A Coefficient Density Adaptive Quantization Approach for Lossless Color Image Compression
Dr.P.Suresh Babu Dr.S.Sathappan
Associate Professor & Head Associate Professor
Department of Computer Science Department of Computer Science Bharathidasan College of Erode Erode Arts & Science
Arts and Science, College, Erode
Abstract
Lossless color image compression is considered to be the efficient compression scheme as it primarily preserves the image sharpness without the loss of vital elements. In our previous works, we have introduced MHPCA for encoding the chrominance images Cuand Cvand MHPBLI for encoding the luminance channel Y. Then the Context adaptive arithmetic coding is applied to achieve efficient lossless image compression. In the MHPBLI coding scheme, a division of 8×8 non overlapping blocks is made in the luminance channel Y. After that blocks are classified into black, white and gray blocks and then are quantized and encoded. The performance of this approach can further be improved by applying a suitable transform to the blocks before quantization. In this paper, Coefficient Density Adaptive Quantization (CDAQ) approach is introduced to improve the image quantization for achieving lossless color image compression. In this work, the Discrete Cosine Transform (DCT) is applied to improve the performance of image compression performance. For efficient division of the image into 8×8 chunks, DCT is applied in JPEG-LS based compression schemes. Then the blocks are categorized and the density functions of DCT coefficients for the gray and black blocks are determined globally and also locally from which the magnitude of each DCT coefficient is determined. By determining the magnitude of the density of coefficients, the images are adaptively quantized which preserves the quality of the image pixels. Result of the CDAQ shows that it provides better performance than earlier works and can enhance the image compression efficiency.
Keywords: Reversible Color Transform, MHPCA, MHPBLI, CDAQ approach, Discrete Cosine transform
1. Introduction
The main aim of data compression is to reduce the storage and transmission problems that occur in various fields handling the multimedia contents. Image compression schemes are developed to reduce the high resolution images in order to cope up with the low resolution supported devices. The major challenge in the image compression process is preserving the class of the image and sharpness of the image even after decompression. Though many compression schemes have been introduced in the recent past to achieve efficient image compression, the flaws in the performance led to image degradation. For instance, the prediction methods employed in the image compression schemes mostly depends on the raster search prediction which are inefficient in the high frequency regions. As in previous hierarchical prediction methods applied only pixel interpolation is made, the raster search prediction problem cannot be completely resolved. Seyun Kim et al [1] proposed a scheme for the efficient compression of the images with prediction in hierarchical manner. The proposed scheme called as HPCA which effectively overcomes the raster search prediction problem by utilizing the border
directed predictor and context adaptive model. The chrominance images Cu and Cv are encoded using the HPCA coding while the luminance channel Y is encoded using the lossless gray scale coders.
Lossless image compression, as the name suggests, gives competent image compressions without the losing vital elements. Lossless encoders are utilized for encoding the luminance channel Y as the statistics of the chrominance images and the luminance images differ from each other. CALIC, JPEG 2000, JPEG-LS are some of the well known lossless image coders. Lossless image compression coders utilize compliant transforms for the maintenance of the quality of the images even after compression. For example, JPEG 2000 employs discrete wavelet transform (DWT) and JPEG-LS employ discrete cosine transform (DCT) [2]. DCT is best compliant to the JPEG-LS when the image has 8×8 blocks division. Selective quantization approach can be much helpful in the image quality preserving as it adaptively adjusts the quantization scale for the informative pixels higher than the non-informative image pixels.
Efficient image compression can be achieved when best suitable encoding schemes are utilized. In our previous work, we have introduced MHPCA [3] inorder to effectively encode the chrominance images in the YCuCv color scheme. The approach included the vertical, horizontal and diagonal pixels of the images as predictors in the encoding phase for effective preserving of the sharpness of the image even after image compression. But still the luminance channel Y has not been encoded efficiently. Hence in another work, we introduced MHPBLI [4] for effective encoding of the luminance image. The approach is based on a block based encoding using the hierarchical prediction. Then the images are quantized and encoded. But still the efficiency of image compression can be improved if the quantization is performed adaptively.
Hence in this paper, we are introducing Coefficient Density Adaptive Quantization (CDAQ) approach which quantizes the blocks of the image adaptively based on the density of the DCT coefficients. Initially after dividing the image into blocks, the gray and black blocks are transformed into frequency domain using discrete cosine transform.
Then the density values of the DCT coefficients for each block is determined locally and also globally. Then the magnitude of the density functions is calculated using the local and global values. Finally the blocks are quantized adaptively based on the density of the DCT coefficients. Thus the quantization performance can be improved which in turn improves the performance efficiency of image compression.
The rest of the paper is prepared as follows: Section 2 describes the previous researches related to the hierarchical prediction and block based JPEG LS and their features. Section 3 describes the proposed methodologies. Section 4 discusses the performance evaluation of the methodologies. The conclusion is given in the Section 5.
2. Related Works
Konstantinos Konstantinides et al [5] proposed a JPEG variable quantization technique to provide flexible compression of the images. The approach uses DCT for the transformation of images into 8×8 blocks. From the divided blocks, the JPEG variable quantization automatically adjusts the quantization scaling factors to make sure the text blocks are compressed at higher quality than the image blocks. The blocks with higher activity are scaled with low scaling while the lower activity blocks are scaled with high scaling factors. This improves the image compression performance. The drawback with the variable quantization is that the introduction of additional overhead bits in the code bit stream.
Julio Pons et al [6] presented a JPEG image coding with the adaptive quantization to provide better results in image compression. The JPEG image coding method reduces the blocking effect that is brings in the JPEG-encoded images by somewhat adjust the quantization algorithm of the JPEG standard. The quantization algorithm decreases the
blocking effect at the cost of rising blurring, as long as in this way images with improved intention and skewed quality than those get with the standard JPEG at the similar rate.
The technique only adds somewhat the computational price of the quantization algorithm used in a standard JPEG encoder. Although there are additions to JPEG that allows changeable quantization by scaling the quantization array by a dissimilar issue for each block of coefficients, most of profitable JPEG decoders do not hold this extension. The algorithm uses a special approach of using the adaptive quantization that is well-matched with the baseline JPEG, so any JPEG decoder can decode the compressed images.
Ingo Bauermann et al [7] presented an algorithm to provide improved lossless compression of the JPEG images. The algorithm uses DCT to transform the images to frequency domain and divides them into blocks. It employs sorting transform for reducing the inter-block redundancy which is not subjugated by the standard JPEG compression algorithm. The main proposal is to cluster the coefficients with similar statistics and encode those clusters in the same context adaptive arithmetic coding. The neighborhood properties and corresponding contexts are determined by the sorting transformation. The only disadvantage of this come up to is that the blocks cannot be decoded individually after the coefficient grouping.
Ichiro Matsuda et al [8] presented a lossless re-encoding of the JPEG images using the block-adaptive intra prediction. In this system, H.264-like block-adaptive intra prediction is applied to use inter-block correlations of quantized DCT coefficients stored in the JPEG file. This prediction is performed in spatial domain of each block, but the corresponding prediction residuals are calculated in DCT domain to make sure lossless rebuilding of the original coefficients. The block-based classification is executed to allow precise modeling of probability density functions (PDFs) of the prediction residuals. A multi-symbol arithmetic coder beside with the PDF model is used for entropy coding of the prediction residual of each DCT coefficient. The drawback with this scheme is that the adaptive intra prediction technique does not perform efficiently in all benchmark tests.
Ramakrishna Kakarala et al [9] presented a method for the block-adaptive quantization to improve the performance of the baseline sequential JPEG compression scheme. The approach uses adaptive quantization based on the region of interests (ROI) in the divided blocks. Thus the approach signals the decoder for the ROI coding of the subject and the background of the image. This adaptive method makes use of empty slots in the Huffman tables. This approach improves the image compression especially while using the ROI coding.
Nejat Kamaci et al [10] presented an effective classification method for each class to get better the statistical replica considerably without an important difficulty enlarge. The proposed method also uses a two-class based move toward in which one class is calm of very low detail blocks, and the other class is calm of high texture blocks and blocks with boundaries. Though the move toward is proposed for the video coders, it uses only the simple mathematically simpler statistical distributions which can ensure the correctness of real statistical distribution of the change coefficients.
Francesc Auli-Llinas [11] presented a motionless probability model for bit plane image coding using the determination of the narrow average of the wavelet coefficients.
Proposed stationary probability model is organized in image coding systems that use bit- plane coding jointly with context-adaptive arithmetic coding. In this approach, the discrete wavelet transform is utilized for the JPEG2000 compression standard. The projected approach assumes motionless statistical performance for emitted signs.
Probabilities are resolute using the instant neighbors of the at present coded coefficient.
3. Methodologies
The projected method is based on the development of Block-based improved JPEG-LS coding by using Discrete Cosine Transform (DCT).
The input RGB images are pre-processed to remove the noises and then they are altered into YCuCvcolor space using the RCT. Transformed images consist of luminance image Y and chrominance images Cuand Cv. In order to efficiently compress the image, the Y, Cu and Cv components of the image has to be encoded in a best suitable manner. In our previous works, we have introduced MHPCA for better encoding of the chrominance images Cu and Cv. Similarly MHPBLI has been introduced for the encoding of the luminance channel Y. The MHPCA and MHPBLI coding schemes provided efficient performance but still there is a scope for improvement.
From our continuous research, it is found that the performance of the MHPBLI coding can be further improved by including the process of discrete cosine transform in the blocks of Y luminance image. Especially the black and gray blocks are transformed by applying DCT and then quantized based on the DCT coefficients. The DCT coefficients of the blocks are determined globally for both the blocks and also individually for the same blocks. Based on the global and local values the individual magnitude of each DCT coefficients can be estimated. The magnitude of a DCT coefficient is estimated as the arithmetic mean of magnitude of global and local values. Depending upon the density of the DCT coefficients, each block is quantized adaptively. Then Context Adaptive Arithmetic Coding can be applied on the quantized images for efficient lossless image compression.
Block Classification & Representation
The JPEG images are divided into non-overlapping 8×8 blocks as shown in Figure 3.1 in order to apply effective coding schemes. Then the blocks are transformed into the frequency domain using the DCT. The output of the DCT is then quantized and coded. In this approach, the divided 8×8 blocks are categorized into black, gray and white blocks based on the edge content and the color variation of each blocks [4].
A sample x of the luminance image Y is taken and categorized into two regions: featured (gradated, structural) and non-featured regions. The categories are fixed using the location of the edge pixels and the color variation of the blocks. For determining the edge pixels, simple edge detection algorithm is utilized. Using the edge detector, the blocks with border pixels are categorized as systemic blocks. Next the color variance is founded with the remaining blocks.
Color variation v is given by
(3.1) In the above equations R, G. B are the components of color and x, y are the pixel indices.
, , are the mean values of the color components in a pixel. They are given as (3.2) (3.3) (3.4) Where the size of the non-overlapping block is given by S×S. i.e. S=8.
Luminance image Y
Region Classification &
Block division
Featured
blocks Non-featured
blocks
Gradated
blocks Structural
blocks Reserved
Exemplars
Black
blocks Gray
blocks White
blocks
Figure 3.1 Block Classification
The chunks with the color difference smaller than a pre-defined threshold VTis termed as gradated blocks while the rest of the blocks are non-featured blocks.
The gradated blocks are present in the region where the hue changes smoothly and the gradation patterns are formed by the within the gradients. The parametric allocation of the gradated region can be given as
(3.5) The gradient g in the discrete form is represented as piecewise smooth form as given below.
(3.6) (3.7) Where is a division of an image domain and L is the number of sub- areas.
Similarly, structural region blocks have boundaries inside which means the important features are the border location and border differences. An edge can be modeled as a Gaussian function.
(3.8)
I(r) denote the pixel strength whose space to the adjacent border pixel is r. are the 2 intensities at a convinced space away from the 2 sides of the edge. s(r) is a function and is the scale of the Gaussian kernel.
Using edge function, the parametric division of the systemic region is
(3.9) In the above equation e(x,y)=0 denotes the border position and v(e) is the border variation. The border position can be found by the border detection during the area classification at the pixel plane while the border variation is estimated at the block level taking into account the reliability along the boundaries as well as the encoding competence.
Edge variation in structural block can be given as
(3.10) Where and are the differences of pixel assessment on the 2 sides of the edge without including the edges itself.
Then the blocks are categorized. Some of the featured blocks are reserved as exemplar blocks and the other featured blocks are then categorized into black, gray and white blocks. The blocks other than the exemplars are called as dropped blocks. The dropped graded blocks are categorized as black blocks. The dropped structural blocks with zero edge variation are categorized as white blocks and those with one edge variation are categorized as gray blocks.
Algorithm 1: Block classification Input: Luminance image Y Output: Block classification Step 1: Divide image into 8×8 blocks
E = Exemplar blocks Step 2: Region & Block Classification
Estimating the edge content If (block contains edge pixels)
Structural blocks
Determine edge variation v(e) using equation (3.10) If (v(e) =0)
White blocks W Else if (v(e) = 1)
Gray blocks G End if
Else if
Determine Color variation V using (1) If (V < VT)
Gradated blocks = Black blocks B Else Non-featured blocks
End if End if
DCT Coefficients
DCT is applied in the black and grey blocks before quantization. In JPEG image formats, a 64 DCT coefficients is generated with each 8×8 block of pixels. An 8×8 block of the image f(x,y) pixels of DCT coefficients F(u,v) is given by the general DCT representation.
General DCT representation is given by
(3.11)
Where
(3.12) For each block, the DCT coefficient can be expressed as
(3.13)
Where 0 ≤ u, v ≤ 7 and and ; u= 1,……,7.
By determining the DCT coefficients of each block, the adaptive quantization can be achieved. The density function of the DCT coefficients can be given by the Laplacian probability density function (PDF) model [12].
After applying DCT for each 8×8 sub-block, an 8×8 block of coefficients are generated.
Each of the 64 coefficients is treated as distinct random variable across the multiple blocks of the image. The arrangement of 8×8 coefficient block is shown in figure 3.2.
,0)(0 (0
,1) (0
,2) (0
,3) (0
,4) (0
,5) (0
,6) (0
,7) ,0)(1 (1
,1)
,0)(2 (2
,2)
,0)(3 (3
,3)
,0)(4 (4
,4)
,0)(5 (5
,5)
,0)(6 (6
,6)
,0)(7 (7
,7) Figure 3.2. 8×8 DCT coefficient block
Mode is a term used to represent one of the 64 coefficients at a specific location in the block. Here (0,0), (1,1), etc are called as modes. The DCT coefficient is categorized into DC and AC coefficients. The mode (0,0) is called as DC coefficient as the DCT coefficient at (0,0) is the average of the level shifted pixel values in the block. It has been empirically proved in the recent past that the PDF of the DC coefficient is much different from the AC modes of the DCT coefficients. The coefficients at modes other than (0,0) are called as AC coefficients, have PDF that are very similar to each other. Hence naturally the AC coefficients are taken for the image compression.
Although many PDF models are used for determining the PDF functions, the Laplacian model is considered to be the simplest and most common model. The PDF of AC DCT coefficients can be given as
(3.14) Where is the mean of the distribution and b is the shape control parameter, related to the variance of the distribution.
Using the equation, the density is determined for each of the AC coefficient block and then the local value is calculated for individual blocks while global variable for the black and gray blocks together.
Local and Global value Estimation
Let the PDF of coefficients within the same block are given as p(X) based on the equation (3.14). The purpose of the probabilities for bits from X considers the information regarding its area (Xn). The approach considers N=4 instant neighbors of X to replica the probabilities. The magnitude of the coefficient is estimated through the magnitude of its neighbors. The local average is the arithmetic mean of the neighbors’ magnitude. It is estimated by
(15) The condition that is needed to satisfied is that the PDF X is correlated with . This can be proved by computing the marginal PDF for which is denoted as . The major point in considering is that its value is almost zero which proves that most of the coefficients have similar magnitude to its local average. This can be efficient in developing probability models based on and . But as is typically characterizes zero-magnitude coefficients, disguising the fewer recurrent coefficients that have bigger magnitudes. This is a error for the probability model since it prevents the determination of dependable probabilities which can be overcome by globally determining the density of coefficients within the blocks. The global PDF for Xngiven X can be determined as
(3.16) Where m can be determined by
(3.17) By determining the local and global values of the DCT coefficients, the magnitude of each DCT coefficient can be determined. The magnitude of a DCT coefficient is predictable as the arithmetic mean of the magnitude of global and local values. The transformed blocks are then quantized using the coefficient density adaptive quantization.
The level of quantization depends on the density of the DCT coefficient of each block.
Coefficient Density Adaptive Quantization
The process of coefficient density adaptive quantization is shown in Figure 3.3. Let yi be the input block taken for quantization. Yidenote the output block of DCT and YQedenote the quantized output block. Let q-scale > 0 be the scalar multiplier for the quantization matrix. It should be assumed that q-scale = 1.0 is a situation there is no scaling of the quantization tables Qe.
The important process of adaptive quantization is to distinguish the image regions by determining the activity measures [8]. The activity of the block can be measured by using the DCT data. Let Yi[k] be the elements of Yiwhere k=0,1,2,….63. Similarly YQMi[k] be the elements of Yiquantized using the quantization matrix QM.
(3.18) The activity measure can be estimated as Mi.
(3.19) After determining the activity measure, the relationship between the quantization scale and activity measure is needed to be determined to provide effective quantization. Thus the quantization can be performed and then the quantized blocks can be encoded using context adaptive arithmetic coding for efficient image compression.
The process of quantizing and encoding the DCT coefficients can be performed as given in the following pseudo code.
Step 1: Applying DCT for each block using equation (3.11) & (3.13) Step 2: Determining PDF of each block using equation (3.14)
Step 3: Compute Local value & global value of DCT coefficients using equation (3.15) &
(3.16)
Step 4: Apply Adaptive Quantization
Determining Quantization scale & activity measure using equation (3.19) Step 5: Applying context adaptive arithmetic coding on the quantized blocks
Thus the 8×8 blocks of image can be quantized adaptively based on the on the density of DCT coefficient of each block. This approach helps in achieving efficient image encoding which improves the image compression performance.
Figure 3.3 Coefficient Density Variable Quantization Approach
4. Results and Discussion
In this section, the proposed CDAQ Approach based Image compression is compared with the performance of the DCT-MSVQ [14], HPCA coding [1] with JPEG variable quantization method [8], MHPCA coding [3] and MHPBLI coding [4].
Performance evaluation is done using a set of parameters to estimate the efficiency of the proposed approach. The parameters are Bits per pixel (BPP), Compression ratio and Peak Signal-to-Noise Ratio (PSNR). By comparing the evaluation results, it can be proved that the proposed CDAQ approach based Image compression outstand the other compression schemes.
A) Bits per pixel (BPP)
BPP is defined as the number of bits of information stored per pixel of a given image. The more number of bits per pixel in an image ensures more number of colors can be represented but it increases the memory required to store and display the image.
8×8 Blocks DCT
Quantization Table QM
Quantizer
Computation of activity Mi
Compute Scale
Quantization Table Qe
Quantizer Yi
Yi
q-scale YQMi
Quantized blocks
05 1015
BPP
Images
Bits Per Pixel
HPCA MHPCA MHPBLI CDAQ Figure 4.1 BPP
Figure 4.1 shows the comparison of CDAQ approach based image compression with the performance of some of better existing schemes in terms of BPP. The images are taken along the x-axis and the BPP values are taken along y-axis. For the Barbara image, DCT- MSVQ has BPP value of 13.1, HPCA has 11.7, MHPCA has 8.9, and MHPBLI has 4.8502 while the proposed CDAQ approach has 3.3353. This shows that the proposed CDAQ approach based image compression has better performance interms of BPP values.
The numerical comparisons of both the existing and proposed methods in terms of BPP are shown in Table 4.1.
Table 4.1 BPP
Images HPCA MHPCA MHPBLI CDAQ
Barbara 11.36 09.75 4.85 3.34
Lena 09.87 08.43 3.92 2.97
Peppers 10.31 08.57 3.89 2.20
Vegetables 08.80 07.48 2.58 2.13
Room 12.10 10.41 4.25 2.33
Compression Ratio:
Compression ratio is described as the ratio of an original image and compressed image.
(20)
100 2030 4050
Compression ratio (%)
Images
Compression Ratio
HPCA MHPCA MHPBLI CDAQ
Figure 4.2 Compression Ratio
Figure 4.2 shows the comparison of CDAQ approach based image compression with the performance of some of better existing schemes in terms of compression ratio. The images are taken along the x-axis and the compression ratio in % is taken along y-axis.
For the Barbara image, DCT-MSVQ has compression ratio of 25%, HPCA has 27%,
MHPCA has 33%, and MHPBLI has 38.802% while the proposed CDAQ approach has 41.7694%. This shows that the proposed CDAQ approach based image compression has better performance interms of compression ratio.
The numerical comparisons of both the existing and proposed methods in terms of Compression ratio are shown in Table 4.2.
Table 4.2 Compression Ratio (%)
Images HPCA MHPCA MHPBLI CDAQ
Barbara 26.33 31.33 38.80 41.77
Lena 26.52 30.61 31.39 31.95
Peppers 29.00 30.00 31.15 35.25
Vegetables 09.40 13.45 20.66 26.19
Room 17.91 21.35 34.02 37.31
Peak Signal to Noise Ratio (PSNR):
Peak Signal to Noise Ratio is defined as the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation.
200 4060
PSNR
Images
PSNR
HPCA MHPCA MHPBLI CDAQ Figure 4.3 PSNR
Figure 4.4 shows the comparison of CDAQ approach based image compression with the performance of some of the better existing schemes in terms of PSNR. The images are taken along the x-axis and the PSNR is taken along y-axis. For the Barbara image, DCT- MSVQ has PSNR of 25.6, HPCA has 28, MHPCA has 28.1, and MHPBLI has 37.3556 while the proposed CDAQ approach has 41.7962. This shows that the proposed CDAQ approach based image compression has better performance interms of PSNR values.
The numerical comparisons of both the existing and proposed methods in terms of PSNR are shown in Table 4.3.
Table 4.3 PSNR
Images HPCA MHPCA MHPBLI CDAQ
Barbara
28.43 28.57 37.36 41.79
Lena
34.14 34.28 38.33 42.11
Peppers
31.84 32.28 38.49 42.25
Vegetables
32.38 32.61 38.82 42.17
Room