Abstract JPEG2000 is known as an efficient standard toencode images. However, at very low bit-rates, artifacts ordistortions can be observed in decoded images. In order toimprove the visual quality of decoded images and make themperceptually acceptable, we propose in this work a new pre-processing scheme. This scheme consists in preprocessingthe image to be encoded using a nonlinear filtering, consid-ered as a prior phase to JPEG 2000 compression. More specif-ically, the input image is decomposed into low- and high-frequency sub-images using morphological filtering. After-ward, each sub-image is compressed using JPEG2000, byassigning different bit-rates to each sub-image. To evaluatethe quality of the reconstructed image, two different met-rics have been used, namely (a) peak signal to noise ratio, toevaluate the visual quality of the low-frequency sub-image,and (b) structural similarity index measure, to evaluate thevisual quality of the high-frequency sub-image. Based on thereconstructed images, experimental results show that, at lowbit-rates, the proposed scheme provides better visual qual-ity compared to a direct use of JPEG2000 (excluding anypreprocessing).
L. Bennacer (B) · B. BouledjfaneLaboratoire d’Etude et de Recherche en Instrumentation etTélécommunications Avancées (LERICA), Université BadjiMokhtar, B.P. 12, 23000 Annaba, Algériee-mail: [email protected]
A. Nait-AliLaboratoire Images, Signaux et Systèmes Intelligents (LISSI, EA 3956),Université Paris-Est Créteil (UPEC), 61 Ave du Générale de Gaulle,94010 Créteil, Francee-mail: [email protected]
JPEG2000 Joint Photographic Experts Group commit-tee in 2000
DWT Discrete wavelet transformDCT Discrete cosine transformIDWT Inverse discrete wavelet transformI (x, y) Image with spatial coordinate x and yS Structuring elementI ⊕ S Dilation of I by SI � S Erosion of I by SI ◦ S Morphological opening of I by SI•S Morphological closing of I by Sg, f g is the mask and f is the markerRg( f ) Reconstruction of g from fγ (rec)( f, g) Opening by reconstruction of g from fILow Decomposed image I at low frequencyIHigh Decomposed image I at high frequencyRate Compression ratioα Compression ratio of the low-frequency
sub-image (bit per pixel)β Compression ratio of the high-frequency
sub-image (bit per pixel)Ψ (ILow, α) Compression operator of ILow by αΨ (IHigh, β) Compression operator of IHigh by βCompLow Compressed low-frequency sub-imageCompHigh Compressed high-frequency sub-imageΨ−1(ILow, α) The inverse compression operator of ILow
by α
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Ψ−1(IHigh, β) The inverse compression operator of IHigh
by βbpp Bit per pixelMSE Mean square errorPSNR Peak signal to noise ratioSSIM Structural SIMilarityl() Luminance comparison functionc() Contrast comparison functions() Structure comparison functionμ f The average of fσ 2
f The variance of fσ f g The covariance between f and gL. The dynamic range of the pixel valuesB The bit depth used for noncompressed
image codingC1,C2 Two variables to stabilize the division with
Nowadays, standards are highly considered when deal-ing with information technology systems, especially fordata transmission and storage. The well-known Joint Pho-tographic Experts Group (JPEG) standard is intensivelyemployed in multimedia applications, and the JPEG2000 hasbeen proposed as an alternative. JPEG2000 standard allowsmany useful options. In particular, it uses wavelet transforminstead of discrete cosine transform (DCT), which makes thequality of the reconstructed image at a given bit-rate, muchbetter than the one obtained using JPEG. The JPEG2000standard supports lossy and lossless compression of single-component (e.g., grayscale) and multicomponent (e.g., color)images. Due to its excellent coding performance, JPEG2000is employed in numerous application fields, including imagearchiving, Internet and Web browsing, medical image storageand transmission, etc [1,2]. However, the major drawback ofstandard JPEG2000 is that at a low compression bit-rates,numerous artifacts can be observed such as ringing, blur,and false edges [3–5].
The aim of this paper is to present a compression schemerequiring a nonlinear filtering before using JPEG2000 encod-ing phase. More specifically, morphological filters are used todecompose any input image into both high and low frequen-cies, providing, hence, two sub-images. For each sub-image,JPEG2000 encoder is applied by assigning different bit-rates.In order to evaluate the quality of the reconstructed image,two metrics are used: (a) the common peak signal to noiseratio (PSNR) is employed to assess the visual quality of thelow-frequency sub-image, and (b) structural similarity indexmeasure (SSIM) is used to assess the high-frequency sub-image. In this work, it will be shown how one can improve
the quality of the reconstructed image by considering the pro-posed scheme. This paper is organized as follows: Sect. 2 pro-vides a brief description of the observed artifacts when usingdirectly JPEG2000 standard. Section 3 presents some basicmorphological operations and morphology-based filtering,commonly used in image processing. Section 4 describes theproposed new scheme, including the optimization process ofthe required parameters. Afterward, results are highlightedin Sect. 5. Finally, Sect. 6 provides some main conclusions,including some perspectives future work.
2 Artifacts in JPEG2000 standard
A generic JPEG2000 compression scheme is illustrated inFig. 1. In this scheme, three main phases are required, namelythe discrete wavelet transform (DWT), followed by a quan-tization phase, and finally, an entropic encoding phase. Theoutput data are called bitstream, which is required to recon-struct the image through an inverse discrete wavelet trans-form. More details can be obtained in [1].
As specified in [3–5], JPEG2000 may cause blur and ring-ing artifacts. In the reconstructed image, ringing artifactsare caused by the quantization or truncation of the high-frequency transform coefficients resulting from wavelet-based coding. Consequently, in the spatial domain, thiscauses ripples or oscillations around sharp edges or contours.This is also known as Gibbs phenomenon.
Wavelet TransformDWT
Quantization
Entropy coding
Inverse TransformIDWT
InverseQuantization
EntropyDecoding
Input image Reconstructed image
Bitstream
Fig. 1 JPEG2000 block diagrams
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Fig. 2 Illustration of ringing artifacts in JPEG2000 [6]. a Originalimage Flash, b JPEG2000-coded Flash at 0.07825 bpp
The problem of removing ringing artifacts has been con-sidered in [6,7]. For example, Fig. 2a, b shows an origi-nal “Flash” image and the corresponding JPEG2000 recon-structed image at a biterate: 0.07825 bpp.
The purpose of “removing ringing artifacts” is to makethe smooth regions as smooth as they appear in the originalimage, by preserving real edges, considered as useful infor-mation.
On the other hand, blur is due to the attenuation of thehigh spatial frequencies, which commonly occurs during fil-tering or visual data compression. The problem of removingblurring artifacts is considered in [7,8].
Blur and ringing artifacts are defined generally in the spa-tial domain. Both artifacts appear basically along edges orin textured areas. In order to reduce these artifacts, a pre-processing method is often used. Within this context, andby considering that the proposed method is based on mor-phological filtering (as a phase to improve the quality of thereconstructed image), some basis will be described in thenext section.
3 Morphological operators and morphology-basedfiltering
3.1 Morphological operators
Used in numerous applications, morphological operationsare efficient image processing tools employed for imageenhancement, segmentation, edge detection, and featureextraction [9,10]. When considering grayscale morphology,we define two basic operations, namely dilation and erosion.When dealing with two-dimensional gray-level images, mor-phological dilation (erosion) of an image I (x, y) is definedas:
Dilation : (I ⊕ S)(i, j) = min {I (x + i, j + y)/(x, y) ∈ S}(1)
Erosion : (I �S)(i, j) = min {I (x + i, j + y)/(x, y) ∈ S}(2)
In image processing applications, the set S mentioned aboveis usually called the structuring element representing a smallgeometric template (e.g. line segment, disk, and square).
3.2 Nonlinear filtering
Combining morphological dilation and morphological erosionsubsequently, result in two other operations known as morpho-logical opening (◦) and closing (•) defined as:
Opening : (I ◦ S)(i, j) = [(I � S)⊕ S] (3)
Closing : (I • S)(i, j) = [(I ⊕ S)�S] (4)
Morphological opening and closing are the most well-knownnonlinear filters used in image enhancement and noise reduction[11,12]. However, these filters present several drawbacks.
In general, if the undesirable features are eliminated, theremaining structures will be changed. Recently, filters by recon-struction are considered as powerful tools that allow the elimi-nation of undesirable features without affecting desirable ones[13]. Consequently, our preprocessing method includes a 2Dmorphological filter by reconstruction in the proposed compres-sion scheme.
3.3 Filtering by reconstruction
Reconstruction is a morphological transformation requiring twoimages and a structuring element (instead of a single image anda structuring element). The first image (marker) is the startingpoint for the transformation. The second image (mask) con-strains the transformation. The structuring element used definesconnectivity [14,15]. If g is the mask and f is the marker,grayscale morphological reconstruction of g from f is definedby the following iterative procedure:
Step 1: Initialize h1 to be the marker image fStep 2: Create the structuring element SStep 3: Repeat:Step 4: hk+1 = (hk ⊕ S) ∩ g = inf(hk ⊕ S, g)Step 5: until hk+1 = hk
Step 6 : Marker f must be a subset of g, that is f ⊆ g
The symbol ⊕ is used for the dilation operation, and ∩ standsfor the point-wise minimum between the dilated marker imageand the mask image. Filtering by reconstruction is the oldesttype of connected filter [16].
In the case of openings by reconstruction, the marker is theresult of an opening or erosion by some structuring element.Afterward, structures not removed entirely by the opening orerosion are reconstructed exactly, as shown in Fig. 3. The open-ing by reconstruction noted γ (rec)(g, f ) is defined as:
γ (rec)(g, f ) = δ(∞)(g, f )
= δ(1)(δ(1)(. . . δ(1)(g, f ) . . .) (5)
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Image source
Structuring element IHigh
ILowMorphological opening
by reconstruction
Fig. 3 Decomposition of the source image into its low and high-frequency sub-images
The transformation δ(∞)(g, f ) defines the geodesic unitary dila-tion. It is defined by the following expression: δ(1)(g, f ) =Min{δ1(g), f }. The operator δn denotes the morphological dila-tion with a structuring element of n size, and f is the marker. Itis defined as the eroded form of the original image g (mask)with the structuring element S. As with the structuring ele-ment in dilation and erosion operations, the characteristics ofthe marker image determine the processing performed in mor-phological reconstruction. We denote opening by reconstructionas:
Rg( f ) = Rg(g�S) (6)
The opening by reconstruction permits to discard all the imagecomponents that are smaller than a specific size limit (given bythe size of the structuring element) and restore the contours ofthe elements that are not totally erased by the selection.
4 A scheme to improvement of JPEG 2000
The purpose of this section is to show how one can improvethe performances of JPEG2000 (lossy mode) by includingin the scheme, a prior preprocessing phase. The main ideaconsists in distributing the total compression ratio, betweenthe low- and high-frequency sub-images. This phase requiresa preliminary decomposition stage and uses different codersalong with different assigned bit-rates [12]. By consideringthe fact that the information can be distributed in low andhigh frequency [17], we used two metrics to evaluate the qual-ity of the reconstructed image, namely the PSNR and SSIM[18–20].
The distortions of the global information are measured by aPSNR at low spatial frequency, and the distortions of the localinformation are measured by SSIM at high spatial frequency.Therefore, in order to describe the visual quality of the recon-structed image, these two measurements are combined using aproposed metric, denoted here PSNRNew. Using this approach,we will notice that a better visual quality is achieved com-pared with a direct compression scheme using the same globalbit-rate.
More specifically, low-frequency sub-image can be obtainedby smoothing the source image using the filtering by recon-struction. Similarly, high-frequency sub-image corresponds tothe detailed information on an image and can be easily obtained
by a simple subtraction of the low-frequency sub-image fromthe original image.
Figure 3 shows the principle of this decomposition. For agiven image I , and a structuring element S, the smoothed versionof the image by a structuring element S is obtained by openingreconstruction. As specified by the formula (4), it can be definedas:
ILow = RI (I �S) (7)
IHigh = I − ILow (8)
By choosing different compression ratios for both the low-frequency sub-image and the high-frequency sub-image (Fig. 4),one can compress the low- and high-frequency parts of an imageby:
CompLow = Ψ (ILow, α) (9)
CompHigh = Ψ (IHigh, β) (10)
where ψ is the compression operator, CompLow, CompHigh, α
andβ correspond, respectively, to the compressed low-frequencysub-image, high-frequency sub-image, bit-rate for low-fre-quency sub-image and the selected bit-rate for the high-frequency sub-image. Similarly, we can obtain the recon-structed image for low-frequency sub-image (respectively, high-frequency sub-image) using the decompression operator, whichis the inverse of the compression operator. The decompressionoperator can be obtained using the following equations:
IRECLow = Ψ−1(CompLow, α) (11)
COMPHighIHigh
COMPLow
ββ (bpp)
α (bpp)
ILow
JPEG2000 Encoder
JPEG2000 Encoder
Fig. 4 Compression of low and high-frequency sub-images at differentbit-rates by JPEG2000 encoder
Quality measurementof
reconstructed imageIREC
IRECHigh
IRECLow
COMPHigh
ββ (bpp)
α (bpp)
COMPLowJPEG2000
Decoder
JPEG2000Decoder
Fig. 5 Proposed reconstruction
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IRECHigh = Ψ−1(CompHigh, β) (12)
The original image can be reconstructed by summing these twosub-images. The proposed reconstruction is illustrated in Fig. 5.
4.1 Proposed image quality metrics
In order to enhance the visual quality of reconstructed image,we have used an analytical relation between PSNR and SSIMindex. Given a reference image f and a test image g, both ofsize M × N , the PSNR between f and g is defined by:
PSNRn,m = 20 log10
((2B − 1)√
MSEn,m
)(13)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10
0
10
20
30
40
50
60
SSIM
PS
NR
New
(dB
)
σfg
=400
σfg
=100
σfg
=1
Fig. 6 Variation in the PSNR versus the SSIM for different fixed valuesof σ f g : theoretical situation
0.68 0.7 0.72 0.74 0.76 0.78 0.826.4
26.6
26.8
27
27.2
27.4
27.6
27.8
SSIM
PS
NR
New
(dB
)
Fig. 7 Variation in the PSNR versus the SSIM for the image ‘18’ fromKodak dataset: experimental situation
where
MSEn,m = 1
M.N
M−1∑i=0
N−1∑j=0
∥∥∥ f (i, j)− g(i, j)∥∥∥2
(14)
The PSNR value approaches the infinite as the mean squarederror (MSE) approaches zero. This shows that a higher PSNRvalue provides a higher image quality. At the other end ofthe scale, a small value of the PSNR implies high numeri-
Tests achieved at different bit-rates, on image “18” from Kodak datasetPSNRNew1: between the source image and the reconstructed image JPEG 2000 (directly) at total bit-rate (α + β)
PSNRNew2: between the source image and the reconstructed image by the proposed methodα and β correspond, respectively, to bit-rate for low-frequency sub-image and the selected bit-rate for the high-frequency sub-image. (α+β = Rate)SSIM1: Index similarity between test image ‘18’ and the reconstructed image JPEG 2000 (directly) at total bit-rate (α + β)
SSIM2: Index similarity between test image ‘18’ and the proposed methodRow 03 of Table 1 indicates the optimal parameters obtained at rate = 0.011: PSNRNew1 = 26.42 db,SSIM1 = 0.695, PSNRNew2 =27.84 db,SSIM2 = 0.713, α = 0.009 bpp, β = 0.002 bpp, diameter of structuring element = 18 pixels, gain = 1.42 dB
cal differences between images. The SSIM index is a qual-ity metric used to measure the similarity between two images,and it is considered to be correlated with the quality percep-tion of the HVS [18,20]. It is proposed as a good candi-date to improve PSNR and MSE, which have been shown tobe inconsistent regarding human eye perception [18]. SSIMis considered by modeling any image distortion as a combi-nation of three factors, which are loss of correlation, lumi-nance distortion, and contrast distortion [18]. It is definedas
The first term in Eq. 15 is the luminance comparison func-tion, which measures the closeness of the two images meanluminance (μ f and μg ). This factor is maximal and equal to1 only if μ f = μg . The second term is the contrast compari-son function, which measures the closeness of the contrast ofthe two images. Here, the contrast is measured by the standarddeviation σ f and σg . This term is maximal and equal to 1 ifand only if σ f = σg . The third term is the structure comparisonfunction, which measures the correlation coefficient between thetwo images f and g. Note that σ f g is the covariance betweenf and g. The positive values of the SSIM index are within therange [0, 1]. A value equals to 0 means no correlation betweenimages, whereas a value equals to 1 means that f = g. The pos-itive constants C1, C2, C3 are used to avoid a null denominator,
’ 01’ ’ 02’ ’ 03’ ’ 04’
’ 05’ ’ 06’ ’ 07’ ’ 08’
’ 09’ ’ 10’ ’ 11’ ’ 12’
’ 13’ ’ 14’ ’ 15’ ’ 16’
’ 17’ ’ 18’ ’ 19’ ’ 20’
’ 21’ ’ 22’ ’ 23’
Fig. 10 Kodak image dataset
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Table 2 Objective comparison between the proposed method, the reference method [12] and JPEG 2000 (directly)
PSNRNew1: between the source image and the reconstructed image JPEG 2000 (directly) at total bit-rate (α + β)
PSNRNew2: between the source image and the reconstructed image using the reference [12]PSNRNew3: between the source image and the reconstructed image using the proposed methodSSIM1: Index similarity between test image and the reconstructed image using JPEG 2000 (directly) at total bit-rate (α + β)
SSIM2: Index similarity between test image and the reference [12]SSIM3: Index similarity between test image and the proposed method
if C3 = C2/2. The general form of the SSIM between signal fand g is defined as [18]:
SSIM( f, g) = (2μ f μg + C1)(2σ f g + C2)
(μ2f + μ2
g + C1)(σ2f + σ 2
g + C2)(19)
where C1 = (k1L)2, C2 = (k2 L)2 and k1 = 0.01 and k2 =0.03. L the dynamic range of the pixel values (typically this is2B −1). B is the bit depth used for noncompressed image coding(8 bpp).
To establish the relationship between the SSIM and thePSNR, we first derive the relationship between the SSIM andthe MSE, and then, we use that relation to link the SSIM to thePSNR. The MSE in Eq. 14 can be rewritten as:
Fig. 11 Comparison of performances versus bit-rates at low bit-rate, for the proposed, JPEG2000 and the reference method [12], using PSNRnew,and PSNR
σ f g = 1
M.N
M−1∑i=0
N−1∑j=0
( fi j − μ f )(gi j − μg) (24)
The PSNR defined in Eq. 13 can be rewritten as:
PSNRNew = 10 log10(255)2 − 10 log10
( a
SSIM+ b
)(25)
where
a = l( f, g)∗(2σ f g + C2)
b = (μ f − μg)2 − (2σ f g + C2).
Using l( f, g) = 1, which also means μ f = μg and C2 = 58.5,Eq. 25 is rewritten as:
PSNRNew =48.13 + 10 log10
[SSIM
(2σ f g +58.5) ∗ (1 − SSIM)
](26)
As indicated by Eq. 25, there is an interesting correlationbetween the PSNR and the SSIM. It shows that the values ofthe SSIM and those of the PSNR are not independent. Figure 6illustrates PSNR versus the SSIM, for various values of σ f g
in the interval[0 . . . 2552
]in Eq. (26). Figure 7 illustrates an
application example for the image ‘18’ from Kodak dataset.This novel image quality metric allows taking into considera-
tion both the global and local distortions existing in different spa-tial frequency components of the image. The global distortionis measured by the PSNR in the decomposed low sub-images,and the local distortion is measured by the SSIM metric in the
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decomposed high sub-images. We define the PSNRNew mea-surement of the low-frequency sub-image (respectively, high-frequency sub-image) to evaluate the visual influences of thelocal and global distortion. Finally, the image quality of recon-structed image is predicted by the fusion of both local and globalinformation using the PSNRNew metrics (Fig. 8). To obtain anoptimal PSNRNew, an algorithm has been implemented to assessthe visual image quality for the low bit-rate (Fig. 9).
4.2 An algorithm to optimize the proposed methodparameters
The proposed algorithm consists in finding the optimal alpha–beta and SSIM values as well as the diameter of the disk-shapedstructuring element that maximize a certain quality measure onthe reconstructed image.
It is used for the morphological reconstruction filtering dueto its higher smoothing capabilities and easy adaptation toany type of image. For implementation purpose, we have used“Jasper Software”, to compress and decompress test images.The following steps describe the operation of the proposedalgorithm:
Step 1: decompose the input image data into low and high-frequency sub-images.Step 2: for each decomposed image, computes PSNR for lowsub-images, and SSIM for high sub-images.Step 3: set a bit-rate as follows: RATE = αn + βn where αn =[0.01, . . . , 0.04] and βn = [0.04, . . . 0.01].Step 4: construction of a predefined set of structuring elementSk for k = 1 . . . .N .Step 5: each test image is filtered by opening by reconstruction,starting from the first structuring element in the set. The result-ing kth low- and high-frequency sub-images is iteratively com-pressed and then reconstructed by αn and βn for n = 1 . . . N .Step 6: PSNRNew of the reconstructed images is calculated andstructured into a K × N matrix by choosing k and n indices(Fig. 9).Step 7: PSNR of the same image compressed by JPEG2000(direct compression) and reconstructed at the RATE is cal-culated and then compared with the previously constructedPSNRNew matrix. The highest value of PSNRNew in the matrix,which is greater than the PSNR obtained from the direct com-pression at the RATE, has been selected.Step 8: the optimum structuring element size α and β valuesfor the tested image are extracted from the highest PSNRNew.
The results obtained by the proposed algorithm are summa-rized in Table 1.
5 Experiment results
In this section, we have considered 23 test original images fromKodak dataset (see Fig. 10). Dataset includes uncompressed768 × 512 grayscale images, with various statistical features.
Fig. 12 Performance comparison in terms of perceptual distortionmetric on zoomed Kodak image “01” at 0.007 bpp a reference image;b JPEG2000 with PSNRNew = 24.14 dB; c proposed method withPSNRNew = 24.30 dB, α = 0.005 bpp, and d = 20 pixels; d reference[12] with PSNRNew = 24.26 dB, α = 0.005 bpp
PSNRNew and PSNR are used to compare objectively at lowbit-rate, the performance of the proposed method with respectto both the reference one [12] and JPEG2000 (directly).
As shown in Table 2 and Fig. 11, it can be pointed out thatthe results obtained using the proposed method outperform thoseobtained by both JPEG 2000 (directly) and the reference method[12]. Moreover, Fig. 12 illustrates the visual effect of the imageKodak image “01”, highlighting best filtering result obtained bythe proposed method. Objectively, Fig. 11 illustrates the perfor-mance curves versus bite-rate, showing the superiority of thePSNRNew in comparison with other techniques [21].
6 Conclusion
In this work, we have presented a new scheme that allows animprovement in JPEG 2000 performances in lossy compressionmode. More specifically, morphological filtering by reconstruc-tion has been used. Based on two metrics, we have shown thatthe visual quality can be improved (by reducing the effect of arti-facts) compared with the direct use of JPEG2000, or with thereference method. From the experiment result, we have obtainedan optimal PSNRNew using a disk-shaped structuring elementfor image filtering, by opening reconstruction.
In terms of metrics, the study shown that a simple analyticalcorrelation exists between the PSNR and the SSIM. It appearsthat the values of the PSNR can be predicted from the SSIM andvice-versa. Moreover, we believe that the quality of the recon-structed image can be enhanced using other shapes of structuringelement that should be adapted to image features.
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