CHAPTER 3 IMAGE RESOLUTION ENHANCEMENTshodhganga.inflibnet.ac.in/bitstream/10603/24460/8/08_chapter3.pdf · The unprocessed high resolution spatial data and low resolution spectral

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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

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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(xk-1) f(xk) F(xk+1) f(xk+2)

(a) f(xk)

1/2 ½ 1/2 ½

(b) g(xn)

g(xn)g(xn+1)

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(c) l(xk) l(xk-1) l(xk) L(xk+1) l(xk+2)

Figure 3.1 Interpolation of signal (a) original data sequence (b) down

sampled version of original data sequence and (c)

interpolated data sequence

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The discrete sequence )( kxf of length N as shown in Figure 3.1

(a) and this sequence is filtered and down sampled by 2, thereby getting

another sequence )( nxg of length 2/N as shown in Figure 3.1 (b). The

interpolation process aims at estimating a sequence )( kxl of length N as

shown in Figure 3.1 (c), which is as close as possible to the original discrete

sequence )( kxf .

3.2.1 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

xx

xx

2/122/12/11

2/10)(0

(3.1)

The basis for this scheme is interpolating and it is a pixel repetition

process.

3.2.2 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

||101||||1

)(1

xxx

x (3.2)

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3.2.3 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)

2||14||8||5||1||01||)3(||)2(

)(23

23

xxxxxxx

x (3.3)

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-

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InputImage

Low pass filter

High pass filter

2

2

Low pass filter

Low pass filter

High pass filter

High pass filter

2

2

2

2

LL

LH

HL

HH

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.

Figure 3.2 DWT filter bank of level 1

Figure 3.3 LL sub-band image

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Figure 3.4 LH sub-band image

Figure 3.5 HL sub-band image

Figure 3.6 HH sub-band image

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3.4 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 jH is interpolated by putting )12( 1j zeros between each of

the coefficient of the original filter 0H , so does for jL . 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.

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LLj

Lj

Hj

HHj+1

HL j+1

LH j+1

LL j+1

Lj

Hj

2

2

2

2

Lj

Hj

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.

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InputImage

WZP

Shift DWT WZP Shift

Shift DWT WZP Shift

Shift DWT WZP Shift

.

.

.

OutputImage

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.

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 .

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InputImage

Low frequency sub-band images

High frequency sub-band images

Interpolationwith factor

Interpolated Highfrequency sub-band images

Interpolationwith factor /2

IDT-CWT

DT-CWT

Highresolution

output image

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.

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Input Image

Undecimated L-levelwavelet transform

Locate features withcorrelation

Extrapolated featureposition

Create newsub-band

Extrapolate magnitudedecay

2

2

G(z)

H(z)

Interpolatedimage

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. )(zH and )(zG are analysis

filters.

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.

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Without loss of generality, assume that the low resolution image

jiX , of size WH directly comes from WH 22 i.e. jiji XY ,2,2 .

While using this edge preserving interpolation technique, interpolate

the interlacing lattice 12,12 jiY from the lattice jiji XY ,2,2 .

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 sub-

bands. 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.

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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

InputImage

DWT

SWT

LL

LH

HL

HH

LL

LH

HL

HH

InterpolatedLH

+

+

+

InterpolatedHH

InterpolatedHL

IDWT

High Resolution Image

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Figure 3.11. 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 sub-

bands of SWT of the input image. This will preserve more high frequency

components after the interpolation.

3.10 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.

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(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 sub-

band 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.

3.11 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.

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Table 3.1 Performance comparison between SWT and DWT based

interpolation technique

Sl.No

Region TitleStationary WaveletTransform - PSNR

(dB)

Proposed DWT basedInterpolation Technique

- PSNR (dB)

1 Kochi 32.62 33.15

2 Kanyakumari 32.76 36.58

3 Kolkata 32.91 35.39

4 Visakhapatnam 32.28 35.16

5 Sydney 32.49 35.00

Figure 3.12 Graphical representation of performance of SWT and DWT

based interpolation technique

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(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

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(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 sub-

band images of Kochi region and Figure 3.14 depicts (a) SWT and (b) DWT

based interpolation technique resolution enhanced images of Kochi region.

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(c) HL sub-band and (d) HH sub-band images of

Kanyakumari region

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Kanyakumari region

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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.




(c) HL sub-band and (d) HH sub-band images of Kolkata

region

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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.

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(c) HL sub-band and (d) HH sub-band images of

Visakhapatnam region

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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.

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(c) HL sub-band and (d) HH sub-band images of Sydney

region

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Sydney region

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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 sub-

band 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

Image Title

Resolution Enhancement Techniques

Stationary WaveletTransform - PSNR

(dB)

Proposed DWT basedInterpolation Technique

- PSNR (dB)

Barbara 37.20 41.49

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(c) HL sub-band and (d) HH sub-band images of Barbara

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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.

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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

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From the experimental results it reveals that newly developed image

resolution enhancement technique preserves the image edge information with

rich textures.

3.12 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

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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.

3.13 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.

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CHAPTER 3 IMAGE RESOLUTION ENHANCEMENTshodhganga.inflibnet.ac.in/bitstream/10603/24460/8/08_chapter3.pdf · The unprocessed high resolution spatial data and low resolution spectral