arts (high p ass components) of the resultant image (L1H1, L1H2, L2H1, L2H2, H1L1, H1L2, H1H1, H1H2, H2L1, H2L2, H2H1, H2H2), as shown in figure (3-b), and leave the low-p ass components as it is which is used in the next st ep. H1H1 L1L1 L2L1 H1L1 H2L1 L1L2 L2L2 H2H1 L2H1 H2H2 H1H2 L2H2 L1H2 L1H1 H1L2 H2L2 IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3 ) 2010 3. Obt ain the Wavelet t ransformation coefficients for each p art of the low-p ass comp onents (L1H1, L1L2, L2L1, L2L2), as shown in figure (3-c). Each p art will give four sub-band (LL,LH,HL,HH) as shown below:- 4.Each part will be p rocessed as the p revious way then repeat st ep (2) on the resultant high- p ass components only (L1H1, L1H2, L2H1,L2H2, H1L1, H1L2, H1H1, H1H2, H2L1, H2L2, H2H1, H2H2) by app lying mean filter on that comp onents and leave the low-p ass comp onents, as shown in figure (3-d). 5.Inverse the Wavelet t ransformation coefficients, as shown in figure (3-e) 6.Inverse the M ultiwavelet transformation coefficients of the resultant image from the p revious step two t imes to get t he reconstructed image, as shown in figure (3-f). Figure (2) will illustrate the fill block diagram for the prop osed algorithm. Evaluation te sts The goal of this sy st em is to enhance a color image (using the BM P image format). BM P (Bitmap) file format is used for bitmap graphics on t he window p latform only .[10] Unlike other file format, which st ores image data from top to bottom and p ixels in Red, Green, Blue order, the BM P forma st ores image data from bottom to top an p ixels in Blue, Green, Red order. This means that if memory is tight, BM P graphics will sometimes app ear drawn from bottom to top . BM P files are usually very large, and when saving a file of BM P format, it should be add “.BM P” files extension to t he end of its file name. Dep ending on the M ultiwavelet t ransform with an enhancement filter (mean filter). The sy st em is designed by dividing into t hree main parts:-  M ultiwavelet transform way using a Critical-Samp led Scheme of Prep rocessing (2 nd norm ap p roximation) and it's inverse, as shown in figure (3-a and 3-f).  Wavelet t ransforms way and its inverse, as shown in figure (3-c and 3-e).  Smoothing filter which is app lied two times, as shown in figure (3-b and 3-d). The running of this technique is shown in figure (3). Conclusion This p aper mixed two transforms Wavelets and M ultiwavelet uses to obtain enhancement image. Wavelets are a useful tool for signal p rocessing app lications such as image comp ression, enhancement, and denoising.[1] Unt il recently , only scalar wavelets were known: wavelets H1H1 L1L1 L2L1 H1L1 H2L1 L1L2 L2L2 H2H1 L2H1 H2H2 H1H2 L2H2 L1H2 L1H1 H1L2 H2L2 LL LH HH HL LL LH HH HL LL LH HH HL LL LH HH HL IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3 ) 2010 generated by one scaling function. But one can imagine a situation when there is more than one scaling function. This leads to the notion of M ultiwavelet, which have several advantages in comp arison to scalar wavelets. Such features as short sup p ort, orthogonality , sy mmetry , and vanishing moments are known to be imp ortant in signal p rocessing.[5] A scalar wavelet cannot p ossess all these prop erties at t he same time. On t he other hand, a M ultiwavelet system can simultaneously p rovide p erfect reconst ruction while p reserving length (orthogonality ), good p erformance at the boundaries (via linear-p hase sy mmetry ), and a high order of app roximation (vanishing moments). Thus M ultiwavelet offers the p ossibility of sup erior p erformance for image p rocessing app lications, comp ared with scalar wavelets. During a single level of decomposition of an image using a scalar wavelet, the two-dimensional data is replaced with four blocks. T hese blocks corresp ond to the sub-bands that rep resent either low- p ass filtering or high-p ass filtering in each direction. The p rocedure for wavelet decomposition consists of consecutive op erations on rows and columns of the two dimensional data. From this p aper above we study and conclude that gated image passes t hrow many step s of enhancement. Every st ep increases t he enhance of the image. Re ferences 1. M ALLAT, S. (1999) “A Wavelet Tour of Signal Processing” 2nd Ed. San Diego: Academic Press;pp .322-350 2. LU, M . N.and DO, Y. (2005) “A Directional Extension for M ultidimensional Wavelet Transforms”, IEEE Transactions on Image Processing, submitt ed;.132-200 3. M ariantonia Cotronei, Laura, B. M ontefusco, and Luigia Puccio, (1998), M ultiwavelet Analysis and Signal Processing”, IEEE Transactions on Circuits and Sy st ems-2: Analog and Digital Signal Processing ,45(8) 4. Thesis (Ph. D.)-- Strela. (1996) M assachusett s Inst itut e of Technology , Dep t. of M athematics 5. Strang, G. and Ngy en, T. (1995). “Wavelet and Filter Banks”, Wellesley , M A: Wellesley -Cambridge Press.12-50 6. Lucchese, L.S. K. ;M itre, & J. M uk herjee, (2001),A new algorithm based on saturation and desid eration in the xy chromati city diagram for enh ancement and re-rendition of cooler images, Proc. 8th IEEE Conf. On Image Processing, Thessalonik i,Greece,45- 48 7. Toet, A. (1992), M ultiscale color image enhan cement, Pattern Recognition Letters, 13(3),. 8. Lu, J.& Hearly , D. M . (1994), Contrast enhancement via multi-scale gradient transformation, SPIE Conf. On Wavelet Application，Orlando，FL，U SA，p p 345-365. 9. Brown, T . J. (2000), An adaptive st rategy for wavelet based image enhancement, Proc. IMVI Conf. on Irish Machine Vision and Image Processing, Belf ast, Nort hern Ireland,pp 55-67, 10. Ledley , M . Buas, R. S. &. Colab, T. J 1988 Fundamentals of true-color. R. Boy le and R. Thomas Computer Vision: A First Course, Blackwell Scientific Publications, , pp 32 - 34. 11. Davies, E. (1990), M achine Vision: Theory, Algorithms and Practicalities, Academic Press, Chap. 3. 12. Vernon, D. (1991), M achine Vision, Prentice-Hall, Ch ap. 4. IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3 ) 2010 Fig. (1) :- (a) Original, (b) After a Single-Level of DMWT Usi ng a Critical-S ampled S cheme of Preprocessing (2 nd norm Approximati on), (c) After applying the inverse of DMWT (a) (b) (c) Un-Enhanced Image Mean Filter DMWT DWT Mean Filter Inverse DWT Inverse DMWT Enhanced Image Multiwavelet Coefficients Wavelet Coefficients Fig. (2) : A block diagram for the implemented algorithm. IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3 ) 2010 Input image a. DMWT (2nd) b. Smo othing of high-freq. c. DWT on low freq. L1L1 L1L2 L2L1 L2L2 d. Smo othing of high-freq. e. Inverse DWT f. Inverse DMWT (Final Image) Fig. (3): A step by ste p of implementing the algorithm IHJPAS 2010) 3( 23مجلة ابن الھیثم للعلوم الصرفة والتطبیقیة المجلد نتحسین الصورة باستخدام التحویلی Wavelet و multiwavelet معا بیداء جعفر الخفاجي جامعة بغداد، ابن الهیثم، كلیة التربیة، قسم الحاسبات الخالصة " فضال multiwaveletو wavelet نالتحویلی ة لتحسین الصورة باستخدام تركیب منیتضمن البحث طریقة مقترح في حساب الحرجة التقریبیة استخدمت طریقة العینة (mean filter)استخدام احد فالتر التنعیم للصورة وهو عن multiwaevelet قبل المعالجة. ان التحسین المستخدم في الطریقة المقترحة في ، اذالتقریب من الرتبة الثانیة استخدم لتسریع االجراءات والحسابات .ق التقلیدیة االخرى عند المقارنة بینهمائالبحث افضل بكثیر من الطر Visual B ستخدام الكومبیوتر ولغة البرمجةا أاداء هذه التقنیة وتطبیقه aisec.6 package IHJPAS