Application of Haar Wavelets on Medical Images - Semantic Scholar
Journal of Electronic Commerce in Organizations, 13(2), 41-49, April-June 2015 41
Application of Haar Wavelets on Medical Images R. El Ayachi, Faculty of Science and Technology, Université Sultan Moulay Slimane, Beni Mellal, Morocco M. Gouskir, Faculty of Science and Technology, Université Sultan Moulay Slimane, Beni Mellal, Morocco M. Baslam, Faculty of Science and Technology, Université Sultan Moulay Slimane, Beni Mellal, Morocco
ABSTRACT Recently, the information processing approaches are increased. These methods can be used for several purposes: compressing, restoring, and information encoding. The raw data are less presented and are gradually replaced by others formats in terms of space or speed of access. This paper is interested in compression, precisely, the image compression using the Haar wavelets. The latter allows the application of compression at several levels. The subject is to analyze the compression levels to find the optimal level. This study is conducted on medical images. Keywords:
Compression Level, Haar Wavelets, Image Compressing, Medical Image, Segmentation
1. INTRODUCTION In recent years, the information is multiplied exponentially. This makes their manipulations difficult in terms of raw storage and transmission. The solution is to represent the information, the image that is precisely the goal of this work, in another form in order to overcome these problems. This change of representation can be performed using the compressing. The area of image compression is extensively studied and still attracts many researchers (Tim Bruylants & all, 2015, S. Rupa & all, 2014, Rakotomalala M. A. & all, 2010). This motivation appears in the research and development of algorithms to find other forms of imagerepresentation. Furthermore, image compression plays a crucial role in medical imaging, allowing efficient manipulation, storage, and transmission of binary, grey-scale, or color images.There are two types of compressing: lossless and lossy. The first type is used for the images that must remain identical to their originals. The second type is used for images whose quality is limited to perceptions. Haar wavelets are an example of lossy compressing algorithm. DOI: 10.4018/JECO.2015040104 Copyright © 2015, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
42 Journal of Electronic Commerce in Organizations, 13(2), 41-49, April-June 2015
The aim of this paper is to develop the Haar wavelet algorithm to be used in many levels of image compression (Z-E. Baarir& all, 2004, Sylvain Durand & all, 2003) and allows to find the optimal level that maintains the validity of diagnosis. The optimal level of compression must guarantee two things: the maximum gain and the image quality. For the quality (A. TAMTAOUI & all, 2003, Habiba Loukil Hadj Kacem& all, 2005), there are several methods that can be used, namely: MSE (Mean Square Error) and PSNR (peak signal-to-noise ratio). These methods require that the two sizes of the processed image and the original image must be identical. Unfortunately, the two sizes for our case are different, hence the need to introduce another quality criterion that considers this major problem. To overcome this difficulty we use the segmentation method as criteria to detect the optimal level of compression in which the number of the regions of the compressed image is still the same as in the original image. The rest of the paper is organizedas follows. Section 2 presents the Haar wavelet method and its principle of use for image compression. Section 3 is dedicated to the analysis of the compression level, it begins with an analytical study, and then, it explains the criterion control level proposed. Section 4 is devoted to the experimentalresults obtained. Finally, the conclusion is given in section 5.
2. PRINCIPLE OF HAAR WAVELETS In 1909, ALFRED HAAR was created a special function called « Haar wavelets » (Figure 1) (Myung-Sin Song, 1991, Ronald A. DeVore & all, 1992, Kamrul Hasan Talukder & all, 2007). This type of waveletallows a decomposition of data. Specifically, in image processing, it is used for compressing. Consider the image M to be compressed. For a compression level h, Haar wavelets divide the compressed imageMh-1 at the level h-1 into four blocks (Figure 2): The left upper block representing the compressed image Mh and the other containing the details ((horizontal DHh, vertical DVh and diagonal DDh). Obtaining the compressed image at level h is based on the compressed image at level h-1. The compressed image is computedas follows:
M h = *M h −1 * Ah
(1)
where • • •
M h : Compressed image for a level h Ah :Haar wavelets coefficients for a level h Aht : Transposed of Ah The Haar wavelets coefficients can be calculated by the following formulas:
Aij = 1 if j ≤ N and i = 2*j + 1 or i = 2*j 2 2
(
)
Aij = 1 if N < j ≤ N and i = 2* j − N − 1 2 2 2
(2)
Copyright © 2015, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
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Application of Haar Wavelets on Medical Images R. El Ayachi, Faculty of Science and Technology, Université Sultan Moulay Slimane, Beni Mellal, Morocco M. Gouskir, Faculty of Science and Technology, Université Sultan Moulay Slimane, Beni Mellal, Morocco M. Baslam, Faculty of Science and Technology, Université Sultan Moulay Slimane, Beni Mellal, Morocco
ABSTRACT Recently, the information processing approaches are increased. These methods can be used for several purposes: compressing, restoring, and information encoding. The raw data are less presented and are gradually replaced by others formats in terms of space or speed of access. This paper is interested in compression, precisely, the image compression using the Haar wavelets. The latter allows the application of compression at several levels. The subject is to analyze the compression levels to find the optimal level. This study is conducted on medical images. Keywords:
Compression Level, Haar Wavelets, Image Compressing, Medical Image, Segmentation
1. INTRODUCTION In recent years, the information is multiplied exponentially. This makes their manipulations difficult in terms of raw storage and transmission. The solution is to represent the information, the image that is precisely the goal of this work, in another form in order to overcome these problems. This change of representation can be performed using the compressing. The area of image compression is extensively studied and still attracts many researchers (Tim Bruylants & all, 2015, S. Rupa & all, 2014, Rakotomalala M. A. & all, 2010). This motivation appears in the research and development of algorithms to find other forms of imagerepresentation. Furthermore, image compression plays a crucial role in medical imaging, allowing efficient manipulation, storage, and transmission of binary, grey-scale, or color images.There are two types of compressing: lossless and lossy. The first type is used for the images that must remain identical to their originals. The second type is used for images whose quality is limited to perceptions. Haar wavelets are an example of lossy compressing algorithm. DOI: 10.4018/JECO.2015040104 Copyright © 2015, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
42 Journal of Electronic Commerce in Organizations, 13(2), 41-49, April-June 2015
The aim of this paper is to develop the Haar wavelet algorithm to be used in many levels of image compression (Z-E. Baarir& all, 2004, Sylvain Durand & all, 2003) and allows to find the optimal level that maintains the validity of diagnosis. The optimal level of compression must guarantee two things: the maximum gain and the image quality. For the quality (A. TAMTAOUI & all, 2003, Habiba Loukil Hadj Kacem& all, 2005), there are several methods that can be used, namely: MSE (Mean Square Error) and PSNR (peak signal-to-noise ratio). These methods require that the two sizes of the processed image and the original image must be identical. Unfortunately, the two sizes for our case are different, hence the need to introduce another quality criterion that considers this major problem. To overcome this difficulty we use the segmentation method as criteria to detect the optimal level of compression in which the number of the regions of the compressed image is still the same as in the original image. The rest of the paper is organizedas follows. Section 2 presents the Haar wavelet method and its principle of use for image compression. Section 3 is dedicated to the analysis of the compression level, it begins with an analytical study, and then, it explains the criterion control level proposed. Section 4 is devoted to the experimentalresults obtained. Finally, the conclusion is given in section 5.
2. PRINCIPLE OF HAAR WAVELETS In 1909, ALFRED HAAR was created a special function called « Haar wavelets » (Figure 1) (Myung-Sin Song, 1991, Ronald A. DeVore & all, 1992, Kamrul Hasan Talukder & all, 2007). This type of waveletallows a decomposition of data. Specifically, in image processing, it is used for compressing. Consider the image M to be compressed. For a compression level h, Haar wavelets divide the compressed imageMh-1 at the level h-1 into four blocks (Figure 2): The left upper block representing the compressed image Mh and the other containing the details ((horizontal DHh, vertical DVh and diagonal DDh). Obtaining the compressed image at level h is based on the compressed image at level h-1. The compressed image is computedas follows:
M h = *M h −1 * Ah
(1)
where • • •
M h : Compressed image for a level h Ah :Haar wavelets coefficients for a level h Aht : Transposed of Ah The Haar wavelets coefficients can be calculated by the following formulas:
Aij = 1 if j ≤ N and i = 2*j + 1 or i = 2*j 2 2
(
)
Aij = 1 if N < j ≤ N and i = 2* j − N − 1 2 2 2
(2)
Copyright © 2015, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
7 more pages are available in the full version of this document, which may be purchased using the "Add to Cart" button on the product's webpage: www.igi-global.com/article/application-of-haar-wavelets-onmedical-images/133395?camid=4v1
This title is available in InfoSci-Journals, InfoSci-Journal Disciplines Business, Administration, and Management. Recommend this product to your librarian: www.igi-global.com/e-resources/libraryrecommendation/?id=2
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