CHAPTER 3 IMAGE RESOLUTION ENHANCEMENT

Transcription

1 51 CHAPTER 3 IMAGE RESOLUTION ENHANCEMENT This chapter discusses the three traditional interpolation techniques: bilinear, nearest neighbor and bicubic interpolation and the proposed discrete wavelet transform based resolution enhancement and gradient image. The basis of all these techniques is wavelet transform. 3.1 INTRODUCTION One of the major problems in images used in research is their resolution. The unprocessed high resolution spatial data and low resolution spectral data of satellite images are related with each other. Therefore, spatial and spectral resolution enhancement of satellite images is desirable. The main focus of this research is to improve the classification accuracy of noisy images. In order to improve the accuracy of satellite images efficiently, preservation of edges and contour information is very important. Images are being analyzed and processed to obtain the enhanced resolution and classified result. Interpolation is one of the techniques generally used for image resolution enhancement. This is mainly used to increase the number of pixels in a digital image. Interpolation has been widely used in many image processing applications such as facial reconstruction introduced by Yi-bo et al (2007), multiple description coding developed by Rener et al (2008), feature extraction, image denoising and super resolution. Image resolution enhancement in the wavelet domain is a relatively new

2 52 research topic and recently many new algorithms have been proposed by Gupta and Rajiv (2007). 3.2 IMAGE INTERPOLATION The interpolation of an image aims at estimating intermediate pixels between the known pixel values in the available low resolution image. The image interpolation process is nothing but the image synthesis operation. This process is performed row by row and then column by column. f(x k -1) f(x k ) F(x k+1 ) f(x k+2 ) (a) f(x k ) 1/2 ½ 1/2 ½ (b) g(x n ) g(x n ) 1 g(x n+1 ) 1 (c) l(x k ) l(x k -1) l(x k ) L(x k+1 ) l(x k+2 ) Figure 3.1 Interpolation of signal (a) original data sequence (b) down sampled version of original data sequence and (c) interpolated data sequence

3 53 The discrete sequence f x ) of length N as shown in Figure 3.1 ( k (a) and this sequence is filtered and down sampled by 2, thereby getting another sequence g x ) of length N / 2 as shown in Figure 3.1 (b). The ( n interpolation process aims at estimating a sequence l x ) of length N as shown in Figure 3.1 (c), which is as close as possible to the original discrete sequence f x ). ( k ( k Nearest Neighbour Interpolation Nearest neighbour interpolation is the simplest interpolation scheme. The basis function associated with nearest neighbour interpolation is given by Equation (3.1) as follows 0 ( x) x 1/ 2 1/ 2 1/ 2 x x 1/ 2 (3.1) process. The basis for this scheme is interpolating and it is a pixel repetition Bilinear Interpolation The bilinear interpolation has a large popularity due to its simplicity of implementation. The basis function used in bilinear interpolation is given by Equation (3.2) as follows 1 ( 1 x x 1 x ) (3.2) 0 1 x

4 Bicubic Interpolation Another one method which is significantly effective in signal is the bicubic interpolation. The bicubic interpolation basis function is interpolating and can be expressed in Equation (3.3) 3 2 ( 2) x ( 3) x 1 0 x 1 x ) 3 (3.3) x 5 x 8 x 4 1 x 2 ( 2 where is an optimization parameter. It may be adaptive from point to point depending on the signal local activity levels. This chapter discusses the following resolution enhancement techniques: Discrete wavelet transform Stationary wavelet transform WZP-CS based image resolution enhancement DT-CWT based image resolution enhancement Directional wavelet transform Image resolution enhancement using SWT and DWT The proposed DWT based interpolation technique 3.3 DISCRETE WAVELET TRANSFORM Turgay and Huseyin (2009) discussed the 1-D discrete wavelet transform is applied along the rows of the image rst, and then along the columns to produce 2-D decomposition of image. Discrete wavelet transform decomposes an image into four sub-bands namely low-low, low-high, high-

5 55 low and high-high. These four sub-bands can also be used to generate the original image. The LL sub-band consists of illumination information, where as the remaining sub-bands contain the information of edges. The manipulation of these sub-bands gives the improved image i.e., the enhancement in resolution. Figure 3.2 shows the block diagram of discrete wavelet transform filter bank of level 1, to generate different sub-band frequency images. An example of DWT sub-band images are shown in Figure 3.3 to Figure 3.6. Low pass filter LL Low pass filter High pass filter LH Input Image Low pass filter HL High pass filter High pass filter HH Figure 3.2 DWT filter bank of level 1 Figure 3.3 LL sub-band image

6 56 Figure 3.4 LH sub-band image Figure 3.5 HL sub-band image Figure 3.6 HH sub-band image

7 STATIONARY WAVELET TRANSFORM Hasan and Gholamreza (2011) discussed the wavelet transform can also provide a scale-based decomposition. The wavelet transform of an image typically consists of a large number of small coefficients i.e., it contains little information and a small number of large coefficients i.e., it contains significant information. Thus each wavelet coefficient is in two states namely significant and insignificant. For discrete time signals, discrete wavelet transform is implemented by filtering the input signal with a low-pass filter and a high-pass filter and down sampling the outputs by a factor of 2 as shown in Figure 3.2. Applying the same decomposition to the low pass channel output yields a two-level wavelet transform; such schemes can be iterated in a dyadic way to generate a multilevel decomposition. The synthesis of the signal is obtained with a scheme symmetrical to that of the analysis stage, i.e., by upsampling the coefficients of the decomposition and by low-pass and high-pass filtering. It can be shown that if the down sampler removes from the analysis stage and the up samplers removes from the synthesis stage, then perfect reconstruction can still be achieved. Filter H j is interpolated by putting ( 2 j 1 1) zeros between each of the coefficient of the original filter H 0, so does for L j. The decrease of bandwidth is accomplished by zeros padding of the filters instead of down sampling of wavelet coefficients. This decomposition is called as Stationary Wavelet Transform (SWT) or undecimated wavelet transform shown in Figure 3.7.

8 58 L j 2 HH j+1 L j H j 2 HL j+1 LL j L j 2 LH j+1 H j H j 2 LL j+1 Figure 3.7 Stationary wavelet transform 3.5 WZP-CS BASED IMAGE RESOLUTION ENHANCEMENT Temizel and Vlachos (2005) discussed the two important steps of Wavelet domain Zero Padding Cycle Spinning (WZP-CS) algorithm as follows: 1) An initial approximation of unknown high resolution image is generated using wavelet domain zero padding. 2) Next, the cycle-spinning method is used to manage the following tasks: Using the high resolution image in step (1), a number of low resolution images are generated by spatial shifting, wavelet transforming and discarding the high frequency sub-bands. The high resolution images are obtained by applying the WZP processing to all those low resolution images.

9 59 The final high resolution image is reconstructed by re-aligning and averaging these intermediated high resolution images. Figure 3.8 shows the block diagram of the WZP-CS based image resolution enhancement. Shift DWT WZP Shift Shift DWT WZP Shift Input Image WZP... Output Image Shift DWT WZP Shift Figure 3.8 WZP-CS based image resolution enhancement 3.6 DT-CWT BASED IMAGE RESOLUTION ENHANCEMENT Hasan and Gholamreza (2011a) discussed the Dual Tree-Complex Wavelet Transform (DT-CWT) is used to decompose an input low resolution image into different sub-bands. Then, the high-frequency sub-band images and the input image are interpolated. The combination of all these sub-bands is used to generate a new high-resolution image. The resolution enhancement is achieved by using directional selectivity provided by the complex wavelet transform. The sharpness of the high frequency details are contributed by six different directions of high frequency sub-bands. Figure 3.9 shows details of DT-CWT based image resolution enhancement technique, where the enlargement factor through the resolution enhancement is.

10 60 Low frequency subband images Interpolation with factor /2 Input Image DT-CWT IDT- CWT High resolution output image High frequency subband images Interpolation with factor Interpolated High frequency sub-band images Figure 3.9 DT-CWT based image resolution enhancement 3.7 REGULARITY PRESERVING IMAGE INTERPOLATION Conventional interpolation methods work in the time domain. Turgay and Huseyin (2009) discussed in regularity preserving image interpolation technique, the low-pass output of the wavelet analysis is considered as the image to be interpolated. The original image can be given as a single wavelet synthesis stage along with the high frequency sub-bands to produce an image interpolated by a factor of two in both vertical and horizontal directions. The formation of unknown high-frequency sub-bands is required in the regularity-preserving interpolation strategy. There are mainly two steps that are carried out to obtain the unknown high-frequency sub-bands separately. In the first step, the correlation across scales is identified in each row edge with significant correlation. Then, near these edges the rate of decay of the wavelet coefficients is extrapolated to approximate the high-frequency sub-band required to re-synthesize a row of twice the original size.

11 61 In second step, the same procedure as in first step is then applied to each column of the row-interpolated image. Figure 3.10 shows the block diagram of interpolation system for 1-D row and column signals. H (z) and G(z) filters. are analysis Input Image Create new sub-band 2 G(z) Undecimated L-level wavelet transform Interpolated image Locate features with correlation Extrapolate magnitude decay Extrapolated feature position 2 H(z) Figure 3.10 Block diagram of interpolation signals 3.8 EDGE DIRECTED INTERPOLATION An edge directed interpolation is a combination of bilinear and covariance-based adaptive interpolation. This is used to reduce the overall computational complexity. Conventional linear interpolation schemes such as bilinear and bicubic interpolations are based on space-invariant models. These are not able to capture the information around edges and produce interpolated images with blurred edges and annoying artifacts. Geometric regularity is very much essential for the visual quality of a natural image such as the sharpness of edges and the freedom from artifacts.

12 62 Without loss of generality, assume that the low resolution image X i, j of size H W directly comes from 2H 2W i.e. Y i,2 j X i, j 2. While using this edge preserving interpolation technique, interpolate the interlacing lattice Y 2i 1,2 j 1 from the latticey i,2 j X i, j 2. The hybrid approach used in edge directed interpolation technique is covariance-based interpolation. This is applied to pixels near an edge and for pixels in smooth regions (non-edge pixels), use simple bilinear interpolation. Based on the observation that this approach is benefited for edge pixels. 3.9 IMAGE RESOLUTION ENHANCEMENT USING DWT AND SWT The main loss of interpolation technique in image resolution enhancement is its high frequency components (i.e., edges), which is due to the smoothing effect caused by interpolation. In order to increase the quality of the resolution enhanced image, preserving the edges is essential. In this technique, to preserve the high frequency components of the image DWT has been employed. Hasan et al (2011) discussed the resolution enhancement using DWT and SWT uses bicubic interpolation with enlargement factor of two of the high frequency sub-band images. While performing downsampling in each of the DWT sub-bands causes information loss in the respective subbands. So as to minimize this loss SWT is employed. The interpolated high frequency sub-bands and the SWT high frequency sub-bands have the equal size which means that can be added with each other. The new corrected high frequency sub-bands can be interpolated further for higher enhancement. Also it is well-known that in the wavelet transform domain, the low resolution image is obtained by lowpass filtering of the high resolution image.

13 63 LL DWT LH HL Input Image HH LL SWT LH + HL + HH + Interpolated LH Interpolated HL Interpolated HH IDWT High Resolution Image Figure 3.11 Image resolution enhancement using DWT and SWT Figure 3.11 illustrates the block diagram of the image resolution enhancement using DWT and SWT technique. By interpolating input image by three, high frequency sub-bands by 2 and in the intermediate and final interpolation stages respectively, and then by applying IDWT, as illustrated in

14 64 Figure The resolution enhanced image will contain sharper edges than the interpolated image. This is due to the interpolation of high frequency components and using the corrections obtained by adding high frequency subbands of SWT of the input image. This will preserve more high frequency components after the interpolation THE PROPOSED DWT BASED INTERPOLATION TECHNIQUE Resolution enhancement is a very important technique in satellite image processing that aims to enhance the visual appearance of the image. DWT has been employed to preserve the high frequency components of the image. This work proposes DWT based interpolation technique for satellite image resolution enhancement in high frequency sub-band images and the denoised image. The final resolution enhanced image has been obtained by inverse discrete wavelet transform. In order to obtain a sharper image that preserves the edge information, interpolation technique is used. This technique approximates the high frequency sub-band by subtracting the interpolated LL sub-band from the denoised image. The proposed DWT based interpolation technique consists of three main steps as follows: (i) Decompose the input image into four frequency sub-bands namely, LL, LH, HL and HH. (ii) Find the difference between input image i.e., denoised image and the low frequency sub-band image.

15 65 (iii) The result obtained based on DWT based interpolation is by interpolating the high frequency sub-band by two and performing the IDWT using half of the interpolation factor. The LL sub-band without quantization is used as input for this proposed technique. The interpolation technique uses this low frequency subband image, which contains little information than the denoised image. Therefore, the low resolution image is interpolated with the half of the interpolation factor, to interpolate the high frequency sub-band. The difference between the low resolution denoised image and the interpolated LL sub-band image is a high frequency component. This estimation is calculated by interpolating the high frequency sub-band by two and performing IDWT using half of the interpolation factor. The additional step proposed, that is, adding the difference image with the high frequency components, generates sharper resolution enhanced image EXPERIMENTAL RESULTS AND DISCUSSIONS The proposed work uses the DWT based interpolation technique to enhance the resolution of the denoised image. The performance of this proposed technique is compared with stationary wavelet transform. The quantitative performance is measured using PSNR and it can be improved in the resolution enhanced image compared to the denoised image. The comparison results of SWT and DWT based interpolation technique are shown in Table 3.1 and Figure 3.12 shows the graphical representation of performance comparison of SWT and the proposed technique.

16 66 Table 3.1 Performance comparison between SWT and DWT based interpolation technique Sl. No Region Title Stationary Wavelet Transform - PSNR (db) Proposed DWT based Interpolation Technique - PSNR (db) 1 Kochi Kanyakumari Kolkata Visakhapatnam Sydney Figure 3.12 Graphical representation of performance of SWT and DWT based interpolation technique

17 67 (a) LL sub-band (b) LH sub-band (c) HL sub-band (d) HH sub-band Figure 3.13 Experimental results of (a) LL sub-band, (b) LH sub-band, (c) HL sub-band and (d) HH sub-band images of Kochi region

18 68 (a) Stationary wavelet transform (b) DWT based interpolation technique Figure 3.14 Experimental results of (a) SWT and (b) DWT based interpolation technique resolution enhanced images of Kochi region Figure 3.13 shows the different sub-bands of wavelet coefficient namely (a) LL sub-band, (b) LH sub-band, (c) HL sub-band and (d) HH subband images of Kochi region and Figure 3.14 depicts (a) SWT and (b) DWT based interpolation technique resolution enhanced images of Kochi region.

19 69 (a) LL sub-band (b) LH sub-band (c) HL sub-band (d) HH sub-band Figure 3.15 Experimental results of (a) LL sub-band, (b) LH sub-band, (c) HL sub-band and (d) HH sub-band images of Kanyakumari region

20 70 (a) Stationary wavelet transform (b) DWT based interpolation technique Figure 3.16 Experimental results of (a) SWT and (b) DWT based interpolation technique resolution enhanced images of Kanyakumari region

21 71 Figure 3.15 shows the different four sub-band images of Kanyakumari region and Figure 3.16 depicts (a) SWT and (b) DWT based interpolation technique resolution enhanced images of Kanyakumari region. (a) LL sub-band (b) LH sub-band (c) HL sub-band (d) HH sub-band Figure 3.17 Experimental results of (a) LL sub-band, (b) LH sub-band, (c) HL sub-band and (d) HH sub-band images of Kolkata region

22 72 (a) Stationary wavelet transform (b) DWT based interpolation technique Figure 3.18 Experimental results of (a) SWT and (b) DWT based interpolation technique resolution enhanced images of Kolkata region Figure 3.17 shows the wavelet coefficient sub-bands namely (a) low-low (b) low-high (c) high-low and (d) high-high images of Kolkata region and Figure 3.18 depicts (a) SWT and (b) DWT based interpolation technique resolution enhanced images of Kolkata region.

23 73 (a) LL sub-band (b) LH sub-band (c) HL sub-band (d) HH sub-band Figure 3.19 Experimental results of (a) LL sub-band, (b) LH sub-band, (c) HL sub-band and (d) HH sub-band images of Visakhapatnam region

24 74 (a) Stationary wavelet transform (b) DWT based interpolation technique Figure 3.20 Experimental results of (a) SWT and (b) DWT based interpolation technique resolution enhanced images of Visakhapatnam region Figure 3.19 shows the different sub-band images of Visakhapatnam region and Figure 3.20 depicts (a) SWT and (b) proposed technique resolution enhanced images of Visakhapatnam region.

25 75 (a) LL sub-band (b) LH sub-band (c) HL sub-band (d) HH sub-band Figure 3.21 Experimental results of (a) LL sub-band, (b) LH sub-band, (c) HL sub-band and (d) HH sub-band images of Sydney region

26 76 (a) Stationary wavelet transform (b) DWT based interpolation technique Figure 3.22 Experimental results of (a) SWT and (b) DWT based interpolation technique resolution enhanced images of Sydney region

27 77 Figure 3.21 shows the different sub-bands of wavelet coefficient namely (a) LL sub-band (b) LH sub-band (c) HL sub-band and (d) HH subband images of Sydney region and Figure 3.22 depicts (a) SWT and (b) DWT based interpolation technique resolution enhanced images of Sydney region. In order to evaluate the quantitative performance of DWT based interpolation technique, the well known Barbara image is taken into account to determine the performance of the proposed technique. Table 3.2 shows the performance of resolution enhanced images. While comparing the performance of SWT with DWT based interpolation technique the PSNR value of the Barbara image is improved from 37.20dB to 41.49dB. Figure 3.23 shows the different sub-bands of Barbara image and Figure 3.24 shows SWT and the proposed resolution enhanced images. Table 3.2 Performance comparison of SWT and DWT based interpolation technique resolution enhanced image - Barbara Resolution Enhancement Techniques Image Title Stationary Wavelet Transform - PSNR (db) Proposed DWT based Interpolation Technique - PSNR (db) Barbara

28 78 (a) LL sub-band (b) LH sub-band (c) HL sub-band (d) HH sub-band Figure 3.23 Experimental results of (a) LL sub-band, (b) LH sub-band, (c) HL sub-band and (d) HH sub-band images of Barbara

29 79 (a) Stationary wavelet transform (b) DWT based interpolation technique Figure 3.24 Experimental results of (a) SWT and (b) DWT based interpolation technique resolution enhanced images of Barbara In order to prove the preservation of edges using the proposed technique, the zoomed out results of resolution enhanced images are shown in Figure 3.25.

30 80 Region Name DWT based Resolution Enhanced Image Zoomed out Result (a) Kochi (b) Kanyakumari (c) Kolkata (d) Visakhapatnam (e) Sydney Figure 3.25 Zoomed out results of resolution enhanced images

31 81 From the experimental results it reveals that newly developed image resolution enhancement technique preserves the image edge information with rich textures APPLICATIONS Image Enhancement has contributed for research in a variety of fields. Some of the application areas are listed below In forensics enhancement is used for identification, gathering of evidence and surveillance. Images obtained from fingerprint detection and crime scene investigations are enhanced to help in identification of culprits and protection of victims. In atmospheric science enhancement is used to reduce the effects of haze, fog, mist and turbulent weather for meteorological observations. It helps in detecting the exact shape and structure of remote objects. Satellite images undergo the restoration of images and enhancement to remove noise. In oceanography the study of images reveals interesting features of water flow, sediment concentration, oil spill detection, geomorphology and bathymetric patterns. These features are more clearly observable using satellite images that are digitally enhanced to overcome the problem of moving targets, deficiency of light and obscure surroundings. Virtual restoration of historic paintings and artifacts often employ the techniques of enhancement in order to reduce stains and crevices. Colour contrast enhancement, sharpening and brightening are just some of the techniques used to make

32 82 the images vivid. Enhancement is a powerful tool for restorers who can make informed decisions by viewing the results of restoring a painting beforehand. Medical imaging uses enhancement techniques for removing noise and sharpening details to improve the visual representation of the image. Since miniature details play a critical role in diagnosis and treatment of disease, it is crucial to highlight important features while displaying medical images. Numerous other fields including law enforcement, microbiology, biomedicine, bacteriology, climatology, meteorology, etc., benefit from various enhancement techniques. These benefits are not limited to professional studies and businesses but extend to the common users who employ enhancement to cosmetically enhance and correct their images SUMMARY This chapter works for enhancing the quality of the image and applies discrete wavelet transform which is followed by interpolation based resolution enhancement to obtain a resolution enhanced image. This is done to extract detailed information from the image and add it to the output image of the Inverse Discrete Wavelet Transform in order to get a highly robust resolution enhanced image. These proposed techniques have been tested on landsat remote sensing images, where there PSNR and visual results show the efficiency of the proposed techniques over the conventional resolution enhancement techniques. In order to perform the image classification, feature extraction is the important step. The chapter 4 describes the texture feature extraction techniques used for classification.