Composite Techniques Based Color Image Compression

C ompression for color image is now necessary for transmission and storage in the data bases since the color gives a pleasing nature and natural for any object, so three composite techniques based color image compression is implemented to achieve image with high compression, no loss in original image, better performance and good image quality. These techniques are composite stationary wavelet technique (S), composite wavelet technique (W) and composite multi-wavelet technique (M). For the high energy sub-band of the 3 rd level of each composite transform in each composite technique, the compression parameters are calculated. The best composite transform among the 27 types is the three levels of multi-wavelet transform (MMM) in M technique which has the highest values of energy (En) and compression ratio (CR) and least values of bit per pixel (bpp), time (T) and rate distortion ) R(D)). Also the values of the compression parameters of the color image are nearly the same as the average values of the compression parameters of the three bands of the same image


INTRODUCTION
In the color image, the spatial component correlation among the three bands red, green, and blue is significant.In order to get a good compression performance, the correlation among the three bands must be reduced by converting the color image into the de-correlated color space, Miry, 2009.
For three different kinds of images, standard Lena, satellite urban and satellite rural image, various statistical parameters of the image such as Rate Distortion, Kurtosis, symmetry and Skewness, are derived for Set Partitioning in Hierarchical Trees (SPIHT) compression scheme, they are derived for a fixed level and fixed rate of decomposition for the three kinds of images and they are used for explanation of the Peak Signal to Noise Ratio (PSNR) and Compression Ratio (CR).The results of urban images are the best for SPIHT compression scheme as compared with the satellite rural image, Nagamani, and Ananth, 2012.Abood, 2013 introduced three dimension two level, wavelet transform, multi-wavelet transform and hybrid (waveletmulti-wavelet) techniques.The parameters root-mean-square difference, energy retained, Peak Signal to Noise Ratio, entropy and compression ratio are measured for each 3-D two-level technique.According to these parameters, a comparison between these techniques is presented and the results illustrated that the three dimension two level hybrid technique is the best for image compression.Dhumal and Deshmukh presented image compression technique using Singular Value Decomposition (SVD) transform.This (SVD) can transform the matrix into product, which allows anyone to refactor the digital image into three orthogonal matrices.The using of the singular values of the refactoring allows representing any image with a set of decreased values, which can store the original image useful features, take less storage space in the memory, so it is used for image compression, Dhumal and Deshmukh, 2016.Sudhakar, and Sudha, 2011 introduced an efficient color compression technique i.e. higher compression ratio and better quality by using multi-wavelet transform and the embedded coding of the multi-wavelet coefficients through (SPIHT) algorithm.

COLOR IMAGE COMPRESSION
Images use either 24-bit or 8-bit color.In the case of 8-bit, the range of the pixel value is 0-255 (i.e.256 different colors).In the case of 24-bit, each pixel in the image uses 24-bit and each 8-bit in the 24-bit is used to represent three band colors red, green and blue (R, G, B).
For Images compression, the needing for efficient techniques is usually increasing because the images need large size of disk space so it is a big disadvantage during storage and transmission, Dutta, et al., 2012.

COMPRESSION PARAMETERS 3.1 Bit per Pixel (bpp)
The precision of a sample can be represented by a number of bits in the pixel; the higher precision value is better which represents the picture quality.Here the compression ratio is measured in terms of the bpp, Dutta, et al., 2012.

Computation Time (T)
The computation time is normalized and calculated by: where N 2 is the size of the image, and L is the number of the level, Dia, et al., 2009.

Energy (En)
Energy is the sum of squared elements in the image, Abood, et al., 2013:

Compression ratio (CR)
A logical way to measure how good the compression algorithm compresses an image is to look at the compression ratio which is the ratio of the number of bits that required to represent the image before compression to the number of bits that required to represent the image after compression, Sayood, 2006, so the ratio between the size before compression and the size after compression, Shini, et al., 2016:

Mean Absolute Error (MAE)
If ( ) is the original image and ( ) is the reconstructed image, then the Mean Absolute Error will be, Kumar, and Rattan, 2012:

Rate Distortion R (D)
Rate is the average number of the bits used in representing each sample value.Distortion is the measure of a difference between original image and compressed image.R (D) function is the lowest rate that while keeping the distortion equal to or less than D, the output can be encoded.

TRANSFORMATION
In image compression, it is desirable to select the useful transform that reduces the size of resultant image as compared to the original image, Kharate, and Patil, 2010.If the sampled functions have discrete time and frequency then wavelet transform used is so called Discrete Wavelet Transform (DWT).This technique is based on sub-band coding algorithm.Compression is based on the approximation of regular signal components using the filter coefficients and detailed coefficients, Hamsalakshmi, and Kalaivani, 2016.
Stationary wavelet transform (SWT) is designed to overcome the lack of the translationinvariance of the DWT.The SWT is a redundant scheme, as its output in each level contains a similar number of samples as in the input, Saminu, and Özkurt, 2015.
Algorithms based on the wavelets have been worked well in the image compression.Scalar wavelets don"t possess all properties wanted for a better performance in the compression but "Multi-wavelet" overcomes this problem because it possesses multi-filters, Radhakrishnan, and Subramaniam, 2008.Theoretically, Multi-wavelets should work even better because of the extra freedom in the multi-filters" design, Miry, 2008.

THE PROPOSED ALGORITHM
Fig. 1 shows the block diagram of the overall proposed system, which is illustrated as follows: 1. Input color image, in the other side input the same color image but with isolated bands i.e. taking the red, green and blue bands of the same color image.2. Convert the color image, red, green and blue bands to gray image.3.As a preprocessing, convert each gray image to a double-precision and resize them to be of size (1024*1024).4. Input the processed images to three composite techniques S, W and M as shown in Fig. 2.There are " 3 n " different cases, where " 3 " refers to 3-level composite stationary wavelet transform (s), 3-level composite wavelet transform (w), and 3-level composite multi-wavelet transform (M), while " n " refers to the number of level.The three composite techniques are: a. Composite technique S, which contain (3 n-1 ) different cases of a 3-level composite transform of s, w and M, i.e. sss, ssw, ssM, sws, sww, swM, sMs, sMw and sMw.For example, in swM, the 1 st level is "s", the 2 nd level is "w" and the 3 rd level is "M".Wavelet transform is applied to the high energy sub-band of "s" and multi-wavelet transform is applied to the high energy sub-band of "w".b.Composite technique W, which contain (3 n-1 ) different cases of a 3-level composite transform of w, s and M, i.e. www, wws, wwM, wsw, wss, wsM, wMw, wMs and sMM.For example, in wsM, the 1 st level is "w", the 2 nd level is "s"and the 3 rd level is "M".Stationary wavelet transform is applied to the high energy sub-band of "w" and multi-wavelet transform is applied to the high energy sub-band of "s".c.Composite technique M, which contain (3 n-1 ) different cases of a 3-level composite transform of M, s and w, i.e.MMM, MMs, MMw, MsM, Mss, Msw, MwM, Mws and Mww.For example, in Msw, the 1 st level is "M", the 2 nd level is "s" and the 3 rd level is "w".Stationary wavelet transform is applied to the high energy sub-band of "M" and wavelet transform is applied to the high energy sub-band of "s". 5.For each high energy sub-band of the 3 rd level in each composite technique, the compression parameters are calculated according to Eq"s.1, 2, 3, 4, 5 and 6. 6.The final decision is taken for the techniques that have best compression.

RESULTS AND DISCUSSION
In all tables, the best values are written as red values and the suffix " av " in S av , W av and M av refers to the average of parameters" measurements of the images in the composite S, W and M techniques respectively.Table 1 shows the results of the compression parameters for the color images in the S composite technique, the sMM composite technique has the least values of Bpp, T (in second) and R(D), and has the highest values of En and CR, while ssM has the least value of MAE (3.7004 e-16).Fig. 3 illustrates the chart of these results.
Table 2 shows the results of the compression parameters for the color images in the W av composite technique, the wMM composite technique has the least values of Bpp, T and R(D) (0.0078, 0.0006, 4.5269) respectively, and has the highest values of En and CR (5.247 and 1024) respectively, while WWW has the least value of MAE (2.8291 e-16).Fig. 4 illustrates the chart of these results.Table 3 shows the results of the compression parameters for the color images in the composite M av technique, the MMM composite technique has the least values of Bpp (0.0020), T (0.0001) and R(D) (2.7253), has the highest values of En (41.6531) and CR (4096), while MWW has the least value of MAE (0.6679e-15).Fig. 5 illustrates the chart of these results.
Therefore, using multi-wavelet in the image compression improves the image reconstruction, image compression and decrease the computation time, so, for good compression in the color image the composite techniques sMM, wMM and MMM must be used.
Tables 4, 5 and 6  Therefore, for good compression in the color image of isolated bands the composite techniques sMM, wMM and MMM must be used, so for either color image or color image of isolated bands the composite techniques sMM, wMM and MMM can be used for good compression.
Fig. 12 shows samples of database images used in this work.

CONCLUSIONS
In this study, three composite techniques S, W and M based color image compression is implemented.For color image and color image of isolated bands the best composite technique among the 27 types is the MMM in M technique which has the highest values of En and CR which are 41.6531 and 4096 respectively, and least values of bpp, T and R(D) which are 0.002, 0.0001 and 2.7253 respectively for color image.Also it is concluded that the values of the compression parameters of the color image are nearly the same as the average values of the compression parameters of the three bands of the same image.
This work is useful to achieve image with high compression, no loss in original image, better performance and good image quality.As future works, one can use these composite techniques in speech compression, speech recognition and image recognition to show which technique is the best that gives a high speech compression performance, speech recognition performance and image recognition performance.

REFERENCES
show the results of the compression parameters for the color (red, green and blue bands) images in the S av composite technique, where RS av , GS av and BS av refer to the average of parameters" measurements of the images in the red, green and blow bands of S technique, all bands have the same bpp, T and CR in each composite technique (i.e., in RS av , GS av and BS av , sss has bpp (8), T (0.6562) and CR (1)).The sMM composite technique has the least values of bpp, T and R, and has the highest values of En and CR, while ssM has the least value of MAE (3.7122e-16).Fig. 6 illustrates the chart of the compression parameters for the color (red-band) images in the S av composite technique.Tables 7, 8 and 9 show the results of the compression parameters for the color (red, green and blue bands) images in the W av composite technique, all bands have the same bpp, T and CR in each composite technique (i.e., in RW av , GW av and BW av , www has bpp (0.1250), T (0.0102) and CR (64).The wMM composite technique has the least values of bpp, T and R(D), and has the highest values of En and CR, while www has the least value of MAE (2.0579e-16).Fig's.7 and 8 illustrate the charts of the compression parameters for the color (red and blue bands) images in the W av composite technique.Table 10, 11 and 12 show the results of compression parameters for the color (red, green and blue bands) images in the M av composite technique, all bands have the same bpp, T and CR in each composite technique (i.e., in RM av , GM av and BM av , MWW has bpp (0.0313), T (0.0025) and CR=256).The MMM composite technique has the least values of bpp, T and R, and has the highest values of En and CR, while Mww has the least value of MAE (5.764e-16).Fig's.9, 10 and 11 illustrate the charts of the compression parameters for the color (red, green and blue bands) images in the M av composite Technique.

Figure 1 .
Figure 1.Block diagram the proposed system.

Figure 2 .
Figure 2. Three composite techniques S, W and M.

Figure 4 .
Figure 4. Chart of compression parameters for color W av Technique.Table3.Compression parameters for color M av Technique.

Figure 5 .
Figure 5. Chart of compression parameters for color M av technique.

Figure 8 .
Figure 8. Chart of compression parameters for color BW av technique.

Figure 10 .
Figure 10.Chart of compression parameters for color GM av technique.Table 9. Compression parameters for color BW av technique.

Table 1 .
Compression parameters for color S av technique.
Figure 3. Chart of compression parameters for color S av technique.

Table 2 .
Compression parameters for color W av Technique.

Table 4 .
Compression parameters for color RS av technique.

Table 5 .
Compression parameters for color GS av Technique.

Table 6 .
Compression parameters for color BS av Technique.

Table 7 .
Compression parameters for color RW av Technique.Chart of compression parameters for color RM av Technique.

Table 8 .
Compression parameters for color GW av Technique.

Table 9 .
Compression parameters for color BW av technique.

Table 10 .
Compression parameters for color RM av Technique.

Table 11 .
Compression parameters for color GM av Technique.

Table 12 .
Compression parameters for color BM av Technique .
Figure 12.Samples of database images.