Orientation Filtration to Wavelet Transform for Image Compression Application

Transcription

1 Orientation Filtration to Wavelet Transform for Image Compression Application Shaikh froz Fatima Muneeruddin 1, and Dr. Nagaraj B. Patil 2 Abstract---In the process of image coding, wavelet transformation has an important significance due to its multi resolution coding property. In the approach of image coding while processing over multi resolution, the process accuracy is higher due to independent resolution coding, however due to large data set per resolution it is observed that the processing overhead is increased. This overhead results in lowering of processing efficiency for image compression technique. To achieve a higher performing image coding architecture, in this paper an approach of resolution selection based on orientation filtration is proposed. The proposed approach minimizes the operation coefficient by deriving an orientation relationship between each of the band, to achieve higher performance. Keywords---Wavelet Transformation, Image compression, orientation filtration, coefficient selective. I I. INTRODUCTION MAGE Compression has come to wide usage from past several years. Due to the quality constraint issues and resource constraint environment, the accuracy of image compression operation has got minimized. Various modes of compression schemes were proposed in past to improve the coding efficiency and making the System compatible to the demanded services. Though spatial as well as transform domain approaches were developed to improve PSNR the effect of image coding and the processing coefficient plays an important role in such applications. To improvise the coding process and to reduce processing overhead in this work an orientation based image coding scheme is proposed. Various approaches were developed in past towards the image compression approach. For the effectiveness of image compression DWT based coding are more optimally used [3], [4] at decomposition phase instead of DCT[4].Due to its many advantages, such as multi resolution representation, good energy compaction, and de-correlation, the Discrete wavelet transform (DWT) has become one of the most important techniques for image and video compression in the last decade and been adopted by JPEG2000 standard [1]. ShaikhAfroz Fatima Muneeruddin 1, Dr. Nagaraj B.Patil 2 1 Research Scholar, ShriJagdishprasadJhabarmalTibrewala University, Jhunjhunu, Rajasthan, India, afroz11k@gmail.com, afrozk11@yahoo.com,nagarajbpatil1974@gmail.com, 2 Govt. Engineering College, Yaramarus, Raichur, Karnataka, India. The wavelet-based JPEG2000 not only presents superior coding performance over the DCT-based JPEG [2], but also provides scalabilities in rate, quality and resolution. Conventionally, 2-D DWT is carried out as a separable transform by cascading two 1-D transforms in the horizontal and vertical direction. As a matter of fact, natural images often contain significant direction information, which can be commonly approximated as linear edges on a local level. These edges may be neither horizontal nor vertical. If not taken into account, such a fact will result in large magnitude in these high frequency coefficients. This problem has been recognized not only by image compression researchers [5] [12], but also by many other experts in the image processing area involving feature extraction, enhancement, de-noising, and classification. As well it is observed that in the conventional DWT based coding reveals each band isolate to provide individual bands of variation, however the coding results in memory overhead and reduce the coding performance. The image coding based on DWT also leads to an issue of Diagonal Line Problem, where an occurrence of denser variation is observed at the central band regions than at edge regions [13].To overcome the issue of processing overhead and to improve the visual accuracy in image coding an orientation based image coding approach is proposed. The remainder of this paper is organized as follows: section II gives the details about the basics of an image coding system. It also gives the details about the DWT decomposition. Section III gives the details about the directional filtration. This section also gives the details about the architecture of directional filter bank (DFB). The complete details about the proposed approach are given in section IV. Section V gives the results details. It also gives the details about the comparative analysis of the proposed approach with conventional approach and finally the conclusions are provided in section VI. II. IMAGE CODING SYSTEM For an Image compression system, the fundamental blocks are an encoder and decoder. The function of the encoder is, when an input is given, it creates a set of symbols from the given input data and then the data is transmitted through a channel and then feed to decoder where we can reconstruct the image given as input. There is a possibility that the reconstructed output image can the replica of the input image or the reconstructed image can have distortion is due to channel interference. Fig.1 shows convention block diagram of a compression system. 23

2 image have less magnitude and it can be easily quantized with less distortion. Fig.1. conventional Block Diagram of an Image compression system. One can describe the encoding in different views, according to the mathematical point of view, the transformation of the 2D pixel array into a statically uncorrelated data set. This transformed image is then transmitted and later the decompressed image is obtained from the compressed image. A)Source Encoder The process where the redundancies can be reduced or eliminated in the input image is called source encoder which is shown in Fig.2. The source encoder is built with three units namely the 1) mapper unit 2) quantizer 3) symbol encoder.the function of the mapper unit is it transforms the input image into some format which reduces the pixel redundancy in the image. The mapper output can be restored.and then fed to the quantizer, the function of the quantizer is it fixes the coefficients of the mapper s output with some predetermined values, without affecting the image in order to reconstruct. Then the output of the quantizer is fed to the symbol encoder whose functionality is to assign a short code word of the high probable coefficient where coding redundancy can be removed. Fig..2. Block diagram of a Source Encoder The mapper has the ability to transform the image in two domains; 1. Spatial domain method which perform it operation on the pixels of an image. 2. Transform coding, in order to map the image into a set of transform coefficients a reversible linear transformation is used and then later it is encoded and quantized. B)Transform Coding Transform coding, in order to map the image into a set of transform coefficients a reversible linear transformation i.e. Fourier transform is used and then later it is encoded and quantized. Transform coding is shown in below diagram fig.3. in most of the images, set of coefficients obtained from the Fig. 3 Block diagram of Transform coding Fig. 4 Block diagram of a Source decoder The source decoder as shown in Fig..4 whose functionality is to decoded the encoded compressed image. The encoded image compressed the image bits are given as input to the source decoder encoded compressed bits are decompressed using a decompression algorithm. In the source decoder there is a unit called de-quantizer whose functionality is just inverse to the quantizer unit in order to obtain the data bits. The output of the de-quantizer is then fed to the inverse transformer. The inverse transformer uses an inverse transformation algorithm for the retrieval of the image bits. In many applications, such as image de-noising or compression, wavelet transforms are used to obtain a compact representation of the analyzed image. Spatial filters have long been used as the traditional means of removing noise from images and signals. These filters usually smooth the data to reduce the noise, but, in the process, also blur the data. To overcome these problem wavelet-based methods which uses wavelets to transform the data into a different basis, where "large" coefficients are derived to process on coding and estimation. In the process of wavelet decomposition of an image, in the first level of decomposition, the image is split into 4 sub bands, namely the HH,HL,LH and LL sub bands. The HH sub band gives the diagonal details of the image; the HL sub band gives the horizontal features while the LH sub band represents the vertical structures. The LL sub band is the low resolution residual consisting of low frequency components and it is this sub band which is further split at higher levels of decomposition as illustrated in Fig

3 and135 ). The DFB approach is realized using iterated quincunx filter banks as illustrated in Fig..7. Fig..5: DWT architecture for image decomposition The obtained coefficients in each band are half of the image dimension, and collaboratively they are equal to the original image dimension. Though each band reflect a finer detail coefficient in resolution, the coefficients are extracted based on each directional orientation. Hence the coefficients could be optimized for processing if the orientation of these bands could be extracted appropriately. This can lead to minimization of number of processing coefficient intern reducing the processing overhead as well the proper selection will lead to optimal visualization of the decoded information. Lower the processing coefficient lowers the overhead and lowers the exposure to distortion. With this objective anorientation based selective coding is proposed. To derive the orientation a direction filtration in integration to wavelet transform is proposed. III. DIRECTIONAL FILTRATION In this work, to provide orientation based coding approach for image a directional based filtration approach to the conventional wavelet based coding is proposed. A major property of the DFB [14] is its ability to extract 2D directional information of an image, which is important in image analysis. The DFB is maximally decimated and perfect reconstruction (PR) indicating that the total number of sub band coefficients is the same as that of the original image, and they can be used to reconstruct the original image without error. It can be implemented by a tree structure consisting of three levels of two-band systems. Each level can be implemented by using separable poly-phase filters, which make the structure extremely computationally efficient. Directional filter banks (DFB) decompose the frequency space into wedge-shaped partitions as shown infig..6. Fig..7. Quincunx filter bank. H 0 and H 1 [14] At the first level of the filter bank, a quincunx filter bank (QFB) is applied. The quincunx sampling matrix is defined by. The image is further decomposed by using two other QFBs at the outputs y0and y1. Asa result, four outputs corresponding to the four directions of the filter bands are obtained. Let these four outputs for four directions can be represented as y00, y01, y10 and y11. At higher level QFBs are employed in conjunction with resampling matrices. The resampling coefficients used per direction is as presented below, and Applying these resampling operations to the outputs of the QFB, a normalized oriented coefficient is derived. This coefficient reveals the orientation property of a given band signal. To illustrate the usage of DF over DWT the proposed approach is presented in section 4. IV. PROPOSED SELECTIVE ORIENTATION CODING An integrated model for selective coding in image coding is developed. The block diagram represented below in Fig. 8 gives the pictorial description of the proposed orientation filtering based image coding scheme. Fig..8: Proposed Selective Orientation coding for image compression For the obtained coefficient bands of a normalized magnitude values are computed defined by, Fori,j (1) Fig..6. Directional filter bank frequency partitioning using 8 directions [14] In this DFB Eight directions were used, where directional sub bands of 1, 2, 3, and 4 represent horizontal directions (directions between -45 and +45 ) and the rest5, 6, 7 and 8 stand for the vertical directions (directions between 45 The band density having higher pixel density in such directions is kept unmodified and band having lower normalized values are discarded from coding. As these are made on the directional band density hence the image are least effected on the orientation variations. For this purpose the normalized magnitudes of all directional bands are compared with a normalized threshold value given in (2). The 25

4 Coefficients satisfying the thresholding based criterion are only used for coding, the threshold ( ), is defined by, = (2) The process of thresholding results in selection of effective oriented coefficients in each band and finally the obtained normalized magnitudes in all directional bands are passed to codefor compression. Wherein the selective process reduces the coefficients having similarity in orientation, the reflecting visualization is not degraded due to psycho visual redundancy. On the inverse process of image decoding, the zero coded coefficients are replaced with the nearest decoded orientation and passed for inverse DWT. The performance of the proposed approach is as outlined in next section. V. EXPERIMENTAL RESULTS To evaluate the developed system the quality of the image at the output of the decoder is measured by means of, mean square error (MSE) and peak to signal to noise ratio (PSNR) ratio measurement which measures the maximum signal to noise ratio found on an image has been used as an objective measure for the distortions introduced during the transferring process. The measuring parameters are defined as; 1. Mean squared error: The Mean squared error (MSE) of an estimator is one of the way to quantify the amount by which an estimator differs from the true value of the quantity being estimated. As a loss function, MSE is called squared error loss. MSE measures the average of the square of the error. The error is the amount by which the estimator differs from the quantity to be estimated, Where f is the original image and is the recovered image after Decoding. 2. The PSNR is most commonly used as a measure of quality of reconstructed image.peak signal-to-noise ratio, defined as a ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. PSNR is usually expressed in terms of the logarithmic decibel scale. (3) (4) observed observations are shown below. To present a comparative analysis the proposed approach of selective DWT scheme (DWS) is compared with the conventional DWT based coding scheme. The obtained result observation under variant noise condition is as illustrated below. Animage of size 256 X 256 is taken as a test sample as shown in Fig. 9. Fig. 9: Original Test Sample This test sample is tested under different noise effects. The obtained observation for the case analysis is as outlined below; Case 1: Under Gaussian noise Fig..10: Gaussian noiseeffected image (b)retrieved image by proposed DWT coding Retrieved image by proposed DWS coding Case 2: Under salt & pepper noise (b) WhereIpeakis the peak values of the input signal. 3. Similarity Factor: An objective measure of similarity between the original image and recovered image is stated by SSIM defined as, (5) (b) The similarity factor is approximately nearer to 1 for better imperceptible image quality. For the developed system the Fig..11 : salt & pepper noise effected image (b) Retrieved Image by DWT retrieved image by DWS 26

5 International Conference on Emerging Computer Technologies (ICECT'15) July 14-15, 2015 Harare (Zimbabwe Case 3: under rotation by 45 0 (b) The PSNR value plotted above shows that the quality of the retrieved image is good and not degraded much when noise is added. It is also clear that the obtained PSNR for a given noise density by proposed approach is better compared to previous one. Similarly a performance evaluation parameter SSIM is evaluated for the above tested sample and the obtained SSIM values over varying noise density are plotted in Fig. 15. Fig..12 :( a) rotated image (b) Retrieved image by DWT retrieved image by DWS The calculated values of MSE, PSNR and SSIM for above tested sample are shown in Fig..12, Fig..13 and Fig..14 respectively. Fig..15: SSIM versus noise density It shows that the quality of the retrieved image for proposed approach is good as its SSIM is 0.95 compared to calculate SSIM of conventional one. Thus the algorithm shows that the proposed approach retrieves the original image almost same as that of the original one.similarly the proposed approach is tested over other test samples. The results obtained by testing the DWS over the second sample is shown below. Fig..13: MSE versus noise density The above plot describes the varying nature of MSE over noise density. As the noise density increases MSE for retrieved image also increases. From the above plot it is clear that for a given noise density the MSE of the above tested sample is less in proposed approach compared to conventional approach. Fig..16. Original sample The respective results for the above mentioned attacks are shown below. Fig..17 shows the Gaussian noise effectedimage,(b) shows the retrieved original image by DWT method and shows the retrieved image by DWS method. Fig..14: PSNR versus noise density 27

6 Case 1: under Gaussian noise Case 3: under rotation 45 0 (b) (b) Fig..17 :( a) Gaussian noise effected image (b) retrieved image by DWT retrieved image by DWS Similarly the salt & pepper noise attacked image and retrieved images by DWT and DWS are shown in Fig..18, (b) and respectively. ( c ) Fig..19 :( a) rotated image (b) retrieved image by DWT retrieved image by DWS The numerical analysis is performed by evaluating the MSE, PSNR and SSIM for above original image under varying noise densities and the calculated values are shown in Fig. 20, Fig.21 and Fig.22 respectively. Case 2: under salt & pepper noise (b) Fig..20: MSE versus noise density Fig..18: salt & pepper noise effected image (b) retrieved image by DWT retrieved image by DWS Fig..21: PSNR versus noise density 28

7 Fig..22: SSIM versus noise density Observations for derived PSNR and SSIM for the conventional DWT based approach and proposed DWS based approach is outlined in the given table. A comparative improvement in PSNR is observed in original image due to the low impact of coding process on the original image. TABLE I COMPARATIVE OBSERVATION FOR PROPOSED AND CONVENTIONAL IMAGE CODING SCHEMES Samples DWT DWS PSNR SSIM PSNR SSIM VI. CONCLUSION In this paper, an efficient image coding technique was proposed based on the discrete wavelet transform. The proposed approach uses directional filters for decomposition of an image instead of conventional filters. The directional filters give the orientation information which provides an efficient reconstruction at decoder. Thus for an image suffering from various effects like Gaussian noise, salt and pepper noise and Orientational effects, the reconstruction efficiency is getting increased. This paper measures the performance of proposed approach by considering the image subjected to various effects and applying the proposed approach on those image. The simulation results and the obtained numerical evaluation conclude that the proposed approach gives efficient reconstruction of an image. [5] D. Taubman, Adaptive, non-separable lifting transforms for image compression, in Proc. IEEE Int. Conf. Image Processing, Oct. 1999, vol. 3, pp [6] R. L. Claypoole, G. M. Davis, W. Sweldens, and R. G. Baraniuk, Nonlinear wavelet transforms for image coding via lifting, IEEE Trans. Image Process., vol. 12, no. 12, pp , Dec [7] O. N. Gerek and A. E. Cetin, A 2D orientation-adaptive prediction filter in lifting structures for image coding, IEEE Trans. Image Process., vol. 15, no. 1, pp , Jan [8] C.-L. Chang, A. Maleki, and B. Girod, Adaptive wavelet transform for image compression via directional quincunx lifting, presented at the IEEE Workshop on Multimedia Signal Processing, Shanghai, China,Oct [9] C.-L. Chang and B. Girod Direction-adaptive discrete wavelet transform via directional lifting and bandeletization, presented at the IEEE Int. Conf. Image Process., Atlanta, GA, Oct [10] C.-L. Chang and B. Girod, Direction-adaptive discrete wavelet transform for image compress, IEEE Trans. Image Process., vol. 16, no. 5, pp , May [11] W. Ding, F. Wu, and S. Li, Lifting-based wavelet transform with directionally spatial prediction, presented at the Picture Coding Symp., San Francisco, CA, Dec [12] W. Ding, F. Wu, X. Wu, S. Li, and H. Li, Adaptive directionalliftingbased wavelet transform for image coding, IEEE Trans. Image Process., vol. 16, no. 2, pp , Feb [13] K. Cinkler and A. Mertins, Edge sensitive subband coding of images, inproc. IEEE Int.Conf. Acoust., Speech, Signal Processing, Atlanta, USA, pp , May 1996 [14] Chunling Yang, Duanwu Cao and Li Ma, 32Still Image Compression Algorithm Based on Directional Filter Banks, I.J. Information Technology and Computer Science, ShaikhAfroz Fatima received the B.E. and M.Tech degrees in Computer Science and Engineering from Dr. BabasahebAmbedkarMarathwada University, Aurangabad, Maharashtra and Vieshveshwariah Technological University, Belgaum, Karnataka in 1996 and 2006, respectively. During , she worked as a Lecturer and Assistant professor in several Engineering Colleges. Dr. Nagaraj B Patil received B.E, M.Tech from Gulbarga University Gulberga and PhD in Computer Science and Engineering from Singhania University Rajastan and at present working as Associate Professor and HOD in Govt. Engineering College, Yaramarus, Raichur, Karnataka, India. REFERENCES [1] Information technology JPEG 2000 image coding system: Core coding system, ISO/IEC , [2] Information technology Digital compression and coding of continuous-tone still images: Requirements and guidelines, ITU-T T.81, ISO/IEC IS , [3] M. MozammelHoqueChowdhury and AminaKhatun, Image Compression Using Discrete Wavelet Transform, IJCSI International Journal of Computer Science Issues, Vol. 9, Issue 4, No 1, July [4] NavpreetSaroya, PrabhpreetKaur, Analysis of Image Compression Algorithm Using DCT and DWT Transforms, IJARCSSE, Volume 4, Issue 2, February