Performance Evaluation of Edge Directional Image Interpolation Scheme

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1 Performance Evaluation of Edge Directional Image Interpolation Scheme D. Himabindu 1 V. Ashok Kumar 2 Ch. Srinivasa Rao 3 C.Dharmaraj Department of E.C.E, Aditya Institute of Technology and Managemnt, Tekkali 3 Department of E.C.E, University college of Engineering Vizianagaram, JNTUK. 4 Department of E.C.E,GIT,GITAM University,Visakhapatnam Abstract- Earlier there are different interpolation techniques for denoising of images. When an image is zoomed checkerboard effect/ringing arises in images. In order to remove interpolation artefacts such as image blur and checkerboard effect. The proposed technique DIRETIONAL DENOISE SCHEME tries to amend the interpolation error. Meanwhile edge preservation is a critical issue in both image denoising and interpolation. In this project, we are using directional denoising scheme interpolation method to address the edge preservation. Linear interpolation methods have been introduced without considering specific local information on edges results in to artefacts. Non linear interpolation methods have been suggested to reduce the artefacts of linear method. These nonlinear methods are often computation intensive and they can be more expensive than linear methods for 2D- Images.Further, they become inefficient in the estimation of edge orientation for the classes of edge model with fine scales. More effective interpolation methods are yet to be developed in order to accurately preserve the edge orientation without introducing high computational cost. Peak Signal to Noise Ratio (PSNR) Normalized Cross Correlation (NCC) and CPU Run time are used as quantitative measures to compare the ground truth image with zoomed interpolated images. The new interpolation scheme is expected to result in high resolution images having clearer and sharper edges over existing linear interpolation methods. KEYWORDS: Denoising, Edge preservation, Checkerboard effect, Interpolation. 1. Introduction Images captured from both digital cameras and conventional film cameras will affected with the noise from a variety of sources. These noise elements will create some serious issues for further processing of images in practical applications such as computer vision, artistic work or marketing and also in many fields. There are many types of noises like salt and pepper, Gaussian, speckle and passion. In salt and pepper noise (sparse light and dark disturbances), pixels in the captured image are very different in intensity from their neibouring pixels; the defining characteristic is that the intensity value of a noisy picture element bears no relation to the color of neibouring pixels. Generally this type of noise will only affect a small number of pixels in an image. When we viewed an image which is affected with salt and pepper noise, the image contains black and white dots, hence it terms as salt and pepper noise. In Gaussian noise, noisy pixel value will be a small change of original value of a pixel. A histogram, a discrete plot of the amount of the distortion of intensity values against the frequency with which it occurs, it shows a normal distribution of noise. While other distributions are possible, the Gaussian (normal) distribution is usually a good model, due to the central limit theorem that says that the sum of different noises tends to approach a Gaussian distribution. In selecting a noise reduction algorithm, one must consider several factors: A digital camera must apply noise reduction in a fraction of a second using a tiny on board CPU, while a desktop computer has much more power and time whether sacrificing some real detail information is acceptable if it allows more distortion or noise to be removed (how aggressively to decide whether the random variations in the image are noisy or not) In real-world photographs, maximum variations in brightness ("luminance detail") will be consisted by the highest spatial frequency, rather than the random variations in hue ("chroma detail"). Since most of noise reducing techniques should attempt to remove noise without destroying of real detail from the captured photograph. In addition, most people find luminance noise in images less objectionable than chroma noise; the colored blobs are considered "digital-looking" and artificial, compared to the mealy appearance of luminance noise that some compare to film grain. For these two reasons, most of digital image noise reduction algorithms split the image content into chroma and luminance components. 606

2 One solution to eliminate noise is by convolving the original image with a mask that represents a low-pass filter or smoothing operation. For example, the Gaussian mask incorporates the elements determined by a Gaussian function. This operation brings the value of each pixel into closer harmony with the values of its neighbours. In general, a smoothing filter sets each pixel to the mean value, or a weighted mean, of itself and its nearby neighbours; the Gaussian filter is just one possible set of weights. However, spatial filtering approaches like mean filtering or average filtering, Savitzky filtering, Median filtering, bilateral filter and Wiener filters had been suffered with loosing edges information. All the filters that have been mentioned above were good at denoise of images but they will provide only low frequency content of an image it doesn t preserve the high frequency information. In order to overcome this issue Non Local mean approach has been introduced. More recently, noise reduction techniques based on the NON-LOCAL MEANS (NLM) had developed to improve the performance of denoising mechanism [1][4][5][9]. It is a data-driven diffusion mechanism that was introduced by Buades et al. in [1]. It has been proved that it s a simple and powerful method for digital image denoising. In this, a given pixel is denoised using a weighted average of other pixels in the (noisy) image. In particular, given a noisy image n i, and the denoised image d = d i at pixel i is computed by using the formula d i = j w ij n j (1) j w ij Where w ij is some weight assigned to pixeli and j. The sum in (1) is ideally performed to whole image to denoise the noisy image. NLM at large noise levels will not give accurate results because the computation of weights of pixels will be different for some neibourhood pixels which looks like same. Most of the standard algorithm used to denoise the noisy image and perform the individual filtering process. Denoise generally reduce the noise level but the image is either blurred or over smoothed due to losses like edges or lines. In the recent years there has been a fair amount of research on center pixel weight (CPW) for image denoising [3], because CPW provides an appropriate basis for separating noisy signal from the image signal. Optimized CPW is good at energy compaction, the small coefficient are more likely due to noise and large coefficient due to important signal feature [8]. These small coefficients can be thresholded without affecting the significant features of the image. The proposed local spayed and optimized CPW correspond to its continuous version sampled usually on a dyadic grid, which means that the scales and translations are power of two [5]. Local spayed and optimized CPW is a simple non-linear technique, which operates on one weighted coefficient at a time. Experiments show the effectiveness of the new technique both in terms of peak signal-to-noise ratio (on simulated noisy images) and of subjective quality (on actual images). Recently, in [14] Zhang and Li proposed a new framework on an image denoising and zooming method using the linear minimum mean square error estimation, which will give far better results than the all above mentioned algorithms. In this letter, we discuss a new transform called Non subsampled Shearlet transform and proposed new solution for better denoising approach. The rest of this thesis has been organized as: Section II existing techniques such as Savitzky-golay, median, bilateral, wavelet filters, and NLM; Section III discusses the NSS Transform; Section IV shows experimental comparisons for various techniques with the new solution; and Section V concludes the thesis. 2.Exisiting Techniques In this section we discussed various spatial filters and their performance when a noisy input will be given to them. Here in this section we had explained about each filter in detail. a. Savitzky-Golay Filter It is a simplified method and uses least squares technique for calculating differentiation and smoothing of data. Its computational speed will be improved when compared least-squares techniques. The major drawback of this filter is: Some of first and last data point cannot smoothen out by the original Savitzky-Golay method. Assuming that, filter length or frame size (in S-G filter number of data sample read into the state vector at a time) N is odd, N=2M+1 and N= d+1, where d= polynomial order or polynomial degree. b. Median filter This is a nonlinear digital spatial filtering technique, often used to removal of noise from digital images. Median filtering has been widely used in most of the digital image processing applications. The main idea of the median filter is to run through the image entry by pixel, replacing each pixel with the median value of neighboring pixels. The pattern of neighbors is called the "window", which slides, pixel by pixel, over the entire image. c. Bilateral Filter The bilateral filter is a nonlinear filter which does the spatial averaging without smoothing edges information. Because of this feature it has been shown that it s an effective image denoising algorithm. Bilateral filter is presented by Tomasi and Manduchi in The concept of the bilateral filter was also presented in [8] as the SUSAN filter and in [3] as the neighborhood filter. It is mentionable that the Beltrami flow algorithm is considered as the theoretical origin of the 607

3 bilateral filter [4] [5] [6], which produce a spectrum of image enhancing algorithms ranging from the linear diffusion to the non-linear flows. The bilateral filter takes a weighted sum of the pixels in a local neighborhood; the weights depend on both the spatial distance and the intensity length. In this way, edges are preserved well while noise is eliminated out. d. Wavelet Filtering Signal denoising using the DWT consists of the three successive procedures, namely, signal decomposition, thresholding of the DWT coefficients, and signal reconstruction. Firstly, we carry out the wavelet analysis of a noisy signal up to a chosen level N. Secondly, we perform thresholding of the detail coefficients from level 1 to N. Lastly, we synthesize the signal using the spayed detail coefficients from level 1 to N and approximation coefficients of level N. However, it is generally impossible to remove all the noise without corrupting the signal. As for thresholding, we can settle either a level-dependent threshold vector of length N or a global threshold of a constant value for all levels. e. Classic Non local means It is a data-driven diffusion mechanism that was introduced by Buades et al. in [1]. It has been proved that it s a simple and powerful method for digital image denoising. In this, a given pixel is denoised using a weighted average of other pixels in the (noisy) image. In particular, given a noisy imagen i, and the denoised image d = d i at pixel i is computed by using the formula d i = j w ij n j (2) j w ij Where w ij is some weight assigned to pixeli and j. The sum in (2) is ideally performed to whole image to denoise the noisy image. NLM at large noise levels will not give accurate results because the computation of weights of pixels will be different for some neibourhood pixels which looks like same. w l,j = exp G β n l+k n 2 k P j +k /2h (3) In this each weight is computed by similarity quantification between two local patches around noisy pixels n l and n j as shown in eq. (3). Here, G β is a Gaussian weakly smooth kernel [1] and P denotes the local patch, typically a square centered at the pixel and h is a temperature parameter controlling the behavior of the weight function. f. LMMSE framework The linear minimum mean square-error estimation (LMMSE) technique [11] was used in [12, 13] to estimate the missing samples. In [10], Zhang et al. proposed an interpolation algorithm by computing the directional estimates of the missing samples and then fusing them optimally. Directional edge guided interpolation has proved to be very effective in preserving the edges for image enlargement. Although denoising and interpolation have been studied for many years as two independent problems, they can be modeled under the same framework of signal estimation. In this paper, we propose a directional denoising and interpolation algorithm to estimate both the noiseless and missing samples from the noisy image under the LMMSE framework. For each noisy pixel, a local window centered at it is used to analyze the local statistics. To calculate and preserve the directional information for image interpolation, we first compute multiple estimates of a noisy pixel along different directions. Those directional estimates are then fused for a more accurate output. The data fusion is adaptive to the statistics of the directional estimates to ensure the denoising being along the main direction of the local window. Such a directional denoising process naturally provides a directional interpolator, which consequently enlarges the image to a HR. 3. PROPOSED NSS TRANSFORM 3.1 Introduction to Shearlet Shearlets are a multi scale framework which allows to efficiently encode anisotropic features in multivariate problem classes. Originally, shearlets were introduced for the analysis as well as sparse approximation of functionsf L 2 R 2. They are a natural extension of wavelets to accommodate the fact that multivariate functions are typically governed by anisotropic features such as edges in images. However, wavelets as isotropic objects are not capable of capturing such phenomena. Shearlets are constructed by parabolic scaling, shearing and translation applied to few generating functions. At fine scales, they are essentially supported within skinny and directional ridges following the parabolic scaling law, which reads length² width. Similar to wavelets, shearlets arise from the affine group and allow a unified treatment of the continuum and digital situation leading to faithful implementations. Although they do not constitute an orthonormal basis forl 2 R 2, they still form a frame allowing stable expansions of arbitrary functions f L 2 R 2. Shearlets are to date the only directional representation system which provides sparse approximation of anisotropic features while providing a unified treatment of the continuum and digital realm in the sense of allowing faithful implementation. Extensions of shearlet systems to L 2 R d, d 2 are also available. Shearlet Transform (ST) is a new multi-scale geometric analysis algorithm which inherits advantages of contourlet and curvelet transform [18]. ST theory is based on 608

4 composite wavelets. In dimension n=2, the affine systems with composite dilations are the collections of the form [15, 16]: Ω AB Ψ = Ψ j,l,k x = det A j 2 Ψ B l A j x k j, l Z, k Z 2 (4) WhereΨ L 2 R 2, A, B are 2 2 invertible matrices and det B = 1. When for any f R 2, Ω AB Ψ forms a Parseval frames (also called tight frame), we call the elements of Ω AB Ψ composite wavelet. And the Fig1. Trapezoidal frequency support of the classical shearlet dilations A j are associated with scale transformations, while the matrices B l are associated to geometrical transform of area-preserving, such as rotations and shear [15-17]. Normally, A = A 0 = 4 0 is the anisotropic dilation 0 2 matrix, and the shear matrix is B = B 0 = 1 1 in (4), 0 1 then, we construct a tiling of the frequency like fig.2 map from pseudo-polar coordinate systems into Cartesian system to satisfy the property of shift-invariance [16]. 4.Experimental Results In this section, we had presented the experimental results of proposed and conventional denoising algorithms. And the simulations were done under the MATLAB R2014a environment with Intel Core i3 CPU at 4.0 GHz. For comparison, we employ the directional filtering based denoising schemes [10, 11] and the LMMSE framework denoising scheme [11, 12 and 13] to denoise the LR image and then interpolate the denoised images using the state-of the-art algorithms. The peak-signal-to-noise ratio (PSNR) is a commonly used metric to evaluate the reconstructed image quality. However, it is well known that PSNR may not be able to faithfully reflect the image perceptual quality. How to better assess the image quality is still an open problem. Wang et al. proposed in [19], the structural similarity (SSIM) index and multi-scale SSIM (MSSIM) for image quality assessment (IQA). SSIM and MSSIM have been used as new IQA measures in many image processing applications. Here we also employ MSSIM to evaluate the image denoising results in the experiments. Fig.2 Frequency tiling of the shearlet transform The discretization process of NSST [16] is composed of two phases: multi-scale factorization and multi-orientation factorization. Non Sub-sampled pyramid is utilized to complete multi-scale factorization, which can produce (k+1) sub-images which consist of one low-frequency image and k high-frequency images whose sizes are all the same as the source image, where k denotes the number of decomposition levels. The multi-orientation factorization in NSST is realized via improved shearing filters. For shearing filter used in ST, NSST makes the standard shearing filter 609

5 Quality Metrics PSNR in db CPU Time (in sec) NCC lmmse Shearlet Fig4. Performance comparison of existing and proposed schemes with PSNR, NCC and CPU running time Directional LMMSE Proposed SSIM Fig5. Performance comparison with SSIM index 5.Conclusion Fig3. Original image, Noisy image, Directional denoising, LMMSE and Proposed frame works The proposed method is successfully developed and implemented with improved PSNR and NCC over Linear minimum mean square-error estimation technique. The overall analysis also shows that the proposed technique works better than the existing interpolation technique. All the examples shown indicate our technique is efficient for Directional Denoising interpolation scheme and has good subjective and objective quality. 610

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