A proposed multi-image compression technique

Abstract

Image compression is a process that reduces memory space required to store an image. The image compression techniques are broadly classified into two categories a) Lossless technique b) Lossy technique. Lossy compression technique achieves higher result, but due to data loss it may cause spatial inconsistency, blocking artifact, quantization noise in the decompressed image degrading the image quality. Most of the existing compression techniques are applicable on single image separately. In this study an image compression method is proposed where multiple images of the same size are combined together and compressed to achieve higher compression ratio while keeping image quality as close as standard image compression techniques. Luminance channel of each image is compressed separately using Vector Quantization (VQ) algorithm while two chrominance channels, Cb and Cr of all images are combined into a three dimensional matrix that forms training vector. Clustering is applied on the training vector to get the initial color representatives. Thus, for the chrominance channels of n number of images, the proposed method generates one index matrix and one centroid matrix of size 256×2× n where 256 is the number of clusters. This centroid matrix contains one 256×2 dimensional centroid matrix for each individual image. This 256×2 matrix contains centroid of each cluster. The centroids of each and every cluster of an image are updated individually using optimization technique to get a better centroid (Cb, Cr) pair. This process updates the color representative pair of Cb and Cr further. This method has been applied on standard images in literature and images collected from UCID v. 2 color image database. Experimental results are analyzed in terms of PSNR and space reduction. Experimental results show that the proposed method achieves a higher compression ratio retaining almost similar image information as other standard lossy compression algorithm.

Keywords

Color image quantization de-correlated color space JPEG K-Means clustering lossless compression lossy compression optimization PSNR Vector Quantization YCbCr

1. Introduction

Image compression reduces the space required to store a digital image in storage media keeping resolution and visual quality of the reconstructed image as close as possible to the original image [1 –14]. Image compression techniques reduce the number of bits required to represent an image by taking advantage of the three basic data redundancies- a) Coding redundancy, b) Inter pixel redundancy and c) Psychovisual redundancy [13, 16]. Generally two types of image compression techniques are found in the literature-1) Lossless technique and 2) Lossy technique. In lossless compression [2 –4] technique, the amount of space reduction is less compared to the lossy techniques. Run length, Arithmetic coding, PiCture eXchange(PCX) [6] etc are some well-known lossless compression techniques. Lossy compression techniques give a high degree of compression, but due to data loss spatial inconsistency, blocking artifact, quantization noise may arise in the decompressed image. Vector Quantization [7 –13], JPEG [27 –31], GIF, Color Image Quantization [17 –24] are examples of lossy compression technique. Most of these image compression algorithms are applied on an individual image separately.

Vector Quantization (VQ) [7 –13] algorithm is an example of lossy image compression [4] technique. VQ is a very effective compression algorithm with high compression ratio. But blocking artifacts [28, 29] appear in the decompressed image. Sometime blocking artifacts become explicit in the decompressed image and the visual appeal of the decompressed image is affected seriously. In the literature, many attempts have been made to reduce the compression time for better codebook generations of VQ. S.D Thepade et al. [10] proposed a clustering algorithm for Vector Quantization using slant transform in 2013. D. K. Mahapatra and U. R. Jena [11] also proposed partitioned K-Means clustering based on hybrid DCT-Vector Quantization for image compression in 2013. In 2016, C. Karri [12] proposed a method for fast vector quantization using a Bat algorithm. In 2017, A. Hasnat et al. [13] proposed modified Vector Quantization method applicable on de-correlated color space where luminance channel is compressed using a different approach to further improve quality of the decompressed image.

Color Image Quantization (CIQ) [15 –24] is a lossy image compression technique [4] that decreases the number of color palette as low as possible in an image by maintaining the less amount of distortion so that the visual appeal of the regenerated image is very near to the original image. Color quantization is used in many image processing fields like compression, segmentation, texture analysis, watermarking, non-photorealistic rendering, detection, content-based retrieval etc. Designing optimal color pallet/code to retain crucial color information of the image is a major challenge in CIQ as data loss occurs in the process. Evolutionary algorithms such as PSO [22, 25], GA [25, 26] are applied to CIQ [15 –24] to further improve the color pallet. Freisleben and Schrader [15] proposed a quantization method by combining the evolutionary algorithm (EA) [23, 25] and a standard search strategy. Obtaining higher compression ratio is a major objective of CIQ [15 –24] while satisfying many criteria- i.e. minimization of information loss, less distortion, less complexity of algorithm etc.

JPEG [27 –31] is a lossy image compression technique and it stands for the Joint Photographic Experts Group. JPEG was designed specifically to discard information those human eyes cannot recognize. It works on frequency domain. JPEG also suffers from blocking artifact. In 2007 B. Oztana et al. [30] proposed a method to reduce blocking artifact from a JPEG compressed image where artifacts arise on block sides. In 2014 Jonathan Quijas [29] proposed a post processing technique to remove blocking artifact from a JPEG compressed image. In 2016 Zhangyang Wang et al. [31] proposed a method for fast restoration of JPEG compressed images which are mainly post processing technique to remove blocking artifact. In 2017, Jae Woong Soh et al. [32] proposed an image compression method based on Karhunen Lo‘eve Transform (KLT). This method is same as JPEG but instead of DCT, Image Adaptive Transform (IAT) approach (derived from the KLT) is used. They claimed that the method performs better than JPEG as IAT shows better result in the high bit region of the image. The method shows better performance for very high resolution images like 4K images only [31].

JPEG2000 [33] is an image compression standard developed in the year of 2000 by the Joint Photographic Experts Group (JPEG), part of the International Organization for Standardization (ISO). JPEG2000 uses Discrete Wavelet Transform (DWT) which gives high compression ratio and good quality of image than JPEG. JPEG2000 has significant advantage over JPEG where blocking artifacts are less visible but it requires more computational power to process. In 2015 M. M. Rahman et al. [33] proposed a technique to improve the JPEG2000 compression method by adding adaptive threshold. But in this technique coding algorithm is much more complex and computational needs are much higher.

Most of the compression algorithm compresses an image separately or individually. VQ, JPEG and JPEG2000 suffer from blocking artifact problem. These algorithms have an upper bound of space reduction also. Whereas CIQ achieves higher PSNR but the compression ratio is not comparable to VQ, JPEG or JPEG2000. This study proposes a multi-image compression method exploiting features of Vector Quantization [7 –13] and Color Image Quantization [15 –24] to achieve higher compression ratio. Proposed method works on de-correlated color space i.e. YcbCr [13], YUV, CIELAB [35]. This method compresses multiple images of the same size together. The luminance channels of all images are compressed separately using Vector Quantization algorithm. The other two chrominance channels Cb and Cr of each image first combined into a three dimensional matrix. The K-Means clustering algorithm is applied to generate one centroid matrix and one index matrix for the chrominance channels of all images (taken together). This step helps to achieve higher compression ratio. The centroid of each and every cluster of an image is updated individually using optimization technique again to get a better centroid (Cb, Cr) pair.

This proposed image compression method has been applied on several images collected from standard images available in literature and images from UCID v.2 [34] database.

The article is organized as- In section 2 brief discussion is given on existing methods- vector quantization, color image quantization and JPEG. Section 3 discusses proposed method. Section 4 gives an experimental result and its analysis. Section 5 concludes the article.

2. Related works

This section briefly discusses standard lossy image compression techniques below.

2.1. Vector quantization

Vector Quantization [7 –13] is a simple and lossy compression technique that achieves very high compression ratio. The steps of the algorithm are discussed below.

Step 1: VQ divides an image in several p × p blocks. One block forms one training vector x of size k where k = p × p. Thus a m number of training vectors are created for the complete image which is the training vector set.

Step 2: Generate a codebook containing an N number of codeword where each codeword vector is of size k using a standard codebook generation algorithm. Let the code vectors CB = {C₁, C₂, C₃, … C_N} in R^k; where R^k is the k-dimensional Euclidean space. This generated codebook is the representative of all the training vectors. So each training vector is mapped to one of the code vectors. Thus, there is an index array indicating specific training vector mapping to a specific code vector.

So the code vector and the index array are stored as compressed image. During the decompression procedure, a sub image of p × p is formed using the code vector indicated by the index array. Thus combining all the sub-image the decompressed image is constructed.

One important objective is to minimize the distortion between original image and reconstructed image during codebook generation process. Linde-Buzo-Gary (LBG) [13] algorithm is widely used in VQ for code vector generation.

A training vector, x_m = (x_i,1, x_i,2, x_i,3, … …, x_i,k) is a k dimensional matrix where m = 1, 2, 3, … ….., M. Let N is the number of code vector in the codebook and a code vector c_i = {c_i,1, c_i,2, ….. c_i,k}; where i = 1, 2, 3 … …, N. Let T = (x₁, x₂, x₃, …., x_k) be a training vector.

Let S_n be the encoding region associated with the code vector c_n. Let S = {S₁, S₂, S₃, ….., S_N} denotes the partition of the space if the source vector x_m in the encoding region S_n then approximation (Q (x_m)) is c_n given by Equation 1. $(Q (x_{m})) = c_{n} if x_{m} \in S_{n}$ (1) The average distortion is given by Equation 2. $D_{avg} = \frac{1}{M_{k}} \sum_{m = 1}^{m} {x_{m} - Q (x_{m})}^{2}$ (2) Where $e ∥^{2} = e_{1}^{2} + e_{2}^{2} + e_{3}^{2} + . . . . . . . + e_{k}^{2}$ . The design problem can be succinctly stated as follows: Given T, N, C & S such that D_ave is minimized.

If C and S are a solution to the above minimization problem, then it must satisfy the following two criteria.

Nearest neighbor condition $S_{n} = {{x : ∥ x - c_{n} ∥}^{2} \leq ∥ x - c_{n^{'}} ∥^{2};$ (3) $\forall n^{'} = 1, 2, . . . . . ., N}$

This condition says that the encoding region S_n should consist of all vectors these are closer to c_n than any of the other code vectors.

Centroid condition $c_{n} = \frac{\sum_{x_{m} \in S_{n}} x_{m}}{\sum_{x_{m} \in S_{n}} 1}; n = 1, 2, . . . N$ (4)

This condition says that the code vector c_n should be average of all those training vectors which are in encoding region S_n.

Vector Quantization [7 –13] uses block shaped vectors which cause blocks at vector boundaries. The standard VQ algorithm produces blocking artifacts in the decompressed image. Larger code vector size degrades quality of image but, required space to store the image decreases. If code vector size decreases, then space requirement increases but image quality improves. Therefore VQ [7 –13] not only produces perceptually distracting blocking artifacts, but there is limit of reduction of space requirement.

2.2. Color image quantization (CIQ)

Color quantization [15 –24] is a lossy image compression technique [4]. Color quantization works in two steps a) pallet design- selection of suitable number of colors generally 8 to 256 and b) pixel mapping- replaces each pixel color with the color in the pallet. CIQ can be formally defined as follows.

Given a set of N_S′ color where S′ ⊂ R^{N
_d} and N_d is the dimension of data space. The color quantization is mapped f_q : S′ → S″ where S″ is a set of N_S″ colors such that S″ ⊂ S′and N_S″ < N_S′. The objective is to minimize quantization error resulting from replacing a color c ⊂ S′ with its quantized value f_q (c) ∈ S″ [18, 24].

The steps of CIQ algorithm are shown below.

Step 1: All color triplets in the image are quantized using a standard clustering algorithm.

Step 2: a) Based on the analysis, the color lookup table is filled with values. b) The true color values are mapped to the values of the color table. The color values are mapped to the nearest color entries in the color table.

Step 3: Lastly, each and every pixel of original image is transformed to the appropriate index of the table.

2.3. Joint photographic experts group (JPEG)

JPEG [27 –31] stands for Joint Photographic Experts Group. It is a lossy image compression algorithm works in frequency domain. JPEG is designed specifically to discard information those human eyes cannot easily recognize. The steps of JPEG algorithm are shown below.

JPEG compression is typically measured as a percentage of the quality level. Quality factor (QF) plays very important role. The QF is a number that determines the degree of loss in the compression process. For a JPEG compression image with 100% quality factor has almost no data loss whereas with 1% quality data loss is huge and visual quality of the image is drastically affected. The steps of JPEG are discussed below.

Step 1: Transformation- Color images are transformed from RGB to a luminance/chrominance image.

Step 2: Down Sampling- The down sampling is done for colored component and not for luminance component. Down sampling is done or at a ratio 2 : 1 horizontally and 1 : 1 vertically (2 h 1 V).

Step 3: Organizing in Groups- The pixels of each color component are organized in groups of 8×8 pixels called “data units”. If number of rows or columns is not a multiple of 8, the bottom row and the rightmost column are duplicated.

Step 4: Discrete Cosine Transform- Discrete Cosine Transform (DCT) is applied to each data unit to create 8×8 map of transformed components. DCT involves some loss of information due to the limited precision of computer arithmetic.

Step 5: Quantization- Each of 64 transformed components in the data unit is divided by a separate number called its Quantization Coefficient (QC) and then rounded off to an integer. This is where information is lost irretrievably, Large QC causes more loss.

Step 6: Encoding- The 64 quantized transform coefficients of each data unit are encoded using a combination of RLE and Huffman coding.

Step 7: Adding Header- The last step adds header and all the JPEG parameters used and output the result.

2.4. JPEG 2000

JPEG2000 [33] is an International standard compression technology developed by the Joint Photographic Experts Group (JPEG), part of the International Organization for Standardization (ISO). It is a compression standard enabling both lossless and lossy storage. This technique improves the quality and compression ratios, but also requires more computational [33].

JPEG2000 is a wavelet based compression technology. It has many benefits over the JPEG format.

The steps of JPEG2000 are discussed below.

Step 1: The source image is decomposed into components. The image and its components are decomposed into rectangular tiles. The tile-component is the basic unit of the original or reconstructed image.

Step 2: The wavelet transform is applied on each tile. The tile is decomposed in different resolution levels.

These decomposition levels are made up of sub bands of coefficients that describe the frequency characteristics of local areas (rather than across the entire tile-component) of the tile component.

Step 3: Markers are added in the bit stream to allow error resilience.

Step 4: The code stream has a main header at the beginning that describes the original image and the various decomposition and coding styles that are used to locate, extract, decode and reconstruct the image with the desired resolution, fidelity, region of interest and other characteristics.

Step 5: The optional file format describes the meaning of the image and its components in the context of the application.

3. Proposed method

This section proposes an image compression technique where multiple images of the same size are combined together and compressed to achieve better compression ratio. It works on de-correlated color model like YcbCr [13], YIQ, Lαβ. In YCbCr color model luminance(Y) channel represents image information and two chrominance channels (Cb and Cr) carry only color information. As luminance channel carries vital image information, so the luminance channel is compressed separately using Vector Quantization algorithm to retain maximum image information. Two chrominance channels Cb and Cr are combined into a three dimensional matrix where × plane denotes number of chrominance channel of an image, y plane represents the number of pixels in an image and z plane represents number of images taken together for compression.Then clustering algorithm is applied on this three dimensional matrix and generates one index matrix and one code vector. In this work, K-Means clustering algorithm is applied. Thus for n × 2 number of chrominance channel of n images only one index matrix and one code vector are generated. The steps of the proposed method are explained below.

Algorithm 1:

Input- Multiple images of same size of r × c in de-correlated color model; Output: Compressed images.

3.1. Compression process

Step 1: Compress luminance channel of each image separately using Vector Quantization [7 –13] algorithm.

Step 2: From chrominance channels of an image a two dimensional matrix of size p × 2 is formed where p is the total number of pixels of the image i.e. p = r × c. In 1st and 2nd column of the matrix Cb and Cr values of respective pixels are stored. A two dimensional matrix is shown in Fig. 1. For n number images n numbers of matrices are formed.

Step 3: Stack all two dimensional matrixes of n number of images to form a three dimensional matrix where × plane denotes number of chrominance channels of an image(In this case two), y plane represents the number of pixels in an image and z plane represents number of images taken for compression. This three dimensional matrix is of size 2 × p × n where p represents the number of pixels of an image, n denotes number of images are taken for compression and 2 for two chrominance channels i.e. Cb and Cr. A three dimensional matrix formation is shown in Fig. 2.

Fig. 1

A two dimensional matrix where Cb and Cr color values of an image are arranged in 1^st and 2^nd column respectively.

Fig. 2

Three dimensional matrix(training data) formation: X plane represents Cb and Cr channels, Y plane denotes number of pixels of an image and Z plane represents number of images are considered for compression.

Fig. 3

A sample three dimensional matrix of four standard images Girl, Couple, Jelly beans and Girl in red shirt each of size 256x256 with actual Cb and Cr values.

Figure 3 shows a sample three dimensional matrix containing Cb and Cr values of four standard same size “Girl”, “Couple”, “Jelly Beans” and “Girl in red shirt” images. The size of each image is 256 × 256. In first two dimensional matrix Cb and Cr values of “Girl” image are stored in 1st and 2nd column respectively. In a similar way chrominance(Cb and Cr) values of “Couple”, “Jeally Beans” and “Girl in red shirt” images are stored in second, third and fourth matrices respectively.

Step 4: Then K-Means clustering algorithm is applied on the 3 dimensional matrix. A single training vector is considered by taking Cb and Cr values at same pixel position of all images in the 3D matrix. For n number of images n number of training vector are generated. A sample training vector formation by the first pixel position of n number of images is shown in Fig. 4. The K-Means clustering algorithm returns a index matrix image and a code vector matrix. The size of cluster index matrix is p × 1 where p is the total number of pixels of an image and size of code vector matrix is k × 2 × n where k represents the number of clusters and n is number of images.

Fig. 4

A single training vector: Cb₁₁ and Cr₁₁ stands for Cb and Cr values of 1st pixel of first image.

Fig. 5

Flowchart of the proposed multi-image compression technique.

Flowchart of the proposed method shown in Fig. 5.

Thus for two chrominance channels of n number of images, only one cluster index matrix and one code vector matrix are generated and required space to store n × 2 number of chrominance channels are decreased reasonably in this step.

Fig. 6

Centroid update process using Particle Swarm Optimization.

Step 5: In the next step, Particle Swarm Optimization (PSO) is applied to find better color representation for each cluster of a specific image. Each plane contains a code vector for a single image. By PSO each centroid ((Cb, Cr) pair) is updated individually by searching a better color representative. Initially all (Cb, Cr) pairs of original image of a cluster are selected using index matrix and code vector matrix. These color pairs of a cluster are considered as a search space for PSO to upgrade single centroid. The same process is applied on each and every cluster to update all centroids (code vectors of an image). The same process is repeated to update color code plane (Centroid plane) of all other images. This step results updated centroids that eventually minimize data loss further. Centroid updating procedure using PSO is shown in Fig. 6.

The same process is repeated to update code vector of all the images in the group. In this way three dimensional code vectors are updated second time. This step helps to retain better colour information.

PSNR of compressed “Girl” image before and after updating code vector using PSO and is shown in Table 1.

It can be seen from the Table 1, The updated code vector using PSO results in better PSNR. This updated 3 dimensional code vectors are finally stored.

Table 1

Effect of centroid update using pso on girl image

Image	Before update			Updated code vector using PSO
	Y	Cb	Cr	Y	Cb	Cr
Girl	34.66	34.74	30.75	34.66	35.99	31.81

Fig. 7

Flowchart of the proposed decompression algorithm.

3.2. Decompression process

The decompression process is a reverse process of compression. The steps are shown below.

Algorithm 2:

Input: VQ compressed luminance channels, one index matrix and one three dimensional code vector matrix of chrominance channels of all images.

Output: Decompressed blocking artifact reduced images.

Step 1: Luminance channel reconstruction

1. a. Luminance reconstruction steps

Luminance channel of each image is retrieved using code vector and index matrix of the respective image.

1. b. Blocking artifacts removal from luminance channel

Fig. 8

a) Original Image, decompressed images using b) Vector Quantization c) Color Image Quantization d) JPEG e) JPEG2000 f) Proposed Method(Cluster size cosidered for VQ and proposed method is 256, for CIQ it is 128. In case of JPEG algorithn, Quality Factor is set to 50 and 60 for “Girl”and Jelly Beans”, images respectively whereas in case of JPEG2000, Quality Factor is set to 30 and 40 respectively to keep image quality almost same as proposed method in terms of PSNR) **Here space requirments of proposed method for output images is much lesser than the VQ, CIQ, JPEG and JPEG2000 algorithms).

In decompressed image blocking artifacts may arise. The method proposed by B. Oztana et al. [30] in 2007 is applied to reduce these artifacts. Blocking artifacts appear at the edge area of the compressed image. These artifacts are reduced using the following steps.

i. Tag all pixels in luminance channel as edge/non-edge.

ii. Identify the region that belongs to q × q tile boundary. If the edge is not tagged then every pixel in boundary region and its next region are replaced by average value of previous and next pixel. If the edge is not found, every pixel belongs to row number multiple of q and q + 1 is replaced by the average pixel value of (q - 1) ^th and (q + 1) ^th row.

iii. Similarly the column number multiple of q and q + 1 are replaced by the average pixel value of (q - 1) ^th and (q + 1) ^th column.

Step 2: Chrominance channel reconstruction

By index matrix and code vector matrix chrominance channels (Cb, Cr) each image are retrieved.

Respective luminance and two chrominance (Cb, Cr) channels are combined together to reconstruct images. Decompression process is shown in Fig. 7.

4. Experimental result

The proposed method is implemented using MATLAB2017 and tested on standard images in the literature and color images of UCID.V2 [34] database. Using several YCbCr images multiple groups are formed where each group contains three to six number images of the same size. Amount of space reduction depends on the number of images in the group. More number of images increases space reduction, but image quality is degraded further.

Figures 8(a) to 8(f) show the original image, decompressed image using Vector Quantization, Color Image Quantization, JPEG, JPEG2000 and proposed method respectively.

The image quality of “Girl” and “Jelly Beans” decompressed images shown in Fig. 8(d) using JPEG, in Fig. 8(e) using JPEG2000 and decompressed images shown in Fig. 8(f) using proposed method almost same in terms of PSNR. But space reduction using JPEG are 82.74%, 78.96% respectively. The space reduction using JPEG2000 are 86.64%, 83.31% respectively whereas space reduction using proposed method are 93.09%, 93.49% respectively. Therefore storage space requirement using proposed method is less than the existing methods.

Table 2
Space reduction using VQ, CIP, JPEG, JPEG2000 and proposed method (taking six images at once) with 256 clusters

Image name Space for original image VQ CIQ JPEG (QF is set to keep PSNR almost same) JPEG2000 (QF is set to keep image quality (PSNR) almost same) Proposed method

Total Reduction % Total Reduction % QF Total Reduction % QF Total Reduction % Total Reduction %

Girl 196608 22659 88.47 40875 79.20 50 33917 82.74 30 26248 86.64 13567 93.09

Couple 196608 22271 88.67 41275 79.00 50 30925 84.27 40 32801 83.31 13419 93.17

Jelly beans 196608 20767 89.43 28916 85.29 60 41358 78.96 40 32801 83.31 12799 93.49

Girl in red 196608 22829 88.38 34169 82.62 50 35881 81.75 40 32801 83.31 13603 93.08

House 196608 21335 89.14 45865 76.67 50 33217 83.10 40 32801 83.31 12889 93.44

Tree 196608 21633 88.99 42951 78.15 55 60369 69.29 50 39354 79.98 13168 93.30

Tiffany 786432 54097 93.12 165422 78.96 45 111880 85.77 26 78678 89.99 32087 95.91

Baboon 786432 58172 92.60 183901 76.61 48 260460 66.88 50 157321 79.99 33914 95.68

F-16 Jet 786432 49313 92.55 155900 80.17 42 121557 84.54 26 78678 89.99 30292 96.14

Sailboat 786432 55322 92.96 176781 77.52 42 171684 78.16 30 104891 86.66 32751 95.83

Peppers 786432 53232 93.23 151003 80.79 36 120746 84.64 26 78678 89.99 31498 95.99

House 786432 45758 94.18 117938 85.00 36 148450 81.12 30 104857 86.66 30121 96.16

ucid00006 589824 42174 92.84 124294 78.92 29 102271 82.66 26 78677 86.61 32823 94.43

ucid00007 589824 47456 91.95 134100 77.26 27 144947 75.42 30 104891 82.21 34943 94.07

ucid00008 589824 41521 92.96 119783 79.69 40 118350 79.93 26 78677 86.61 32275 94.52

ucid00028 589824 40607 93.11 105953 82.03 45 106506 81.94 26 78643 86.66 32412 94.50

ucid00031 589824 40882 93.06 112084 80.99 40 142595 75.82 30 104857 82.22 34769 94.10

ucid00036. 589824 47039 92.02 143366 75.69 50 179736 69.52 30 104892 82.21 35559 93.97

Image name	Space for original image	VQ	CIQ	JPEG (QF is set to keep PSNR almost same)	JPEG2000 (QF is set to keep image quality (PSNR) almost same)	Proposed method
Girl	196608	22659	88.47	40875	79.20	50	33917	82.74	30	26248	86.64	13567	93.09
Couple	196608	22271	88.67	41275	79.00	50	30925	84.27	40	32801	83.31	13419	93.17
Jelly beans	196608	20767	89.43	28916	85.29	60	41358	78.96	40	32801	83.31	12799	93.49
Girl in red	196608	22829	88.38	34169	82.62	50	35881	81.75	40	32801	83.31	13603	93.08
House	196608	21335	89.14	45865	76.67	50	33217	83.10	40	32801	83.31	12889	93.44
Tree	196608	21633	88.99	42951	78.15	55	60369	69.29	50	39354	79.98	13168	93.30
Tiffany	786432	54097	93.12	165422	78.96	45	111880	85.77	26	78678	89.99	32087	95.91
Baboon	786432	58172	92.60	183901	76.61	48	260460	66.88	50	157321	79.99	33914	95.68
F-16 Jet	786432	49313	92.55	155900	80.17	42	121557	84.54	26	78678	89.99	30292	96.14
Sailboat	786432	55322	92.96	176781	77.52	42	171684	78.16	30	104891	86.66	32751	95.83
Peppers	786432	53232	93.23	151003	80.79	36	120746	84.64	26	78678	89.99	31498	95.99
House	786432	45758	94.18	117938	85.00	36	148450	81.12	30	104857	86.66	30121	96.16
ucid00006	589824	42174	92.84	124294	78.92	29	102271	82.66	26	78677	86.61	32823	94.43
ucid00007	589824	47456	91.95	134100	77.26	27	144947	75.42	30	104891	82.21	34943	94.07
ucid00008	589824	41521	92.96	119783	79.69	40	118350	79.93	26	78677	86.61	32275	94.52
ucid00028	589824	40607	93.11	105953	82.03	45	106506	81.94	26	78643	86.66	32412	94.50
ucid00031	589824	40882	93.06	112084	80.99	40	142595	75.82	30	104857	82.22	34769	94.10
ucid00036.	589824	47039	92.02	143366	75.69	50	179736	69.52	30	104892	82.21	35559	93.97

Table 3

PSNR between original and decompressed image using VQ, CIQ, JPEG, JPEG2000 and proposed method (taking six images together), with 256 number of clusters

Image name	VQ			CIQ			JPEG			JPEG2000			Proposed method
	Y	Cb	Cr	Y	Cb	Cr	Y	Cb	Cr	Y	Cb	Cr	Y	Cb	Cr
Girl	34.66	38.39	36.87	37.32	38.13	36.67	34.29	37.87	36.48	35.11	38.52	37.01	34.66	35.99	31.81
Couple	35.31	39.93	38.70	38.56	39.88	38.59	34.36	39.18	38.17	35.73	40.02	38.93	35.31	35.90	33.79
Jelly beans	37.06	37.98	37.14	40.00	37.88	37.13	36.58	37.45	36.72	38.52	38.14	37.28	37.06	33.49	33.31
Girl in red	36.13	37.62	35.70	38.59	37.10	35.54	34.85	37.06	35.70	36.86	37.66	35.80	36.13	32.10	31.78
House	35.52	37.10	35.48	38.41	37.02	35.41	34.24	36.69	35.90	35.72	37.01	35.52	35.52	33.77	31.86
Tree	29.64	36.52	33.42	34.04	36.61	33.53	30.44	36.35	33.31	29.67	36.91	33.61	29.64	31.86	29.56
Tiffany	34.62	34.91	36.80	37.90	34.90	36.84	33.96	34.53	36.39	34.81	34.88	36.71	34.62	30.46	31.68
Baboon	26.04	30.65	31.54	31.30	30.80	31.66	26.56	30.72	31.61	26.47	30.94	31.85	26.04	28.77	29.93
F-16 Jet	33.35	37.58	37.34	38.60	37.54	37.22	33.34	36.87	37.45	33.20	37.72	37.59	33.35	30.20	35.22
Sailboat	30.48	34.18	32.40	34.43	34.25	32.38	31.01	34.03	32.27	30.81	34.39	32.51	30.48	31.35	29.54
Peppers	33.51	35.17	34.73	36.04	34.76	34.68	33.00	34.66	34.18	34.13	35.22	34.77	33.51	31.13	30.78
house.tiff	31.21	36.17	33.34	36.24	35.99	33.15	31.04	35.51	33.00	31.62	36.51	33.53	31.21	31.60	29.89
ucid00006	25.82	36.11	35.53	32.45	36.58	36.07	25.42	35.50	35.15	25.31	36.86	36.34	25.82	35.22	34.99
ucid00007	25.06	33.76	34.37	33.05	34.44	35.17	25.31	33.33	34.14	24.77	34.77	35.61	25.06	32.94	33.64
ucid00008	28.34	37.65	37.39	34.29	38.03	37.83	28.48	37.30	37.24	27.89	38.33	38.17	28.34	36.21	36.55
ucid00028	30.37	40.52	39.25	30.37	40.86	39.71	30.80	40.27	39.21	30.15	41.46	40.15	30.37	38.05	38.14
ucid00031	27.26	36.53	35.46	36.19	37.46	36.22	27.89	36.74	35.63	27.16	37.78	36.43	27.26	35.99	35.44
ucid00036	27.03	35.95	34.24	32.25	36.03	34.48	27.58	35.90	34.26	26.55	36.51	34.67	27.03	34.34	33.39

The performance of the image compression method is analyzed using two parameters- required memory space reduction and quality of the decompressed image. PSNR [10, 11] is used to measure the quality of reconstructed image using lossy compression [4]. While comparing compression algorithms, a higher PSNR generally indicates that the reconstruction is of higher quality. Peak signal-to-noise ratio (PSNR) is computed between Y, Cb and Cr channels of the original color image and decompressed image separately. When comparing the quality of the decompressed image, a higher PSNR generally indicates better compression algorithm. PSNR is defined by Mean Squared Error (MSE) [22] using Equation 5.

PSNR = 20 {log}_{10} (\frac{{MAX}_{f}}{\sqrt{MSE}})

(5)

Where Mean Squared Error (MSE) [22] is defined using Equation 6.

MSE = \frac{1}{mn} \sum_{1}^{m} {\sum_{1}^{n} ∥ I (i, j) - I_{c} (i, j) ∥}^{2}

(6)

where I, I_c represent the matrix data of the original image and the decompressed image respectively. m, n represent number of rows and number of columns respectively in the images. MAX_f is the maximum signal value that exists in the original image. The memory space reduction percentage is calculated using Equation 7.

M_{R} = \frac{S - S_{c}}{S} \times 100

(7)

where S=space required to store the uncompressed image, S_c =space requirement to store the compressed images.

Table 4

Space reduction using VQ, CIQ, JPEG, JPEG2000 and proposed method (five images at once) with 256 clusters

Image name	Space for original image	VQ		CIQ		JPEG (QF is set to keep PSNR almost same)			JPEG2000 (QF is set to keep image quality			Proposed method (PSNR) almost same)
		Total	Reduction %	Total	Reduction %	QF	Total	Reduction %	QF	Total	Reduction %	Total	Reduction %
Girl	196608	22659	88.47	40875	79.20	50	33917	82.74	30	26248	86.64	14032	92.86
Couple	196608	22271	88.67	41275	79.00	50	30925	84.27	40	32801	83.31	13884	92.93
Jelly beans	196608	20767	89.43	28916	85.29	60	41358	78.96	40	32801	83.31	13264	93.25
Girl in red	196608	22829	88.38	34169	82.62	50	35881	81.75	40	32801	83.31	14068	92.84
House	196608	21335	89.14	45865	76.67	50	33217	83.10	40	32801	83.31	13354	93.20
Tree	196608	21633	88.99	42951	78.15	55	60369	69.29	50	39354	79.98	13373	93.19
Tiffany	786432	54097	93.12	165422	78.96	45	111880	85.77	26	78678	89.99	36884	95.31
Baboon	786432	58172	92.60	183901	76.61	48	260460	66.88	50	157321	79.99	34103	95.66
F-16 Jet	786432	49313	92.55	155900	80.17	42	121557	84.54	26	78678	89.99	30481	96.12
Sailboat	786432	55322	92.96	176781	77.52	42	171684	78.16	30	104891	86.66	35531	95.48
Peppers	786432	53232	93.23	151003	80.79	36	120746	84.64	26	78678	89.99	31687	95.97
House	786432	45758	94.18	117938	85.00	36	148450	81.12	30	104857	86.66	30310	96.14
ucid00006	589824	42174	92.84	124294	78.92	29	102271	82.66	26	78677	86.61	36196	93.86
ucid00007	589824	47456	91.95	134100	77.26	27	144947	75.42	30	104891	82.21	38316	93.50
ucid00008	589824	41521	92.96	119783	79.69	40	118350	79.93	26	78677	86.61	36005	93.89
ucid00028	589824	40607	93.11	105953	82.03	45	106506	81.94	26	78643	86.66	35648	93.95
ucid00031	589824	40882	93.06	112084	80.99	40	142595	75.82	30	104857	82.22	35785	93.93
ucid00036.	589824	47039	92.02	143366	75.69	50	179736	69.52	30	104892	82.21	35938	93.90

Table 5

PSNR between original and decompressed image using VQ, CIQ, JPEG, JPEG2000 and proposed method (taking five images at once), with 256 number of clusters

Image name	VQ			CIQ			JPEG			JPEG2000			Proposed method
	Y	Cb	Cr	Y	Cb	Cr	Y	Cb	Cr	Y	Cb	Cr	Y	Cb	Cr
Girl	34.66	38.39	36.87	37.32	38.13	36.67	34.29	37.87	36.48	35.11	38.52	37.01	34.66	36.47	33.22
Couple	35.31	39.93	38.70	38.56	39.88	38.59	34.36	39.18	38.17	35.73	40.02	38.93	35.31	36.48	34.98
Jelly beans	37.06	37.98	37.14	40.00	37.88	37.13	36.58	37.45	36.72	38.52	38.14	37.28	37.06	34.95	35.34
Girl in red	36.13	37.62	35.70	38.59	37.10	35.54	34.85	37.06	35.70	36.86	37.66	35.80	36.13	33.59	33.06
House	35.52	37.10	35.48	38.41	37.02	35.41	34.24	36.69	35.90	35.72	37.01	35.52	35.52	34.96	33.39
Tree	29.64	36.52	33.42	34.04	36.61	33.53	30.44	36.35	33.31	29.67	36.91	33.61	29.64	33.01	30.82
Tiffany	34.62	34.91	36.80	37.90	34.90	36.84	33.96	34.53	36.39	34.81	34.88	36.71	34.62	30.84	32.32
Baboon	26.04	30.65	31.54	31.30	30.80	31.66	26.56	30.72	31.61	26.47	30.94	31.85	26.04	29.40	30.50
F-16 Jet	33.35	37.58	37.34	38.60	37.54	37.22	33.34	36.87	37.45	33.20	37.72	37.59	33.35	32.92	35.79
Sailboat	30.48	34.18	32.40	34.43	34.25	32.38	31.01	34.03	32.27	30.81	34.39	32.51	30.48	32.02	30.34
Peppers	33.51	35.17	34.73	36.04	34.76	34.68	33.00	34.66	34.18	34.13	35.22	34.77	33.51	31.96	31.59
house.tiff	31.21	36.17	33.34	36.24	35.99	33.15	31.04	35.51	33.00	31.62	36.51	33.53	31.21	32.14	30.72
ucid00006	25.82	36.11	35.53	32.45	36.58	36.07	25.42	35.50	35.15	25.31	36.86	36.34	25.82	35.32	35.15
ucid00007	25.06	33.76	34.37	33.05	34.44	35.17	25.31	33.33	34.14	24.77	34.77	35.61	25.06	33.32	34.12
ucid00008	28.34	37.65	37.39	34.29	38.03	37.83	28.48	37.30	37.24	27.89	38.33	38.17	28.34	36.49	36.73
ucid00028	30.37	40.52	39.25	30.37	40.86	39.71	30.80	40.27	39.21	30.15	41.46	40.15	30.37	38.31	38.40
ucid00031	27.26	36.53	35.46	36.19	37.46	36.22	27.89	36.74	35.63	27.16	37.78	36.43	27.26	36.18	35.55
ucid00036	27.03	35.95	34.24	32.25	36.03	34.48	27.58	35.90	34.26	26.55	36.51	34.67	27.03	35.18	33.95

In case of JPEG, required space is calculated by maintaining PSNR value for each individual image almost same as proposed method by adjusting quality factor (QF) accordingly.

Table 6

Space reduction using VQ, CIQ, JPEG, JPEG2000 and proposed method (taking four images at once) with 128 clusters

Image name	Space for original image	VQ		CIQ		JPEG (QF is set to keep PSNR almost same)			JPEG2000 (QF is set to keep image quality			Proposed method (PSNR) almost same)
		Total	Reduction %	Total	Reduction %	QF	Total	Reduction %	QF	Total	Reduction %	Total	Reduction %
Girl	196608	22659	88.47	40875	79.20	50	33917	82.74	30	26248	86.64	10927	94.44
Couple	196608	22271	88.67	41275	79.00	50	30925	84.27	40	32801	83.31	10779	94.51
Jelly beans	196608	20767	89.43	28916	85.29	60	41358	78.96	40	32801	83.31	10159	94.83
Girl in red	196608	22829	88.38	34169	82.62	50	35881	81.75	40	32801	83.31	10963	94.42
House	196608	21335	89.14	45865	76.67	50	33217	83.10	40	32801	83.31	9629	95.10
Tree	196608	21633	88.99	42951	78.15	55	60369	69.29	50	39354	79.98	9908	94.96
Tiffany	786432	54097	93.12	165422	78.96	45	111880	85.77	26	78678	89.99	43044	94.52
Baboon	786432	58172	92.60	183901	76.61	48	260460	66.88	50	157321	79.99	44871	94.29
F-16 Jet	786432	49313	92.55	155900	80.17	42	121557	84.54	26	78678	89.99	41078	94.77
Sailboat	786432	55322	92.96	176781	77.52	42	171684	78.16	30	104891	86.66	41249	94.75
Peppers	786432	53232	93.23	151003	80.79	36	120746	84.64	26	78678	89.99	34949	95.55
House	786432	45758	94.18	117938	85.00	36	148450	81.12	30	104857	86.66	33696	95.71
ucid00006	589824	42174	92.84	124294	78.92	29	102271	82.66	26	78677	86.61	38212	93.52
ucid00007	589824	47456	91.95	134100	77.26	27	144947	75.42	30	104891	82.21	40332	93.16
ucid00008	589824	41521	92.96	119783	79.69	40	118350	79.93	26	78677	86.61	38021	93.55
ucid00028	589824	40607	93.11	105953	82.03	45	106506	81.94	26	78643	86.66	37664	93.61
ucid00031	589824	40882	93.06	112084	80.99	40	142595	75.82	30	104857	82.22	36159	93.86
ucid00036.	589824	47039	92.02	143366	75.69	50	179736	69.52	30	104892	82.21	38516	93.46

Table 7

PSNR between original and decompressed image using VQ, CIQ, JPEG, JPEG2000 and proposed method (taking four images at once), with 128 number of clusters

Image name	VQ			CIQ			JPEG			JPEG2000			Proposed method
	Y	Cb	Cr	Y	Cb	Cr	Y	Cb	Cr	Y	Cb	Cr	Y	Cb	Cr
Girl	34.66	38.39	36.87	37.32	38.13	36.67	34.29	37.87	36.48	35.11	38.52	37.01	34.66	36.62	33.73
Couple	35.31	39.93	38.70	38.56	39.88	38.59	34.36	39.18	38.17	35.73	40.02	38.93	35.31	36.16	34.85
Jelly beans	37.06	37.98	37.14	40.00	37.88	37.13	36.58	37.45	36.72	38.52	38.14	37.28	37.06	35.08	35.99
Girl in red	36.13	37.62	35.70	38.59	37.10	35.54	34.85	37.06	35.70	36.86	37.66	35.80	36.13	33.88	32.93
House	35.52	37.10	35.48	38.41	37.02	35.41	34.24	36.69	35.90	35.72	37.01	35.52	35.52	34.50	32.86
Tree	29.64	36.52	33.42	34.04	36.61	33.53	30.44	36.35	33.31	29.67	36.91	33.61	29.64	33.44	31.31
Tiffany	34.62	34.91	36.80	37.90	34.90	36.84	33.96	34.53	36.39	34.81	34.88	36.71	34.62	32.18	33.35
Baboon	26.04	30.65	31.54	31.30	30.80	31.66	26.56	30.72	31.61	26.47	30.94	31.85	26.04	30.02	30.94
F-16 Jet	33.35	37.58	37.34	38.60	37.54	37.22	33.34	36.87	37.45	33.20	37.72	37.59	33.35	35.37	35.79
Sailboat	30.48	34.18	32.40	34.43	34.25	32.38	31.01	34.03	32.27	30.81	34.39	32.51	30.48	32.23	30.57
Peppers	33.51	35.17	34.73	36.04	34.76	34.68	33.00	34.66	34.18	34.13	35.22	34.77	33.51	32.31	32.01
house.tiff	31.21	36.17	33.34	36.24	35.99	33.15	31.04	35.51	33.00	31.62	36.51	33.53	31.21	33.50	31.50
ucid00006	25.82	36.11	35.53	32.45	36.58	36.07	25.42	35.50	35.15	25.31	36.86	36.34	25.82	35.67	35.46
ucid00007	25.06	33.76	34.37	33.05	34.44	35.17	25.31	33.33	34.14	24.77	34.77	35.61	25.06	33.86	34.58
ucid00008	28.34	37.65	37.39	34.29	38.03	37.83	28.48	37.30	37.24	27.89	38.33	38.17	28.34	36.81	37.11
ucid00028	30.37	40.52	39.25	30.37	40.86	39.71	30.80	40.27	39.21	30.15	41.46	40.15	30.37	38.55	38.57
ucid00031	27.26	36.53	35.46	36.19	37.46	36.22	27.89	36.74	35.63	27.16	37.78	36.43	27.26	36.40	35.66
ucid00036	27.03	35.95	34.24	32.25	36.03	34.48	27.58	35.90	34.26	26.55	36.51	34.67	27.03	35.30	34.05

Table 2 shows the percentage of space reduction using Vector Quantization, CIQ, JPEG, JPEG2000 and proposed method, taking six images (by grouping image number 1 to 6, 7 to 12 and 13 to 18 at once with 256 number of clusters.

Table 8

PSNR between jpeg and proposed method by mainaining required space almost same for both the methods

Image name	Original image size	QF	Space requirements		PSNR
			JPEG	Proposed method	JPEG			Proposed method
					Y	Cb	Cr	Y	Cb	Cr
Girl	196608	17	14110	13567	30.34	35.78	32.79	34.66	35.99	31.81
Couple	196608	19	13562	13419	30.96	35.91	34.81	35.31	35.90	33.79
Jelly beans	196608	13	13181	12799	29.76	32.51	32.58	37.06	33.49	33.31
Girl in red shirt	196608	14	13603	13603	29.78	32.74	31.91	36.13	32.10	31.78
House	196608	14	13486	12889	28.72	31.14	32.33	35.52	33.77	31.86
Tree	196608	9	13844	13168	24.00	30.60	28.72	29.64	31.86	29.56
Tiffany	786432	11	32657	32087	29.09	30.84	32.03	34.62	30.46	31.68
Baboon	786432	6	34047	33914	21.01	25.61	25.49	26.04	28.77	29.93
F-16 Jet	786432	7	30720	30292	25.36	29.18	31.30	33.35	30.20	35.22
Sailboat on lake	786432	6	34077	32751	23.69	26.26	26.40	30.48	31.35	29.54
Peppers	786432	7	33734	31498	25.99	27.55	27.70	33.51	31.13	30.78
house.tiff	786432	6	33255	30121	23.50	26.89	26.04	31.21	31.60	29.89
ucid00006.tiff	589824	9	34532	32823	22.49	30.35	30.07	25.82	35.22	34.99
ucid00007.tiff	589824	6	38068	34943	19.83	26.15	26.27	25.06	32.94	33.64
ucid00008.tiff	589824	9	32755	32275	24.11	30.80	29.32	28.34	36.21	36.55
ucid00028.tiff	589824	9	33379	32412	25.13	29.79	29.12	30.37	38.05	38.14
ucid00031.tiff	589824	7	35499	34769	22.14	29.56	28.29	27.26	35.99	35.44
ucid00036.tiff	589824	10	35168	35559	23.28	31.06	29.75	27.03	34.34	33.39

Fig. 9

a) Original image, b) Decompressed image using JPEG c) Decompressed image using JPEG2000 d) Decompressed image using KLT based compression method e) Decompressed image using proposed method.

Comparative result of reduction of space requirement to store the images using different compression algorithms are shown in Table 2. The space reduction using proposed method lies in the range of 93.08% to 96.16% which is higher than space reduction using existing algorithms(while keeping the quality factor same) i.e. VQ(88.47% to 94.18%), CIQ(75.69% to 85.00%), JPEG(66.88% to 85.77%), JPEG2000(79.98% to 89.99%). Therefore, the proposed method outperforms VQ, CIQ, JPEG and JPEG2000 in terms of space reduction.

Table 9

PSNR between jpeg2000, karhunen loeve transform(klt) based compression and proposed method by mainaining required space almost same for all the methods

Image name	Space requirement				PSNR
	JPEG 2000		KLT	Proposed method	JPEG2000 method			KLT based compression			Proposed method
	QF	Size	Size	Size	Y	Cb	Cr	Y	Cb	Cr	Y	Cb	Cr
Girl	17	13140	8896	13567	32.03	38.31	36.72	24.88	38.09	35.59	34.66	35.99	31.81
Couple	17	13140	8054	13419	31.53	39.72	38.68	25.86	38.71	38.22	35.31	35.90	33.79
Jelly beans	17	13141	6781	12799	33.00	37.81	36.91	24.22	38.13	37.28	37.06	33.49	33.31
Girl in red shirt	17	13140	7299	13603	31.42	37.27	35.36	24.19	37.62	35.71	36.13	32.10	31.78
House	17	13140	8940	12889	30.64	36.24	35.44	24.15	36.36	35.58	35.52	33.77	31.86
Tree	17	13141	13814	13168	24.94	36.53	33.19	23.78	36.94	33.73	29.64	31.86	29.56
Tiffany	1	26248	25589	32087	30.83	34.28	35.97	24.08	35.01	36.56	34.62	30.46	31.68
Baboon	1	26248	80998	33914	21.94	30.28	31.19	23.41	31.08	31.94	26.04	28.77	29.93
F-16 Jet	1	26249	27401	30292	27.25	36.14	36.97	24.13	37.70	37.50	33.35	30.20	35.22
Sailboat	1	26249	51005	32751	25.15	33.75	31.31	23.99	34.49	32.55	30.48	31.35	29.54
Peppers	1	26248	34787	31498	28.98	34.45	33.42	24.47	35.17	33.97	33.51	31.13	30.78
house.tiff	1	26248	40296	30121	25.70	35.41	32.43	24.04	36.71	33.50	31.21	31.60	29.89
ucid00006	1	26248	47809	32823	22.46	36.39	35.93	23.38	37.06	36.46	25.82	35.22	34.99
ucid00007	1	26248	58603	34943	19.08	33.59	34.84	23.48	34.93	35.72	25.06	32.94	33.64
ucid00008	1	26248	36086	32275	24.12	37.44	37.61	23.83	38.48	38.16	28.34	36.21	36.55
ucid00028	1	26248	29211	32412	24.91	40.99	39.70	24.23	41.53	40.18	30.37	38.05	38.14
ucid00031	1	26249	44512	34769	21.38	36.85	35.70	24.11	37.40	36.46	27.26	35.99	35.44
ucid00036	1	26249	57390	35559	23.24	35.91	33.98	23.40	36.56	34.78	27.03	34.34	33.39

Fig. 10

Average percentage of space reduction using VQ, CIQ, JPEG, JPEG2000 and proposed method (taking 6, 5, 4,3 images).

Table 3 shows the computed PSNR between the original image and the decompressed image using VQ, CIQ, JPEG, JPEG2000 and the proposed method. Here the proposed method takes six images at once for compression. It is observed from experimental result shown in Table 3 that PSNR values of images using proposed method are almost similar to that of VQ, CIQ, JPEG, JPEG2000 but proposed method achieves better compression ratio.

Table 4 shows the percentage of reduction of required space to store the compressed image using VQ, CIQ, JPEG and JPEG2000 and proposed method, taking five images (taking image number 1 to 5, 2 to 6, 7 to 11, 8 to 12, 13 to 17 and 14 to 18) at once with 256 number of clusters.

From Table 4, it is evident that the space reduction of images using proposed method lies in the range 92.84% to 96.14% which is higher than space reduction of VQ (88.47% to 94.18%), CIQ (75.69% to 85.00%), JPEG (66.88% to 85.77%) and JPEG2000 (79.98% to 89.99%). Therefore, the proposed method again outperforms VQ, CIQ, JPEG and JPEG2000 in terms of space reduction.

Table 5 shows the computed PSNR between the original image and decompressed image using the VQ, CIQ, JPEG, JPEG2000 and proposed method. Here the proposed method takes five images at once for compression. The result in Table 5 shows that PSNR using proposed method are almost similar to the VQ, CIQ, JPEG and JPEG2000 method.

Table 6 shows the percentage of space reduction using VQ, CIQ, JPEG, JPEG2000 and proposed method, taking four images (by grouping image number 1 to 4, 3 to 6 then image number 7 to 10, 9 to 12 last 13 to 16,15 to 18) at once with 128 number of clusters.

From Table 6, it is evident that the space reduction using proposed method lies in the range 93.16% to 95.17% that is higher than space reduction of VQ (88.47% to 94.18%), CIQ (75.69% to 85.00%), JPEG (66.88% to 85.77%) and JPEG2000 (79.98% to 89.99%). Therefore, the proposed method performs far better compared to VQ, CIQ, JPEG, and JPEG2000 in terms of space reduction.

Table 7 shows the computed PSNR between the original image and the decompressed image using the VQ, CIQ, JPEG, JPEG2000 and proposed method. Here the proposed method takes four images together. The result shown in Table 7 shows that PSNR values of images using proposed method and existing VQ, CIQ, JPEG and JPEG2000 are similar.

In Table 8 comparative study of image quality (in terms of PSNR) between JPEG compression and proposed method is shown by maintaining required space almost same for both the methods. Quality factor (QF) of JPEG algorithm is adjusted to a value so that required space of compressed image is near to that of proposed method. It is clear from Table 8 that PSNR of proposed method is better than that of JPEG compression keeping required space almost same. For example, in case of Jelly beans image, PSNR of proposed method of Y, Cb, Cr are 37.06, 33.49 and 33.31 compared to 29.76, 32.51 and 32.58 of JPEG respectively. In ucid00006 image, PSNR of proposed method of Y, Cb, Cr are 25.82, 35.22 and 34.99 are significantly better than PSNR 22.49, 30.35 and 30.07 of JPEG compression.

Figure 9(a) to 9(e) shows the original image, decompressed image using JPEG, JPEG2000, KLT based compression method and proposed method. In JPEG and JPEG2000 quality factor (QF) is set to a specific value to keep required space almost same as proposed method. From Fig. 9, it can be clearly seen that image quality of decompressed image using proposed method is better than the JPEG, JPEG2000 and KLT based compression method.

In Table 9 comparative result of image quality (in terms of PSNR) between JPEG2000, Karhunen Loeve Transform (KLT) based compression [32] and proposed method is shown by maintaining required space near to each other. Quality factor (QF) of JPEG2000 [33] algorithm is adjusted to keep required space of compressed image is very much near to proposed method. Table 9 shows that KLT and JPEG2000 gives better PSNR than proposed method. But PSNR of Y channel is significantly better than KLT & JPEG2000.

Figure 10 shows the average percentage of space reduction using Vector Quantization, CIQ, JPEG, JPEG2000 and proposed method taking (six, five, four and three images at once). It is clearly observed that the amount of space reduction using proposed approach is significantly higher than that of VQ, CIQ, JPEG and JPEG2000.In this study, the experiment has been conducted taking four to six images together. In case of four images average memory space reduction is 92.06% and image quality is better than decompressed image taking five or six images together. Image quality of decompressed images using proposed method depends on the number of images taken ay once for compression. If the number of images increases then visual quality of individual quality degrades but achieves better compression ratio.

The graph in Fig. 11, Fig. 12 and Fig. 13 shows the space requirements versus number of images taken at once for compression for Girl, Baboon and ucid00006 images respectively.

Fig. 11

Space requirement versus number of images taken together for Girl image of size 256 × 256.

Fig. 12

Space requirement versus number of images taken together for Baboon image of size 512 × 512.

Fig. 13

Space requirement versus number of images taken together for ucid00006 image of size 384 × 512.

The graph in Fig. 14 shows the image quality (PSNR) versus number of image taken at once.

Fig. 14

Impact of number of images taken together on Image quality. X-axis is number of image, Y-axis is PSNR.

5. Conclusion

This study proposes a multi-image compression method to achieve better compression ratio where multiple images of the same size are combined together and compressed. It works on de-correlated color space. This method has been applied on standard images available in literature and images collected from UCID v.2 color image database. Experimental results show that the method achieves a higher compression ratio than VQ, JPEG and JPEG2000 while retaining almost similar image information. Future work may be focused on application of post processing technique on the decompressed image to achieve higher PSNR while keeping the same memory space requirement.

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