10th International Conference on Information Science, Signal Processing and their Applications (ISSPA 2010)

IMAGE QUALITY MEASURE BASED ON CURVELET TRANSFORM

Zehira HADDADI.2, Azeddine BEGHDADi, Amina SERIR2, Anissa MOKRAOui

lL2TI, institut Galilee, universite Paris 13 , 2LT1R, faculte d'electronique et d'informatique, USTHB, Alger.

ABSTRACT

This paper presents a new image quality assessment based on the curvelet decomposition. The curvelet transform is introduced for its ability to represent the curves of images at different scales and directions. Unlike existing methods, the proposed image quality assessment takes into account the geometrical content of the image at different scales and directions. The proposed measure has been tested on LIVE database and was compared to other image quality assessments. The obtained results expressed in terms of correlation with subjective evaluation on the database demonstrate the efficiency of the proposed image quality metric.

1. INTRODUCTION

Image quality assessment is of great importance in many tasks such as calibration, mapping, compression, restoration or enhancement. Very often, the quality is evaluated subjectively. But, in many applications, objective evaluation is more practical to use. However, such evaluation requires a reliable measure able to predict the way the human estimate the image quality level. There are three categories of quality image assessment: "Full Reference", "No Reference" and "Reduced Reference". The first category consists of methods in which the original image is provided [1]. So are many objective pixel-based measures such as PSNR or MSE. However, these metrics are not always consistent with human judgment of image quality. These limitations motivate the development of various methods based on Human Visual System (HVS) [2]. Some are fully or partially inspired by the HVS. However, it turns out that HVS-based approaches are complex and depend on many factors. As an alternative, various simple measures based on some local characteristics or structural information extracted from the image signal have been proposed. One of such FR measures, called SSIM has been proven to be efficient in quanti tying some common image distortions [3]. The second category of measures aims to evaluate the quality of an image without any information about the original

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image, which limits their scope [4]. Generally, these measures are designed for specific degradations such as blocking effect [5] or blurring effect [6]. The third category, called Reduced Reference image quality assessment, is a compromise between the two previous ones. In the RR image quality methods a set of relevant characteristics are extracted from the original and the received or treated image and used to estimate the amount of distortion [7]-[8] It is worth to notice that most of the HVS-based image quality measures use some transforms in order to analyze the distortion at different scales and directions. Transform such as Wavelets have been successfully used in the design of image quality metrics [9]. However, wavelet transform and other conventional multi-resolution decompositions like Laplacian pyramid represent today a restricted and limited category of multidimensional signals representations. Indeed, recent work has shown that it is possible to define broader multi­scale representations with a new transforms adapted to geometric structures representation [10]. These multiscale decompositions operate on many frequency directions. The proposed quality measure is based precisely on a transform which result of this new generation of transform. We present in this paper a FR image quality measure based on the curve let transform. This transform in addition to its multi-scale aspect, uses local directional information, which permit to extract more geometrical details from the image. The use of this multiscale and directional decomposition in the design of the image quality metric yield good results. This paper is organized as follows. In section 2, we introduce new geometric wavelet transforms with special attention to Ridgelets, and then to Cruvelet transform which is just an evolution or a generalization of the first transform. Section 3 is devoted to the presentation of the proposed image quality measure. In section 4, we expose and comment the obtained results. The last section concludes this work.

2. GEOMETRIC WAVELET TRANSFORMS

Multiresolution analysis tools, notably wavelets, have been found quite useful for analyzing the information content of images; hence they enjoyed wide-spread popularity in areas like image denoising [11], image

deconvolution and compression [12], [13]. It is true that the wavelets have been used with success for many applications, however they have some drawbacks. The extension to 2-D field isusually performed by a simple tensor product separable. Unfortunately, the wavelet representation of discontinuities along smooth curve is very inefficient and generates many coefficients. To overcome this disadvantage, a long list of new multiscale transforms have been developed [14]. We can distinguish two different classes, adaptive approaches and nonadaptive, ones based on directional and fixed filter banks, the others aim to form a geometric model providing local analysis direction.

2. 1. Ridgelet transform

Ridgelet [15] is defined as a wavelet 'I' a,O,b constructed

along a line "ridge" oriented B and defined in the

Cartesian plane ( XI' Xz ) by the equation

XI cos B + Xz sin B = b : 'I' a,O,b = a -Yz 'I' ( (XI * cos ( B) + Xz * sin ( B) -b) I a) The ridgelets coefficients Ridj of a function fare

obtained by projecting on this basis:

Ridj (a, B,b) = If f( xl'xz ) 'I' a,O,b ( xl'xz ) dxldxz This projection is intimately related to the Radon transform which consists to integrate an image according to a set of lines:

Radj (t, B) = f f ( Xl' xz ) g( -XI sin B + Xz cos B -t) dxldxz Therefore, ridge let transform may be considered as 1 D wavelet transform of radon transform along the translation axis t : Ridj(a,B,b)= fRadj(t,B) a-Yz'I'((t-b)la) dt Figure 1 represents Ridgelet transform via Radon transform.

IMAGE

Radon Transform

Frequency

Figure 1. Ridgelet transform via Radon transform.

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Ridgelet transform have been developed to analyze objects which contain linear discontinuities. The image is assumed to contain locally rectilinear contours, based on this fact, ridgelet transform can be generalized for curved discontinuities (contours). This is the basic idea of curve let transform.

2.2. Curvelet transform

The concept of curve let is closely linked to ridgelets, since curve let is a sort of generalization of ridgelers for nonrectilinear contours. The objective of the curvelet transform [16] is to describe the image as small lines of a certain size and orientation. For this, a multiresolution analysis is applied to the image before applying the ridge let transform locally on dyadic blocks. First, the curve let transform performs multiscale analysis in K levels.

K-I f=All+ L HFll

k=1

Then, each high frequency image is performed in a local ridgelet transform as follows: Initialize the block size BI = Bmin

.

F or each high frequency image HFll, k = K -1, .. ',1 :

Apply locally ridgelet transform.

If B[kl mod 2 = 1 B[k+!] = 2B[kl , ,

Otherwise, B[k+!] = B[kl .

A curve let is defined as a function X = f ( XI' xz ) at the

scale TJ, orientation B, , xU,I) = R-I (k Tj k TjIZ ) by' k 0,1 I 'z .

qJj,l,k ( x ) = qJj (Rol ( x - xV') ) ) Curve let transform is defmed

c(j,[,k)= (i,f/J;,1,k)= f f( x ) qJi,l,k (X )dx ]2

and position

by [16]:

We have seen that the curvelet transform is introduced to address the problem of finding optimally sparse representations of objects, with discontinuities along C2 edges. This curve let transform inherits the ridgelet conception.

3. THE PROPOSED IMAGE QUALITY MEASURE

In this paper, we consider a 2D curvelet decomposition

where the curvelet coefficient c� (Xk' Yk ) corresponds to

the scale k and orientation B. Note f the original image

and f degraded image.

Following the idea developed in [17], the proposed image quality metric is defined by the following formula:

[ Lm�xrks/lc:(xk'Yk)1' ]111 201

X,Y,e mcurv == oglo

II x

�e m�xrk;/lc: (Xk'Yk )-8: (Xk'Yk)

We choose, as a model of the image quality metric, a sort of signal to noise ratio applied to curvelet coefficients for each orientation and scale. This model has different parameters which use our knowledge on the human visual system. To provide a uniform visual sensitivity to different scale and direction subbands for human perception, we introduce a perceptual masking for each subband. We use

a factor rksl •

Many psychovisual studies have been made on texture discrimination by the human visual system [18]- [19]; we approximate this effect by the parameter s which is adapted to the structure of the image to evaluate.

4. EXPERIEMENT RESULTS

Figure 2 represents the curvelet decomposition of a fingerprint image.

log of curve'let coefficrents

100 200 300 400 500 600 700 800 900

Figure 2. Curve let decomposition of a fingerprint image.

For our simulations, we first tested the quality measure on the LIVE database [20]. This database includes several distortions and human visual appreciations corresponding to these degradations. LIVE database contains a total of 982 images comprising 5 types of degradations, JPEG2000, JPEG, Gaussian blur, white noise and bit errors in JPEG2000 bitstream. In the table of Figure 3, we present the correlation results obtained with the LIVE database for the proposed image quality measure Mcurv. In these simulations, we have

used s == 0.5 and I == 2 . In order to compare the obtained

results, we also give the correlation results of the other image quality measures: SSIM [3], SNRwav [9] and VSNR [21].

The results show that the proposed image quality measure Mcurv obtains a better correlation with the humain visual appreciations than other image quality measures except for FF degradation where SNRwav is better and for JPEG degradation where VSNR is better. The curvelet transform IS suitable for the image contours

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representation. The application that seems the best appropriate to this transform is the quality assessment of fingerprint images. Indeed, these images contain many curves and consequently many contours. In the second part of our experiment tests, we choose to use different compressed fingerprint images. Figure 4 displays the proposed image quality measure as a function of the JPEG quality factor.

JPEG2 JPEG WN GB FF

Mcurv 0.9147 0.8877 0.9735 0.9527 0.9131

SSIM 0.899 0.8504 0.9621 0.8558 0.9011

VSNR 0.9101 0.9256 0.9718 0.8871 0.9074

SNRwav 0.8991 0.8703 0.9562 0.9205 0.9276

Figure 3. CorrelatlOn results of LIVE database.

50

20

10

facleur de qualile de compression JPEG

Figure 4. Different image quality measures as function of the JPEG quality factor.

Figure 4 shows the evolution of the image quality measures Mcurv, SSIM and SNRwav as function to the JPEG quality factor. The obtained results show that the proposed image quality measure Mcurv is more appropriate to the fingerprint images. For example, for the fingerprint image with quality factor 10 and a fingerprint image with a quality factor of 100, the proposed Mcurv gives 16.21 for the first image and 53.06 for second; while SSIM gives 0.9646 for the first and 1 second. SSIM is a measure between 0 and 1. Note that, the SSIM value 0.9646 corresponds to a good quality image in contrast to what we can see visually. In Figure 5, we see that a fingerprint image with a quality factor of 10 is an image of poor quality exhibiting a visible blocking effect. Therefore, for a fingerprint image, the SSIM range does not reflect the variation of the corresponding quality factor and is not consistent with the perceptual image quality. We conclude that the proposed measure based on curvelet transform is more suitable for fingerprint images that SNRwav and SSIM.

5. CONCLUSION

This work proposes a new image quality assessment using the curve let transform. This quality measure uses distortions in different scales and orientations of the curvelet decomposition. Evaluate the distortions in an area of very rich representation permits to better assess the image quality and rendering the measurement of very

discriminant quality. The obtained results for the LIVE database confirm the effectiveness of this image quality assessment. The application of this quality assessment is very interesting for images which containing many contours or curves as the case of fmgerprint images.

Figure 5. Fingerprint image with factor quality of 10.

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