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 Department of Computer ,College of Education Ibn-Al-Haitham University of Baghdad Abstract This paper introduces method of image enhancement using the combination of both wavelet and Multiwavelet transformation. New technique is proposed for image enhancement using one smoothing filter. A critically- Sampled Scheme of preprocessing method is used for computing the Multiwavelet.It is the 2 nd norm approximation used to speed the procedures needed for such computation. An improvement was achieved with the proposed method in comparison with the conventional method. The performance of this technique has been done by computer using Visual Baisec.6 package. Introduction Image improvement is a technique which reduces image noise, removes artifacts, and preser details. In this paper, 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 processing tool. However, as a result of a separable extension from 1-D bases, wavelets in higher dimensions can only capture very limited directional information. Different directions are mixed in certain wavelet sub-bands. For instance, 2-D wavelets only provide three directional components, namely horizontal, vertical, and diagonal. Furthermore, the 45◦ and 135◦ directions are mixed in diagonal sub-bands. With the directional extension for wavelets proposed in [2] that mixing problem can be improved, but not totally resolved. However, the wavelet transforms is still very attractive for image processing applications. Multiwavelets are a relatively new addition to the wavelet theory, and have received considerable attention since their introduction [3]. Contrary to ordinary wavelets, Multiwavelet offers simultaneous orthogonal, symmetry , and short support. Similar to performing wavelet decomposition with filters, Multiwavelet decomposition can be realized with filter-banks. The filter coefficients in this case are, however, matrices instead of scalars. Therefore, two or more input streams to the Multiwavelet filter-bank are required to perform the decomposition. Several methods have been developed for obtaining multiple input streams from a given single input stream [3]. This paper uses A Critically Sampled Scheme of Preprocessing 2 nd norm approximation with its inverse as one approach of Multiwavelet. Discrete Wavelet Transform The transformation is a process that translates one object from a given domain to another in order to have some important implicit 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 developed to an efficient transform is called the Wavelet Transform (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 provides a powerful time-space (time-frequency) representation [7]. The effect of the wavelet transform on image is defined as” it abstracts the image in universal space, this contains all information into an approximately orthogonal (statistical independent) spaces (represent projection of the subject) contained in this universal space. By changing the scale in each projection, the algebraic sum of all these projections gives the original subject before abstraction process” [8,9]. This type of transformation can be applied on one as well as on two dimensional signals by using a special 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 Depending on the previous 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 Multiwavelet filter banks require a vector-valued input signal. There is a number of ways to produce 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 approach 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 approach does not work well because it destroys the assumed characteristics of the input signal. It is generally presumed that image data will be locally well-approximated by low-order polynomials, usually constant, linear or quadratic. The high pass filters are Designed to give a uniformly zero output when the input has this form. Taking alternative data points as the filter input alters the character of the input signal. Hence the filter output will no longer be forced to zero, reducing compression performance. Around this problem: one may first pre-filter the two-half length signals before passing them into the multi-filter. Discrete Multiwavelet Transform using a Critically- Sampled Scheme of preprocessing 2nd norm Approximation) By using this method of preprocessing (Approximation-based scheme of preprocessing), the DMWT matrix has the same dimensions of the input image which should be a square matrix NN where N must be power of 2.[2][8] Transformation matrix dimensions which should be equal to image dimensions after preprocessing will be NN for a Critically- Sampled Scheme of Preprocessing. A Computer Test: A general computer program computing a single-level DM WT using a Critical-Sampled Scheme of Preprocessing (2nd norm approximation) 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 :Mean filtering is a simple, intuitive and easy to implement method of smoothing images, i.e. reducing the amount of intensity variation between one pixel and the next. It is often used to reduce noise in images.[11] How It Works :The idea of mean filtering is simply to replace each pixel value in an image with the mean (`average') value of its neighbors, including itself. This has the effect of eliminating pixel 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 represents the shape and size of the neighborhood to be sampled when calculating the mean. Often a 3×3 square kernel is used, as shown in Figure 1, although larger kernels (e.g. 5×5 squares) can be used for more severe smoothing. (Note that a small kernel can be applied more than once in order to produce a similar but not identical effect as a single pass with a large kernel.)[12] 3×3 averaging kernel often used in mean filtering Computing the straightforward convolution of an image with this kernel carries out the mean filtering process. Mean filtering is most commonly used as a simple method for reducing noise in an image. In general the mean filter acts as a low pass frequency filter and, therefore, reduces the spatial intensity derivatives present in the image.[12] A Technique for Image Enhancement using DMWT and DWT with Smoothing In this section, a new technique is proposed for image enhancement using one smoothing filter of type mean filter which is applied two times on some parts of the processed image with a combination between DM WT and DWT, as shown in the figure (3).The steps of the proposed method are as follows:- 1. Apply Multiwavelet transformation on the input image, as shown in figure (3-a). 2. Apply mean filter on specific parts (high pass 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-pass components as it is which is used in the next step. 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. Obtain the Wavelet transformation coefficients for each part of the low-pass components (L1H1, L1L2, L2L1, L2L2), as shown in figure (3-c). Each part will give four sub-band (LL,LH,HL,HH) as shown below:- 4.Each part will be processed as the previous way then repeat step (2) on the resultant high- pass components only (L1H1, L1H2, L2H1,L2H2, H1L1, H1L2, H1H1, H1H2, H2L1, H2L2, H2H1, H2H2) by applying mean filter on that components and leave the low-pass components, as shown in figure (3-d). 5.Inverse the Wavelet transformation coefficients, as shown in figure (3-e) 6.Inverse the Multiwavelet transformation coefficients of the resultant image from the previous step two times to get the reconstructed image, as shown in figure (3-f). Figure (2) will illustrate the fill block diagram for the proposed algorithm. Evaluation tests The goal of this system is to enhance a color image (using the BMP image format). BMP (Bitmap) file format is used for bitmap graphics on the window platform only.[10] Unlike other file format, which stores image data from top to bottom and pixels in Red, Green, Blue order, the BMP forma stores image data from bottom to top an pixels in Blue, Green, Red order. This means that if memory is tight, BMP graphics will sometimes appear drawn from bottom to top. BMP files are usually very large, and when saving a file of BMP format, it should be add “.BM P” files extension to the end of its file name. Depending on the Multiwavelet transform with an enhancement filter (mean filter). The system is designed by dividing into three main parts:-  Multiwavelet transform way using a Critical-Sampled Scheme of Preprocessing (2 nd norm approximation) and it's inverse, as shown in figure (3-a and 3-f).  Wavelet transforms way and its inverse, as shown in figure (3-c and 3-e).  Smoothing filter which is applied two times, as shown in figure (3-b and 3-d). The running of this technique is shown in figure (3). Conclusion This paper mixed two transforms Wavelets and Multiwavelet uses to obtain enhancement image. Wavelets are a useful tool for signal processing applications such as image compression, enhancement, and denoising.[1] Until 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 Multiwavelet, which have several advantages in comparison to scalar wavelets. Such features as short support, orthogonality , symmetry , and vanishing moments are known to be important in signal processing.[5] A scalar wavelet cannot possess all these properties at the same time. On the other hand, a Multiwavelet system can simultaneously provide perfect reconstruction while preserving length (orthogonality ), good performance at the boundaries (via linear-phase symmetry), and a high order of approximation (vanishing moments). Thus Multiwavelet offers the possibility of superior performance for image processing applications, compared 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. These blocks correspond to the sub-bands that represent either low- pass filtering or high-pass filtering in each direction. The procedure for wavelet decomposition consists of consecutive operations on rows and columns of the two dimensional data. From this paper above we study and conclude that gated image passes throw many steps of enhancement. Every step increases the enhance of the image. References 1. MALLAT, 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 Multidimensional Wavelet Transforms”, IEEE Transactions on Image Processing, submitted;.132-200 3. Mariantonia Cotronei, Laura, B. Montefusco, and Luigia Puccio, (1998), Multiwavelet Analysis and Signal Processing”, IEEE Transactions on Circuits and Systems-2: Analog and Digital Signal Processing ,45(8) 4. Thesis (Ph. D.)-- Strela. (1996) Massachusetts Institute of Technology, Dept. of Mathematics 5. Strang, G. and Ngyen, T. (1995). “Wavelet and Filter Banks”, Wellesley, MA: Wellesley-Cambridge Press.12-50 6. Lucchese, L.S. K. ;Mitre, & J. Muk herjee, (2001),A new algorithm based on saturation and desideration in the xychromati city diagram for enhancement and re-rendition of cooler images, Proc. 8th IEEE Conf. On Image Processing, Thessaloniki,Greece,45- 48 7. Toet, A. (1992), Multiscale color image enhancement, 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，USA，pp 345-365. 9. Brown, T. J. (2000), An adaptive strategy for wavelet based image enhancement, Proc. IMVI Conf. on Irish Machine Vision and Image Processing, Belfast, Northern Ireland,pp 55-67, 10. Ledley, M. Buas, R. S. &. Colab, T. J 1988 Fundamentals of true-color. R. Boyle and R. Thomas Computer Vision: A First Course, Blackwell Scientific Publications, , pp 32 - 34. 11. Davies, E. (1990), Machine Vision: Theory, Algorithms and Practicalities, Academic Press, Chap. 3. 12. Vernon, D. (1991), Machine Vision, Prentice-Hall, Chap. 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 Using a Critical-Sampled Scheme of Preprocessing (2nd norm Approximation), (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. Smoothing of high-freq. c. DWT on low freq. L1L1 L1L2 L2L1 L2L2 d. Smoothing of high-freq. e. Inverse DWT f. Inverse DMWT (Final Image) Fig. (3): A step by step 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 تقلیدیة االخرى عند المقارنة بینهمائالبحث افضل بكثیر من الطر .ق ال Visual Baisec.6 package ستخدام الكومبیوتر ولغة البرمجةا أاداء هذه التقنیة وتطبیقه IHJPAS