# Improving JPEG-LS performance using location information.

AbstractJPEG-LS is an international standard for lossless or near-lossless image-compression algorithms. In this paper, a simple method is proposed to improve the performance of the lossless JPEG-LS algorithm. With respect to JPEG-LS and its supplementary explanation, Golomb-Rice (GR) coding is mainly used for entropy coding, but it is not used for long codewords. The proposed method replaces a set of long codewords with a set of shorter location map information. This paper shows how efficiently the location map guarantees reversibility and enhances the compression rate in terms of performance. Experiments have also been conducted to verify the efficiency of the proposed method.

Keywords: JPEG-LS, Lossless compression, Golomb code, Golomb-Rice, Location map

1. Introduction

The JPEG-LS algorithm [1] is a lossless or near-lossless compression standard for still images. Most of the recent compression algorithms accepted the Modeling and Coding [2] concept to achieve an efficient compression. JPEG-LS uses the two-sided geometric distribution (TSGD) model [3] of the prediction error that is based on the median edge detector (MED) [4], and encodes this model by Golomb-Rice (GR) coding [5]-[6]. As a lossless compression algorithm, it performs quite effectively and is superior to most of the other algorithms including JPEG2000 [7]-[10]. A group of authors tried to improve the performance of JPEG-LS by introducing novel prediction methods. Baligar et al. [7] proposed a linear prediction method that minimizes the squared error and exploits quadtree coding. Bedi et al. [8] proposed a prediction method that detects the diagonal edges in addition to the vertical and horizontal edges. While the compression performances of both studies [7]-[8] exceed that of JPEG-LS, the computational complexities of their algorithms are far greater [9]. Kademi et al. [10] paradoxically showed the superiority of JPEG-LS. Kim et al. [11] proposed hierarchical average and copy prediction (HACP) scheme and showed the upper bound of significant bit truncatuon (SBT) coding. Combinations of multiple predictions [12]-[13] are also used to improve the compression rates. Masmoudi et al. [14] proposed a block-based lossless image compression for which finite-mixture models and adaptive arithmetic coding are used. Zhao et al. [15] and Starosolski [16] showed that the context-based adaptive lossless image codec (CALIC) [17] provides high compression rates within reasonable time frames, while JPEG-LS is effective enough and very fast. As a result, the JPEG-LS algorithm is still considered excellent in terms of the compression rate and the compression time.

Mobasseri et al. [18] proposed a method for the embedding of data into the JPEG bitstream, whereby Huffman-code mapping is used, and the data embedding is performed according to a reversible mapping of the unused codewords; notably, only a fraction of the JPEG codewords are actually used. Later, Qian and Zhang [19] improved their method, whereby the most important contribution of their methods from [18] and [19] is a reversible data hiding capability for the improvement of the compression rate; this reversibility is used in this paper for the replacement of long codewords. Ding et al. [20] proposed a modified Golomb coding for an asymmetric TSGD.

Even though JPEG-LS is almost perfect as a lossless algorithm, its performance can still be improved. The goal of this paper is the improvement of the JPEG-LS performance through a slight modification of the long codewords. JPEG-LS accepted the GR code as a main encoding alogrithm, but this GR code can sometimes produce excessively long codewords. A number of techniques can be used to remedy the long codeword artifact of the GR code; that is, the JPEG-LS algorithm modifies these long GR codewords into a fixed-length code (the authors call this modification JPEG-LS GR), while an additional improvement is proposed in this paper. The GR artifact can also be resolved by utilizing the location map. The location map is a tool for the book-keeping of the side information that assures the reversibility of data hiding schemes [21]-[23]. It is mostly used to avoid underflow, overflow or decoding errors at the decoding stage.

This paper shows that the location map can be used for lossless data compression; moreover, it shows that long codewords can be replaced with shorter codewords. The contribution of this paper consists of three methods that reduce the size of the symbol length in bits, as follows; replacing the fixed-length prefixes with location information, reducing the location map itself using a variable-length information, and reducing the suffix.

This paper is organized as follows. Section 2 briefly summarizes the concepts of GR coding and JPEG-LS GR coding. Section 3 revisits the concept of the location map, and includes an explanation of the application of location information for JPEG-LS GR coding; a simple method for the reduction of the location map size is also presented; along with a demonstration of improvements of the JPEG-LS GR method for specific cases. Section 4 presents an analysis of the experiment results, whereby the performances of the JPEG-LS GR method and the proposed method are compared. Section 5 concludes the paper.

2. Golomb-Rice coding vs. JPEG-LS coding

When an integer N is divided by another integer m, a quotient q and a remainder r are derived so that the number N can be represented as N = q x m + r. As long as m is given, the GR code in the JPEG-LS is represented by [unary quotient q] + [one bit for a separator "1"] + [binary remainder r]. JPEG-LS does not encode the pixel value itself, but encodes the prediction error through the GR coding. The integer notation is defined here as follows: [N.sub.D] is the digit expression (either in 8 bits or 16 bits), [N.sub.B] is the binary expression of [N.sub.D], and [N.sub.U] is the unary expression. For example, when [N.sub.D] is [3.sub.(10)] for an 8-bit depth image, [N.sub.B] is [00000011.sub.(2)] and [N.sub.U] is [000.sub.(1)], and they are the same representations. Note that [N.sub.U] has three zeros since [N.sub.D] is 3. Similarly, when a given prediction error in a decimal number is [N.sub.D] = [73.sub.(10)], its binary representation in 8-bit format is expressed as [N.sub.B] = [01001001.sub.(2)]. Let a divisor be m = [2.sup.k], for example, where k = 2, q is the first 8 - k bits of [N.sub.B], which is q = [010010.sub.(2)] = [18.sub.(10)] = [000000000000000000.sub.(1)]; and r is the last k bits of [N.sub.B,] which is r = [01.sub.(2)]. In this case, the corresponding GR code is represented by the following format:

[N.sub.GR] = [000000000000000000|1|01.sub.(2)]

The output [N.sub.GR] is of a pseudo-binary form. Namely, it looks like a binary sequence, but it is actually a combination of binary symbols. The GR code starts with 18 leading zeros that are equivalent to the unary representation of the quotient. The first "1" that separates the quotient and the remainder with two red bars is a separator. The last part of "01" is just the remainder r in binary format.

Another given number [73.sub.(10)] can be represented in a different form depending on the k value. Let k be 1 so that q = [0100100.sub.(2)] = [36.sub.(10)] = [000000000000000000000000000000000000.sub.(1)] and r = [1.sub.(2)]. As a result, its GR code is obtained according to the following format:

[N.sub.GR] = [000000000000000000000000000000000000|1|1.sub.(2)]

In this case, the total length of the GR code is 38 bits, which seems excessively long; therefore, this lengthy GR code [N.sub.GR] is not used whenever q [greater than or equal to] [23.sub.(10)], but a shorter code [N.sub.LS] is used in a different format as follows:

[N.sub.LS] = [00000000000000000000000|1|01001000.sub.(2)]

where the eight LSB bits are represented as [N.sub.D] -1 = [72.sub.(10)] = [01001000.sub.(2)]. Now, 32 bits (i.e., [23 bits of leading zeros] + [1-bit separator "1"] + [8-bits of [N.sub.D] -1]) are needed for [N.sub.LS] rather than 38 bits for [N.sub.GR]. This representation mostly shortens the length of the GR code.

To achieve consistency with the GR code, 23 zeros are leading both the separator and the eight bits of [N.sub.D] --1 itself for the pixels quantized with 8-bit depth; then, maximally 32 bits are needed in any case. A gain by the JPEG-LS GR code is obtained when the quotient is large enough, and the gain of the JPEG-LS GR code is six bits, which is six bits less than the GR code in this example.

Such a gain, however, does not always occur with the use of JPEG-LS GR coding. For example, a given number [47.sub.(10)] can be represented as follows:

[N.sub.B] = [00101111.sub.(2)]

For k = 1, its GR code is represented with 23 leading zeros, as follows:

[N.sub.GR] = [00000000000000000000000|1|1.sub.(2)]

However, the JPEG-LS GR code should be used whenever q [greater than or equal to] 23. The JPEG-LS GR code is, therefore, represented as follows:

[N.sub.LS] = [00000000000000000000000|1|00101110.sub.(2)]

It is obvious that the JPEG-LS GR code needs 32 bits while the GR code needs only 25 bits. Even though the JPEG-LS GR code is not always superior to the GR code, the former code is used in the JPEG-LS algorithm. The length of the JPEG-LS GR code that includes a prefix, a separator, and a suffix is always 32 bits. A combination of the [prefix and separator] of the JPEG-LS GR code is called the replaceable JPEG-LS GR prefix or replaceable prefix for short in this paper. This replaceable prefix consists of 24 bits that comprise 23 leading zeros plus the separator "1". The 8-bit suffix is called intact suffix in this paper. If the prefixes are replaceable, their associated suffixes are intact suffixes.

Notably, most images are quantized with eight bits per pixel and eight bits per color (such as red, green, and blue); however, some accurate images are quantized with 16 bits per pixel and 16 bits per color. In this case, the JPEG-LS GR code consists of a 47-bit prefix, a 1-bit separator, and a 16-bit suffix; therefore, the replaceable JPEG-LS GR prefix is 48 bits for the 16-bit-depth images.

3. Proposed Method

Both the run and regular modes are used for JPEG-LS. The run mode encodes the run length, which is the count of the same continuous values. Either GR or JPEG-LS GR code is used for each codeword when the regular mode is utilized, and this regular mode is the sole focus of this paper.

In this section, three contributions are introduced. First, the replacement of the replaceable JPEG-LS GR prefix with location information can reduce the codeword size. Second, the size of the location information itself can be reduced. Third, the intact suffix code size can also be reduced.

3.1 Use of Location Information & Occurrence Gain

Location information is a kind of side information to guarantee reversibility. The encoder and decoder can perform the same job if they share the same location information. If the encoder modifies the pixel values, the modification can cause an overflow or underflow error. Obviously, in that case, the encoder skips the pixel to avoide the causing of an error, and the pixel should be marked in the location map. The decoder also skips the decoding when it encounters the marked position. A set of the marked position information is called the location map.

The first contribution of this paper is the replacement of the replaceable prefixes. This paper identifies the possibility that the JPEG-LS GR codeword can still be shortened using a simple method; that is, the location information is used instead of the replaceable JPEG-LS GR prefix. Even though the replaceable prefix is removed, the intact suffix is not altered. The position information of the replaceable prefix will be used here instead of the lengthy JPEG-LS GR code.

The location map consists of the simple (row, col) coordinates of such JPEG-LS GR code in this paper. The map of each row and column are of an 8-bit length in the 256 x 256 images, while a 9-bit length applies for the 512x512 images. For the 256x256 images, the coding gains for each replaceable prefix are therefore 8 (i. e., 24 - 2 x 8) bits for the 8-bit-pixel depth, and 32 (i, e., 43 - 2 x 8) bits for the 16-bit depth. For the 512 x 512 images, the coding gains for each prefix are 6 (i. e., 24 - 2 x 9) bits for the 8-bit depth and 30 bits for the 16-bit depth. This location information is subsequent to the total number information of these locations at the beginning of the bitstream.

At a position (row, col) = (339, 211) of the 512x512 image in Table 1, for example, the JPEG-LS GR code is [00000000000000000000000|1|01101110.sub.(2)], and a replaceable prefix [000000000000000000000001.sub.(2)] is encountered. This prefix is removed during the proposed encoding and only the intact suffix of [01101110.sub.(2)] (i.e., [N.sub.D] - 1) remains. After removing the replaceable prefix, its position information of [101010011011010011.sub.(2)], which is equivalent to (339, 211), is recorded at the header of the bitstream and a coding gain of six bits is obtained. The replaceable prefixes are underlined in Table 1.

Let H and W be the height and width of the image, respectively. As long as the value [[log.sub.2] H] + [[log.sub.2]W] is smaller than 24 for the 8-bit depth, or less than 48 for the 16-bit depth, the replacement with the location map results in a coding gain; such a gain is called occurrence gain in this paper. Of course, the number of replaceable prefixes should be delivered to the decoder as a part of the side information.

3.2 Map Gain

The second contribution is a possible reduction of the location information itself. The position information of the first replaceable prefix is marked as it is because the reference information regarding the position is not available; however, for the rest of the replaceable prefixes, the information regarding the previous position is available. The available information can be exploited for the attainment of further gain. In the example in Table 1, four replaceable prefixes appear where the positions are (197, 256), (339, 211), (480, 290) and (480, 394); here, the row positions {197, 339, 480, and 480} are in an ascending order. For the first position (197, 256) for a 512 x 512 image, 18 (i.e., 9 plus 9) bits are needed to record [011000101100000000.sub.(2)]. The next position (339, 211) is [101010011011010011.sub.(2)]; here, because of the fact that 339 [greater than or equal to] 256, it is obvious that 339 is located in the second half (bottom part) of the image, and the subsequent row positions that are larger than 256 indicate that they are located in the second half. As a result, these rows are all marked as [1xxxxxxxx.sub.(2)]. Because both the encoder and the decoder recognize this fact, it is not necessary to encode the first bit of "1", and only the 8-bit [xxxxxxxx.sub.(2)] is needed without the "1" in this case; therefore, only the 17 (i.e., 8 plus 9) bits of [11100000100100010.sub.(2)] are recorded as the location information of (480, 290).

If a replaceable prefix is in the second half of the image, one bit of gain can be attained in the recording of the next piece of location information; similarly, if an i-th replaceable prefix is placed in the fourth quarter, two bits of gain can be attained in the recording of the position of the (i+1)-th prefix.

The column information in the same row can also be reduced by using a similar method because the columns of the same row are of an ascending order; therefore, the location information of (480, 394) in Table 1 is [1110000010001010.sub.(2)] in 16 (i.e., 8 plus 8) bits according to a referencing of the position information of (480, 290).

This type of gain is called map gain in this paper. Of course, the replaceable prefix positions occur randomly; therefore, such a gain is not always achieved.

3.3 K3 (or K10) Gain

The third contribution is a size reduction of the intact suffix. When the replaceable prefix is encountered for a pixel that is quantized by eight bits, the manifestation of the leading 23 zeros means that this sample is encoded by the JPEG-LS GR method, whereby the value of the quotient q [greater than or equal to] 23 and the suffix value is [N.sub.D] - 1; that is, the replaceable prefix does not occur whenever q < 23. By utilizing this fact, the divisor information k can be exploited to reduce the size of the intact suffix. With respect to k = 3 regarding the 8-bit pixel values, for example, the value range of the first five bits of any q is from 0 to 31 ; as a result, [N.sub.B] ranges from [00000xxx.sub.(2)] to 11111[xxx.sub.(2)], where [xxx.sub.(2)] stands for three bits of "don't care" binary numbers (i.e., remainders).

Regarding the quotient part, numbers from 0 to 22 do not appear when q [greater than or equal to] 23, and, in this case, numbers from 23 to 31 appear when k is 3; that is, only nine numbers are actually used. Thus, quotient values from 23 to 31 can therefore be reassigned to other values from 0 to 8, respectively. Table 2 shows the reassigned number representation.

A modified quotient of 0 is equivalent to the unmodified quotient value of 23, a modified quotient of 1 is equivalent to the unmodified quotient value 24, and so on. Only four bits are consequently needed to represent the nine numbers from 0 to 8 ([0000.sub.(2)] to [1000.sub.(2)]), rather than the use of five bits to represent numbers from 23 to 31 ([10111.sub.(2)] to [11111.sub.(2)]); moreover, one more bit can be saved here. Three bits are assigned to represent the numbers from 0 to 6, and four bits are assigned to represent 7 and 8.

[N.sub.B] is used rather than [N.sub.B] -- 1 to record the suffix in this case. The intact suffix of position (480, 290), for example, is [11101110.sub.(2)] in Table 1. The original [N.sub.B] = [11101110.sub.(2)] + 1 = [11101111.sub.(2)] can be split into two parts. If k is 3, then the unmodified-quotient part is [11101.sub.(2)] and the remainder part is [111.sub.(2)]. The unmodified-quotient part of [11101.sub.(2)] (i.e., [29.sub.(10)]) is modified to [110.sub.(2)] (i.e., [6.sub.(10)]) by the subtraction of 23. Through this modification, the intact suffix is changed to [110111.sub.(2)], which requires six bits rather than eight bits, and saves two bits. This type of gain is called K3 gain in this paper.

The same number of bits can be saved for the values that are quantized by a 16-bit depth with k = 10. Then, the [N.sub.B] ranges from 000000[xxxxxxxxxx.sub.(2)] to 111111[xxxxxxxxxx.sub.(2)] in normal case. Similarly, only 17 numbers from 101111[xxxxxxxxxx.sub.(2)] to 111111[xxxxxxxxxx.sub.(2)] are actually replaceable since the replaceable prefix does not occur whenever q < 47. As a result, the assignment of six bits is not required, but five or four bits are enough. Two bits can be saved by assigning short binary numbers from [0000.sub.(2)] to [1110.sub.(2)] (for the unmodified [47.sub.(10)] to [61.sub.(10)], respectively) or one bit can be saved by assinging [11110.sub.(2)] and [11111.sub.(2)] (for the unmodified [62.sub.(10)] and [63.sub.(10))], respectively) (See Table 3). This gain is called K10 gain in this paper.

4. Experiment Results

The performance of the proposed method was compared with that of the JPEG-LS algorithm (see Tables 4 to 8). A variety of uncompressed images ([24]-[25], Figs. 1 and 2) are used for the comparison; here, a few images do not have a replaceable prefix, while most of the images have a sufficient number of replaceable prefixes.

In the experiments, 12 gray-scale images of a 256x256 size and 12 gray-scale 512x512 images, all quantized by eight bits, are used; in addition, 8 color images of varying sizes that have been quantized by eight bits are used (see Fig. 1). The images quantized by 16 bits are shown in Fig. 2, and include 15 gray-scale images and 14 color images.

Before the compressed bitstream is recorded, the overhead representing the number of location information is first recorded.

For the lena (256 x256) image with an 8-bit pixel depth, the replaceable prefixes occur 20 times, and 160 bits (i.e., 20x8) can be reduced purely by the occurrence gain. For the recording of the 20 occurrences, five bits are needed to represent the number [20.sub.(10)] or [10100.sub.(2)], and this number of bits, five, is expressed as [0101.sub.(2)]. The entirety of the overhead information is therefore expressed with nine bits as [0101|10100.sub.(2)] and this overhead header is preserved at the beginning of the binary stream for this image.

Among the nine bits in the overhead header, the first four bits are used to represent the following number of bits representing the number of replaceable prefixes; therefore, the leading four bits can represent numbers from 0 [(0000.sub.(2)]) to 15 ([1111.sub.(2)]). The maximum number of overhead bits is 19 (four bits of leading "1111" plus 15 bits to represent the number of replaceable prefixes).

The exact output bitstream size of JPEG-LS depends on two kinds of zero padding. The first type pads a number of zeros at the end to make the bitstream size a multiple of eight; for example, when the actual output bitstream is [00000000110.sub.(2)] (11 bits), five zeros are padded to make 16 bits in total and the output is then [0000000011000000.sub.(2)]. The second type of zero padding occurs whenever the consecutive eight bits are all "1". For the bit stream [11111111110.sub.(2)], where the first eight bits are all "1", one zero is inserted as a delimiter and four zeros are padded to make [1111111101100000.sub.(2)]. Such a zero-padding rule is briefly stated to calculate the exact number of the output bits of the JPEG-LS algorithm.

For the lena image (256x256), the original GR and JPEG-LS GR output stream size without any padding is 299,901 bits, and 123 bits are added through the padding process to make 300,024 bits; notably, since 300,024 is a multiple of eight, the first type of zero padding is not necessary. In the pure output bit string of 299,901 bits, 123 cases of [11111111.sub.(2)] occurs, and the same number of zero bits are inserted as a second type of zero padding.

In the proposed method of this paper, nine bits of overhead header (i.e., "[0101|10100.sub.(2)]") are added to the pure JPEG-LS output of 299,901 bits; alternatively, 160 bits are reduced by the occurrence gain due to the 20 replaceable prefixes. In addition, six bits are reduced by the map gain; moreover, two bits are reduced by the K3 gain. The modified JPEG-LS output size is therefore 299,742 bits (i.e., 299, 901 +9-160-6-2). Regarding the 299,742 bits, since there are 122 consecutive eight "1"s, 122 zeros are inserted. As a result, the final output size of the modified JPEG-LS is 299,864 (i.e., 299,742 + 122) bits, which is the final result of the lena image because it is a multiple of eight, and this is slightly more favorable than that of the original JPEG-LS. In Table 4, 5 and 7, the numbers in the upper rows of the occurrence gain and the K3 gain (or K10 gain) are shown in bits, while the numbers in parenthesis in the lower rows indicate the number of occurrences of such gain.

For a few images, replaceable prefixes are not encountered; however, some images have a large number of replaceable prefixes. The artificial image (2,048 x3,072) that has been quantized by 16 bits (see Table 7) has 452,775 bits of occurrence gain meaning that the artificial image has 18,111 replaceable prefixes. Since the image size is 2,048x3,072, 23 bits are needed to mark the positions; therefore, the apparent occurrence gain is 25 bits (i.e., 48 - 23, where the replaceable prefix takes 48 bits for the 16-bit depth images). In this case, 19 bits are required as an overhead header to represent the 18,111 replaceable prefixes (i.e., the mandatory four bits to represent 15, and the next 15 bits to represent 18,111); therefore, the overhead header is represented as [1111|100011010111111.sub.(2)], which needs 19 bits in total. Notably, the artificial image is a synthetic image and not a natural one.

For the cameraman (256 x 256) image, 107 replaceable prefixes are encountered, and this means that 856 bits can be reduced; moreover, 32 bits are reduced due to the map gain, and 12 bits are reduced due to the K3 gain. As a result, the output size of the JPEG-LS and the proposed method are 282,488 bits and 281,576 bits, respectively. For the France image (496 x 672), 289 replaceable prefixes are found, while 112 bits and 33 bits are reduced as the map and K3 gains, respectively.

The clegg color image (880 x 814) in Table 6 has 7,872 bits of occurrence gain for the red channel, 6,832 bits for the green channel, and 8,456 bits for the blue channel, since the image has 1,968, 1,708, and 2,114 replaceable prefixes, respectively. For the red color, 7,872 bits, 1,669 bits, and 536 bits are the occurrence gain, map gain, and K3 gain, respectively. For the images quantized with 16 bits, the K10 gain is a counterpart of the K3 gain, as shown in Tables 7 and 8.

5. Conclusion and Discussion

In this paper, a new lossless compression method is proposed. When the codeword length is longer than the position information, the codeword can be replaced with a shorter piece of position information. JPEG-LS reference software uses either 24-bit or 48-bit replaceable prefixes to avoid the long codewords of the GR code; however, it is obvious that they are still long, and that replaceable prefixes of less than 24 bits or 48 bits can be used to enhance the compression rate. Future work includes the employment of various lengths of the replaceable prefix to maximize the performance. In this paper, the potential of the location information is manifested resulting in additional gains.

6. Acknowledgement

This work was supported in part by a National Research Foundation of Korea (NRF) grant funded by the Korean Government (MEST) (NRF-2015R1A2A2A01004587), and Korea University.

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[24] http://links.uwaterloo.ca/Repository.html

[25] http://imagecompression.info/test_images

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Jae Hyeon Woo (1), Hyoung Joong Kim (1)

(1) Graduate School of Information Security Korea University Seoul 136-701, Korea

(1) [e-mail: {bull0330, khj-}@korea.ac.kr]

(*) Corresponding author: Hyoung Joong Kim

Received July 11, 2016; revised September 2, 2016; accepted October 2, 2016; published November 30, 2016

Jae Hyeon Woo received a B.S. degree in Mechanical Engineering and a M.S. degree in Electrical and Computer Engineering from Seoul National University, Seoul, Korea, in 1996, 2002, respectively. He joined Multimedia Security Laboratory at the Center of Information Security and Technology (CIST), Graduate School of Information Management and Security, Korea University, Seoul, Korea in 2007, where he is currently pursuing Ph.D. His research interests include multimedia security, reversible and robust watermarking, steganography, phychology, and big-data.

Hyoung Joong Kim received his B.S., M.S., and Ph.D. degrees from Seoul National University, Seoul, Korea, in 1978, 1986, and 1989,respectively. He joined the faculty of the Department of Control and Instrumentation Engineering, Kangwon National University, Korea, in 1989. He is currently a Professor of the Graduate School of Information Management and Security, Korea University, Korea since 2006. His research interests include parallel and distributed computing, multimedia computing, multimedia security, and big-data.

Table 1. Example of the JPEG-LS codewords for a 512 X 512 image Position [N.sub.D] k Prefix Separator (0, 0) 33 2 00000000 1 (197, 256) 84 1 00000000000000000000000 1 (339, 211) 111 2 00000000000000000000000 1 (480, 290) 239 3 00000000000000000000000 1 (480, 394) 139 0 00000000000000000000000 1 ... ... ... ... (511, 511) ... ... ... ... Position Suffix (0, 0) 01 (197, 256) 01010011 (339, 211) 01101110 (480, 290) 11101110 (480, 394) 10001010 ... (511, 511) ... Table 2. q representation method with K3 gain in 8-bit image Unmodified q Bit expression Modified q Recorded bits 23 10111 0 000 24 11000 1 001 25 11001 2 010 26 11010 3 011 27 11011 4 100 28 11100 5 101 29 11101 6 110 30 11110 7 1110 31 11111 8 1111 Table 3. q representation method with K10 gain in 16-bit image Unmodified q Bit expression Modified q Recorded bits 47 101111 0 0000 48 110000 1 0001 49 110001 2 0010 ... ... ... ... 59 111011 12 1100 60 111100 13 1101 61 111101 14 1110 62 111110 15 11110 63 111111 16 11111 Table 4. Result of 8-bit Gray Images I. Image map K3 (HxW) occurrence gain gain bird gain 0 bits z 0 bits z (256 x 256) 8 bits (1) bridge (256 x 256) 152 bits (19) 0 bits 0 bits cameraman (256 x 256) 856 bits (107) 32 bits 22 bits (12) circles (256 x 256) 24 bits (3) 0 bits 0 bits corsses (256 x 256) 48 bits (6) 2 bits 0 bits goldhill (256 x 256) 64 bits (8) 2 bits 2 bits (1) horiz (256 x 256) 56 bits (7) 4 bits 0 bits lena (256 x256) 160 bits (20) 6 bits 2 bits (1) montage (256 x 256) 504 bits (63) 34 bits 6 bits (3) slope (256 x 256) 648 bits (81) 49 bits 8 bits (4) squares (256 x 256) 24 bits (3) 0 bits 0 bits text (256 x 256) 184 bits (23) 11 bits 0 bits Image output bits (HxW) Original JPEG-LS Proposed bird 524,288 227,272 227,264 (256 x 256) bridge (256 x 256) 524,288 379,264 379,128 cameraman (256 x 256) 524,288 282,488 281,576 circles (256 x 256) 524,288 9,784 9,768 corsses (256 x 256) 524,288 25,048 25,008 goldhill (256 x 256) 524,288 345,896 345,840 horiz (256 x 256) 524,288 5,928 5,880 lena (256 x256) 524,288 300,024 299,864 montage (256 x 256) 524,288 178,240 177,712 slope (256 x 256) 524,288 102,760 102,064 squares (256 x 256) 524,288 4,840 4,824 text (256 x 256) 524,288 106,728 106,536 Table 5. Result of 8-bit Gray Images II. Image occurrence map K3 (HxW) gain gain gain barb (512 x 512) 132 bits (22) 11 bits 0 bits boat (512 x 512) 84 bits (14) 2 bits 2 bits (1) France (496 x 672) 1,445 bits (289) 112 bits 65 bits (33) frog (498 x 621) 60 bits (12) 3 bits 2 bits (1) goldhill (512 x 512) 24 bits (4) 1 bits 0 bits lena (512 x 512) 72 bits (12) 6 bits 0 bits library (352 x 464) 624 bits (104) 50 bits 37 bits (20) mandrill (512 x 512) 492 bits (82) 0 bits 6 bits (3) mountain (480 x 640) 885 bits (177) 99 bits 68 bits (39) peppers (512 x 512) 126 bits (21) 6 bits 2 bits (1) washsat (512 x 512) 36 bits (6) 1 bits 0 bits zelda (512 x 512) 6 bits (1) 0 bits 0 bits Image output bits (HxW) Original JPEG-LS Proposed barb (512 x 512) 2,097,152 1,240,584 1,240,448 boat (512 x 512) 2,097,152 1,113,832 1,113,752 France (496 x 672) 2,666,496 470,664 469,048 frog (498 x 621) 2,474,064 1,870,432 1,870,368 goldhill (512 x 512) 2,097,152 1,234,912 1,234,896 lena (512 x 512) 2,097,152 1,112,240 1,112,176 library (352 x 464) 1,306,624 832,936 832,240 mandrill (512 x 512) 2,097,152 1,582,216 1,581,728 mountain (480 x 640) 2,457,600 1,972,616 1,971,592 peppers (512 x 512) 2,097,152 1,176,472 1,176,344 washsat (512 x 512) 2,097,152 1,082,256 1,082,232 zelda (512 x 512) 2,097,152 1,049,760 1,049,752 Table 6. Result of 8-bit Color Images. Image occurrence map K3 output bits (HxW) gain gain gain Original JPEG-LS R 7,872 1,669 965 5,730,560 1,703,848 G 6,832 1,045 515 5,730,560 1,794,640 clegg B 8,456 1,479 988 5,730,560 1,783,608 (880 x 814) R 4,268 64 1,185 9,883,120 2,431,024 frymire G 4,224 172 993 9,883,120 2,609,960 (1105 x 1118) B 3,818 108 906 9,883,120 2,459,416 R 18 0 0 2,097,152 1,060,280 G 102 6 0 2,097,152 1,207,568 lena B 192 0 8 2,097,152 1,284,120 (512 x 512) R 530 61 6 3,145,728 1,469,288 monarch G 445 45 14 3,145,728 1,469,056 (512 x 768) B 415 38 12 3,145,728 1,510,704 R 114 7 1 2,097,152 1,034,904 peppers G 108 16 2 2,097,152 1,019,296 (512 x 512) B 150 16 2 2,097,152 1,029,288 R 110 3 4 3,145,728 2,060,152 G 100 0 0 3,145,728 2,042,296 sail B 95 5 0 3,145,728 2,050,112 (512 x 768) R 2,972 247 235 3,995,408 826,480 serrano G 3,104 319 304 3,995,408 867,944 (794 x 629) B 2,204 254 269 3,995,408 665,408 R 155 9 0 3,145,728 1,578,680 tulips G 125 8 0 3,145,728 1,656,520 (512 x 768) B 160 15 2 3,145,728 1,701,432 Image Proposed (HxW) 1,693,352 clegg 1,786,264 (880 x 814) 1,772,808 frymire 2,425,608 (1105 x 1118) 2,604,648 2,454,648 1,060,272 lena 1,207,472 (512 x 512) 1,283,944 monarch 1,468,712 (512 x 768) 1,468,576 1,510,240 peppers 1,034,784 (512 x 512) 1,019,176 1,029,120 2,060,040 sail 2,042,208 (512 x 768) 2,050,024 serrano 823,072 (794 x 629) 864,240 662,680 tulips 1,578,520 (512 x 768) 1,656,400 1,701,272 Table 7. Result of 16-bit Gray Images. Image occurrence map K10 (H x W) gain gain gain Original artificial 452,775 22,765 6 100,663,296 (2048 x 3072) (18,111) (3) big building 5,060 0 0 624,847,872 (5412 x 7216) (230) big tree 198 18 0 443,206,400 (4550 x 6088) (9) bridge 120 12 0 178,091,216 (4049 x 2749) (5) cathedral 1,225 84 2 96,256,000 (3008 x 2000) (49) (1) deer 240 0 0 170,841,008 (2641 x 4043) (10) fireworks 4,464 101 0 118,013,952 (2352 x 3136) (186) flower foveon 1,375 20 0 54,867,456 (1512 x 2268) (55) hdr 550 28 0 100,663,296 (2048 x 3072) (22) leaves iso 200 3,350 125 4 96,256,000 (2000 x 3008) (134) (2) leaves iso 1600 3,075 168 4 96,256,000 (2000 x 3008) (123) (2) nightshot iso 100 648 9 0 118,013,952 (2352 x 3136) (27) nightshot iso 1600 2,808 60 0 118,013,952 (2352 x 3136) (117) spider web 575 12 0 193,937,408 (2848 x 4256) (25) zone_plate 1,675 30 56 96,000,000 (2000 x 3000) (67) (30) Image output bits (H x W) JPEG-LS Proposed artificial 27,167,728 26,692,336 (2048 x 3072) big building 451,339,088 451,334,028 (5412 x 7216) big tree 324,584,184 324,583,986 (4550 x 6088) bridge 135,643,808 135,643,688 (4049 x 2749) cathedral 69,526,592 69,525,296 (3008 x 2000) deer 136,309,472 136,309,240 (2641 x 4043) fireworks 60,353,296 60,348,744 (2352 x 3136) flower foveon 33,892,768 33,891,376 (1512 x 2268) hdr 62,900,288 62,899,720 (2048 x 3072) leaves iso 200 70,434,464 70,431,000 (2000 x 3008) leaves iso 1600 74,955,104 74,951,864 (2000 x 3008) nightshot iso 100 72,684,152 72,683,504 (2352 x 3136) nightshot iso 1600 88,672,408 88,669,552 (2352 x 3136) spider web 111,630,984 111,630,400 (2848 x 4256) zone_plate 95,673,640 95,671,872 (2000 x 3000) Table 8. Result of 16-bit Color Images. Image occurrence map K10 (H x W) C gain gain gain Original artificial R 440,400 22,646 14 100,663,296 (2048 x 3072) G 455,325 22,522 5 100,663,296 B 392,650 23,018 6 100,663,296 R 1,210 0 0 624,847,872 big_building G 7,568 2 0 624,847,872 (5412 x 7216) B 990 6 2 624,847,872 R 198 0 2 443,206,400 big_tree G 1,254 6 0 443,206,400 (4550 x 6088) B 176 0 7 443,206,400 R 1,056 37 0 178,091,216 bridge G 48 3 0 178,091,216 (4049 x 2749) B 0 0 0 178,091,216 R 2,125 172 6 96,256,000 cathedral G 2,450 204 0 96,256,000 (3008 x 2000) B 3,025 352 0 96,256,000 R 72 0 0 170,841,008 deer G 0 0 0 170,841,008 (2641 x 4043) B 0 0 0 170,841,008 R 3,864 63 0 118,013,952 fireworks G 2,424 0 4 118,013,952 (1512 x 2268) B 7,104 27 0 118,013,952 R 50 0 0 54,867,456 flower_foveon G 1,025 18 0 54,867,456 (1512 x 2268) B 0 0 0 54,867,456 hdr R 300 22 0 100,663,296 (2048 x 3072) G 250 15 0 100,663,296 B 175 11 2 100,663,296 leaves_iso_200 R 2,550 118 15 96,256,000 (2000 x 3008) G 5,150 251 2 96,256,000 B 1,700 58 8 96,256,000 leaves_iso_1600 R 425 11 9 96,256,000 (2352 x 3136) G 4,025 235 6 96,256,000 B 450 13 2 96,256,000 nightshot_iso_100 R 1,080 9 0 118,013,952 (2352 x 3136) G 1,056 18 0 118,013,952 B 1,944 48 0 118,013,952 nightshot_iso_1600 R 72 0 0 118,013,952 (2352 x 3136) G 2,928 9 0 118,013,952 B 2,712 3 0 118,013,952 R 115 0 0 193,937,408 spider_web G 529 8 0 193,937,408 (2848 x 4256) B 207 2 0 193,937,408 Image output bits (H x W) JPEG-LS Proposed artificial 27,622,520 27,159,592 (2048 x 3072) 26,097,064 25,619,352 22,666,056 22,250,512 471,972,608 471,971,398 big_building 446,166,904 446,159,336 (5412 x 7216) 457,438,424 457,437,434 338,047,656 338,047,458 big_tree 316,958,648 316,957,394 (4550 x 6088) 356,661,248 356,661,072 137,191,176 137,190,088 bridge 139,260,144 139,260,096 (4049 x 2749) 141,927,112 141,927,120 72,049,384 72,047,096 cathedral 65,756,096 65,753,448 (3008 x 2000) 69,606,856 69,603,488 136,085,256 136,085,192 deer 143,742,960 143,742,968 (2641 x 4043) 147,174,488 147,174,496 65,342,088 65,338,176 fireworks 50,603,008 50,600,600 (1512 x 2268) 30,611,824 30,604,712 34,634,848 34,634,800 flower_foveon 25,886,872 25,885,840 (1512 x 2268) 34,599,072 34,599,072 hdr 64,317,448 64,317,136 (2048 x 3072) 64,468,512 64,468,256 66,914,480 66,914,288 leaves_iso_200 71,013,008 71,010,336 (2000 x 3008) 70,067,784 70,062,400 69,239,256 69,237,488 leaves_iso_1600 76,392,784 76,392,352 (2352 x 3136) 74,091,952 74,087,696 73,353,248 73,352,800 nightshot_iso_100 74,671,984 74,670,904 (2352 x 3136) 71,826,064 71,825,000 60,798,592 60,796,608 nightshot_iso_1600 90,512,384 90,512,320 (2352 x 3136) 86,662,496 86,659,568 80,695,226 80,668,410 114,490,864 114,490,752 spider_web 111,667,024 111,666,496 (2848 x 4256) 114,798,856 114,798,656

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Author: | Woo, Jae Hyeon; Kim, Hyoung Joong |
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Publication: | KSII Transactions on Internet and Information Systems |

Article Type: | Report |

Date: | Nov 1, 2016 |

Words: | 7808 |

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