Near lossless image compression using parallel fractal texture identification

Biomedical Signal Processing and Control 58 (2020) 101862

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Near lossless image compression using parallel fractal texture identification R. Suresh Kumar a,∗ , P. Manimegalai b a b

Department of Electronics and Instrumentation Engineering, SNS College of Technology, Coimbatore, India Department of Biomedical Engineering, Karunya Institute of Technology and Sciences, Coimbatore, India

a r t i c l e

i n f o

Article history: Received 8 March 2019 Received in revised form 24 September 2019 Accepted 13 January 2020 Keywords: Peak Signal to Noise Ratio Structural Similarity Index Mode Feature Similarity Index Mode

a b s t r a c t The most important parameters of image processing are resolution of the image and processing speed. The datasets of multimedia are compressed, which are rich in quality and quantity is challenging. This paper develops a novel approach to estimate the affine parameters of fractal texture identification, in order to minimize the complexity of computation. In this proposed NLICPFTI, a pattern dictionary is maintained to hold repeated fractal patterns. Different types of data chunks such as Fractal Pattern Chunk (FPC), Intermediate Raster Chunk (IRC), Intermediate Vector Chunk (IVC), Run Length Encode Chunk (RLEC) and Flood-fill Zone Chunk (FFZC). These chunks are used to store an image into compressed format. Experimental on standard images illustrate that our approach gives more significant improvements in Peak Signal to Noise Ratio, Structural Similarity Index Mode, Feature Similarity Index Mode at high compression ratio. © 2020 Elsevier Ltd. All rights reserved.

1. Introduction Fractal Image Compression (FIC) is one of the significant techniques completely automated by Jacquin [1] for gray scale image coding. The fundamental fractal image compression is based on the surveillance where images typically reveal affine redundancy. Here an image is divided into a number of different sized blocks in addition to the encoding process contains resembling the small image blocks, known as Range blocks (RBs), from the bigger blocks, known as Domain blocks (DBs), of the image, by penetrating the most excellent matching affine transformation from a DB pool, greatly akin to the image compression by vector quantization (VQ) technique [2]. In the process of encoding, different transformations for every RB are attained. For decoding process, the set of affine transformations, while iterated upon random initial image, creates a fixed point (attractor) that estimates back the target image. This Technique, called as Partitioned Iterative Function System (PIFS), was proposed by Fisher [3]. Smoothing and linear filtering operations are easy as well as popular techniques used for removal of noise and restoration of image. However their sturdiness is less, as they hypothesize that the image consists of a stationary signal, created through a linear

∗ Corresponding author. E-mail addresses: [email protected] (R. Suresh Kumar), [email protected] (P. Manimegalai). https://doi.org/10.1016/j.bspc.2020.101862 1746-8094/© 2020 Elsevier Ltd. All rights reserved.

system. On the other hand, real-world images are having nonstationary statistical properties and are usually obtained using non-linear methods. The device of image acquiring capture the intensity distribution is a product of the illumination falling on the scene or object of interest, in addition to its reflectance. Several nonlinear as well as adaptive image denoising techniques have been proposed that had taken these statistical variations into account, and consequently give enhanced output image quality, whereas maintaining the features of high frequency of the input image.

2. Related work There exist different methods on finding fast match depends on meta-heuristic algorithms which is similar to Genetic Algorithm (GA) [4], Particle Swarm Optimization (PSO) [5] etc. These techniques that reduce the encoding time have also been applied in fractal image compression. These evolutionary algorithms have a major draw backs that they do not assurance the most excellent match for the specifieRange blocks. Furthermore, their processing time of encoding is significantly higher contrasted to the feature-vector based techniques and classification. The fractal image encoding by a novel affine transform was offered by Zhao et al. [6]. This technique is basically a more generalized form of usual affine transform that also contains two different scaling parameters. To decrease the computational costs, a fractal coding method based on Huber norm and a novel matching error function,

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Fig. 2. First Level Observation.

Fig. 1. Global View.

next to the no-search method has offered by Lu et al. [7]. There is no work presents dealing with different ways of speed-up other than slight variations of previously discussed methods, to the best of our knowledge [8,9]. On the other hand, a simple surveillance demonstrates that various approach to Fractal Image Compression needs computation of affine parameters for attaining the scaling parameter (s) that engages expensive matrix multiplication step. So, the question is, can we reinstate matrix multiplication with a few cheaper calculations, so that complexity of computational time is reduced without sacrificing the quality of image. This paper is an attempt to answer this point. The method proposed here utilizes an estimation of the scaling parameter that evades the computation of the inner product, by this means considerably speeding up the search process. As well, in this technique we utilize a modified HV partitioning method. In addition, several optimization utilized to reduce the computation of affine transforms gives up a larger compression compared to the conventional HV [10] technique based on partitioning. In recent times, there are so many researches in the field of fractal compression. In that order, Jeng et al. and Lu et al. proposed the fractal image compression technique based on Huber loss function [11,12]. The correlation between range and domain blocks for the Fractal image compression scheme is proposed by Wang et al. [13]. The fractal compression is applied in the field of medical image compression is presented by Bhavani et al. [14]. The applied Discrete Wavelet transform method utilized for fractal image compression method is presented by Wang et al. [15]. Our team also researched on fractal and fractal compression theory and application [16–19].

Fig. 3. Third Level Magnified Observation.

3. Proposed method: near lossless image compression using parallel fractal texture identification (NLICPFTI) 3.1. Fractal patterns Fractals are patterns with recursive occurrences. A small portion of a fractal image can be used to reconstruct the entire Image. The Fractal property is blended with nature in many cases. The fractal patterns are common in nature for both living and non-living existences in this universe. Enforcing identification of the fractal property in an image is very much helpful in compressing images without any significant losses. As an example, the global view of an image, first level observation and third level magnified observation is shown in Figs. 1–3 respectively. The snow flakes and sea shells are other examples of Natural Fractals as shown in Fig. 4(a) and (b). 3.2. Impact of fractal patterns in image compression A 256 × 256 resolution image is taken to explain how fractal can be used in compression. The Image is given as Fig. 5.

Fig. 4. (a): Snow Flakes. (b): Sea Shells.

Examples – Natural Fractals.

If the image is stored directly as a raster raw file (without compression), then it will take 196,608 Bytes of storage in RGB color space. Applying a simple Run Length Encoding (RLE) will consume more memory since the continuity breaks when every empty pixel RGB (255,255,255) breaks with a Pattern pixel RGB(0,0,0). Fig. 6 explains the RLE Compression. The same is applicable to store the image as Vector Graphics. It will take 4476 Bytes of memory to store the square as a vector graphics.

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Table 1 Chunk Identification Bits and Chunk Types. Bits

HEX Value

Chunk Type

000 001 010 011 100 101 110 111

0x00 0x01 0x02 0x03 0x04 0x05 0x06 0x07

Fractal Pattern Chunk (FPC) Intermediate Raster Chunk (IRC) Intermediate Vector Chunk (IVC) Intermediate Run Length Encode Chunk (IRLEC) Flood-fill Zone Chunk (FFZC) Reserved for Future use Reserved for Future use Reserved for Future use

Fig. 5. Fractal Square 256 × 256.

Fig. 8. Movement directions. Fig. 6. RLE Compression breaks.

Fig. 7. Horizontal Split.

Fractal Pattern Identifier (FPI) is used to find repeated fractal patterns in an image. FPI works in special domain with image Horizontal, Vertical and Diagonal splitting process. The first phase is splitting the image by applying Horizontal, vertical and diagonal split processes. Then the divided image blocks are compared with each other using histogram. Whenever there is a match between the blocks identified by the histogram method, different transformations are applied to one of the blocks to get the PSNR match – which is the second phase. If the PSNR value is high, then the image blocks are labeled as the identical fractal patterns – that will get the entry in the fractal pattern dictionary. The fractal pattern is explained in the following diagram as shown in Fig. 7. In the above diagram, Shape A and shape B are similar. The difference is only a single vertical flip. While checking the histogram for the above image, both upper part (Shape A) and lower part (Shape B) will get the same value since the Pixel intensity distribution are

not identical. When the shapes are found to have the same histogram value, there is a higher probability to get the fractal image patterns. To find the exact shape, PSNR test is conducted to the shapes. As per the above diagram, the PSNR value will be a near 0 value. After applying a 90◦ clockwise transformation to shape B, the PSNR Value will be same are previous attempt. But while repeating the same process (90◦ clockwise rotation), the PSNR Value will be very high (near ∞) which shows the exact or relational pattern match between the two shapes – actually one. This process is applied to all the quadrants (Horizontal split and Vertical split) recursively up to 16 levels to detect maximum fractal patterns from an image In this proposed NLICPFTI, a pattern dictionary is maintained to hold repeated fractal patterns. Different types of data chunks such as Fractal Pattern Chunk (FPC), Intermediate Raster Chunk (IRC), Intermediate Vector Chunk (IVC), Run Length Encode Chunk (RLEC) and Flood-fill Zone Chunk (FFZC) are used. These chunks are used to store an image into compressed format. The Fractal Compression format starts with 3-bits chunk identification header – given in Table 1. Then it continues with 64-bits pattern ID field which can hold up to 18446744073709551616 different patterns represented as (x ). The next 16-bits are used to store the initial fractal position (xi .yi ). Successive 1-bit () is allocated to represent the vector or raster pattern storage which is auto selected by Algorithm 1that operates based on the required storage space. The successive 9-bits (to hold 0–360) are used to represent the rotational transformation of the fractal image. The next 3-bits are used to show the movement direction ( ) of the fractal pattern. The movement directions are given in Fig. 8. Next 16-bits are used to store the movement range of the selected fractal pattern x . The NLICPFTI Fractal Pattern Chunk is explained in Table 2. This is a constant length (14 Bytes) data chunk of NLICPFT.

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Table 2 NLICPFTI Fractal Pattern Chunk.

Table 4 Flood-fill data chunk Fields.

Field

Bits

Field

Bits

Chunk Indicator Pattern ID Initial Position Vector/Raster Rotation Movement Direction Movement Range

3 64 16 1 9 3 16

Chunk Identifier Flood-fill location Counts

3 13 24 32

Flood-fill data

RGB Start Location

Table 3 IRC format. Field

Bits

Chunk Identifier start position Raster area width Raster area Height Raster area size Empty bits Raster Data

3 32 16 16 33 4 Variable size 3 × (ω × h) Fig. 9. NLICPFTI Compression Labels l: Left t: Top r: Right b: Bottom.

Table 5 Fractal Pattern Chunk for Left direction. Field

Value

Chunk Indicator Pattern ID Initial Position Vector/Raster Rotation Movement Direction Movement Range

0x00 1 (l,t) 1 0 0 15

Table 6 Fractal Pattern Chunk for bottom direction.

The Intermediate Raster Chunk has the first 3-bits as Chunk Identification bits with the stored value 001. The successive 16bits are used to store the width (ω) of the intermediate raster area. The beginning position of the intermediate raster chunk is stored in next 32-bits. Following 16-bits are used to store the height (h) of the intermediate raster area. The maximum size of an intermediate zone () is permitted is 4294967296 Bytes. This size is stored in successive 33-bits.Next 4-bits are left unused as empty bits to complete a Byte. Then the intermediate raster data occupies further storage of this chunk based on the  – i.e. the size of intermediate zone, thus it is of variable length of 3 × (ω × h) Bytes for RGB color space. Therefore, an IRC will occupy the standard 13 Bytes + Raster data (Variable size). The storage pattern of IRC is given in Table 3. For Flood-fill chunk, the first 3-bits are used as the chunk identifier with the value 100. Next 13-bits are used to store the flood-fill location counts (). The maximum value for this field can be 8192. The location data will be of variable length 3 × 32 bits for RGB Color space. Here the 32-bits are used to store the start locations (x,y) of flood-fill. The flood-fill zone chunk will consume a standard 2 Bytes + variable 12 Bytes. The flood-fill data chunk information is given in Table 4. Ex: NLICPFTI compression of an Image – given in Fig. 5 In fractal Compression, the pattern is identified as a square fractal with the size of 4 × 4 pixels assigned with the pattern-ID 1.The NLICPFTI compression labels are given in Fig. 9. The entire image can be compressed using 4 FPCs given in Tables 5–8.

Field

Value

Chunk Indicator Pattern ID Initial Position Vector/Raster Rotation Movement Direction Movement Range

0x00 1 (l,t) 1 0 6 15

Table 7 Fractal Pattern Chunk for top direction. Field

Value

Chunk Indicator Pattern ID Initial Position Vector/Raster Rotation Movement Direction Movement Range

0x00 1 (r,b) 1 0 2 15

Table 8 Fractal Pattern Chunk for right direction. Field

Value

Chunk Indicator Pattern ID Initial Position Vector/Raster Rotation Movement Direction Movement Range

0x00 1 (r,b) 1 0 4 15

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Fig. 10. Test MRI images of data set 1.

3.3. NLICPFTI fractal patterns parallel identification



ga =

Edge detection is the key-process of identifying Fractal patterns. Oriented Gaussian filter-based edge detection is used in this work. Detecting edges and their directions is a critical task because of the extremely variable nature of the linear and curvy nature. A scale parameter  is introduced in this work to limit the edge detection process based on a threshold as given in the following equation. 1 ga = g (x, y, u , v , ˛) = exp 2 u v

 −

u2a 2u2

−

v2a 2v2

 (1)

∂ ga ∂Va

(2) 

Where ga is the oriented Gaussian filter, ga is the oriented Gaussian alternative filter, ˛ is the direction of the edge pixels, u is the horizontal threshold,  is the vertical threshold, ua = u(x, y : ˛), va = v(x, y : ˛). The values of ua and va are derived by the following



ua

va



 =

cos˛

sin˛

−sin˛

cos˛

  x

y

(3)

6

R. Suresh Kumar and P. Manimegalai / Biomedical Signal Processing and Control 58 (2020) 101862

Fig. 11. PSNR (dB) values for different methods.

Fig. 12. EPSNR (dB) values for different methods. 

A single oriented Gaussian derivative filter ga is used for a single direction ˛. To cover all directions, an array of directions ˛[360] is  created and the filters ga [] are calculated in parallel using Xilinx’s Kintex 7 processor. After finding all edges, they are grouped to form the patterns and repeated patterns are stored in the pattern dictionary. 3.3.1. Experimental setup Since Kintex 7 is the target processor of this work, Xilinx ISE is used to design and emulate the entire process. An user interface is designed using Visual Studio to perform the image input and output processes. Visual Studio is also used to construct the C++ codes which are converted into Register-Transfer-level (RTL) codes by Vivado HLS.

Standard parameters such as PSNR, FSIM, SSIM and compression ratio are measured for the proposed method and compared with existing methods for performance evaluation. 4. Result and discussion The original test MRI images of human brain as shown in Fig. 10 are used to analyze the compression techniques. Five MRI images shown in Fig. 10 are used as the first data set. Similarly ten data sets, each contains 5 MRI different images are used for the analysis of PSNR, EPSNR, SSIM, FSIM and compression ratio. These parameters are compared between the proposed technique NLICPFTI with the exiting techniques which are “An Improved Image Compression Algorithm Using Wavelet and Fractional Cosine Transforms”

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Table 9 Comparison of PSNR (dB) for different methods. Dataset

AIICA [20]

HLSRSVS [21]

VICENLCFAIC [22]

NLICPFTI [Proposed method]

1 2 3 4 5 6 7 8 9 10

35.86 33.50 33.12 33.23 32.70 32.27 32.96 35.76 35.95 32.54

32.87 30.43 29.98 31.57 29.11 31.56 32.96 3144 32.12 30.39

33.87 31.35 30.83 33.14 32.76 31.62 32.96 31.12 32.29 31.47

40.07 41.88 42.88 41.48 39.98 41.68 40.16 41.19 40.06 39.32

Table 10 Comparison of EPSNR (dB) for different methods. Dataset

AIICA [20]

HLSRSVS [21]

VICENLCFAIC [22]

NLICPFTI [Proposed method]

1 2 3 4 5 6 7 8 9 10

24.53 24.99 25.92 25.06 26.93 25.63 25.07 25.85 24.64 26.15

21.78 22.10 22.46 20.61 23.15 20.17 22.71 20.90 22.58 23.08

20.03 19.71 20.20 20.93 19.13 18.48 19.58 20.96 18.74 20.51

32.01 32.33 33.55 31.48 32.34 34.02 31.45 31.25 31.17 32.94

Table 11 Comparison of SSIM (dB) for different methods. Dataset

AIICA [20]

HLSRSVS [21]

VICENLCFAIC [22]

NLICPFTI [Proposed method]

1 2 3 4 5 6 7 8 9 10

0.89 0.88 0.88 0.89 0.89 0.88 0.89 0.90 0.90 0.88

0.87 0.86 0.85 0.86 0.86 0.86 0.85 0.87 0.87 0.87

0.83 0.84 0.83 0.84 0.82 0.84 0.82 0.83 0.82 0.82

0.96 0.96 0.97 0.97 0.96 0.95 0.96 0.95 0.96 0.95

Table 12 Comparison of FSIM (dB) for different methods. Dataset

AIICA [20]

HLSRSVS [21]

VICENLCFAIC [22]

NLICPFTI [Proposed method]

1 2 3 4 5 6 7 8 9 10

0.94 0.94 0.94 0.94 0.93 0.93 0.94 0.94 0.94 0.93

0.93 0.93 0.92 0.92 0.94 0.93 0.94 0.92 0.93 0.93

0.89 0.91 0.89 0.91 0.89 0.90 0.90 0.89 0.90 0.91

0.98 0.98 0.98 0.98 0.98 0.99 0.99 0.99 0.99 0.98

Table 13 Comparison of compression ratio for different methods. Dataset

AIICA [20]

HLSRSVS [21]

VICENLCFAIC [22]

NLICPFTI [Proposed method]

1 2 3 4 5 6 7 8 9 10

1.28 1.21 1.27 1.24 1.25 1.24 1.20 1.26 1.20 1.20

1.42 142 1.42 1.40 1.47 1.46 1.42 1.43 1.44 1.42

1.54 1.54 1.56 1.54 1.51 1.50 1.53 1.51 1.51 1.54

2.39 2.40 2.36 2.36 2.37 2.37 2.40 2.41 2.39 2.40

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Fig. 13. SSIM (dB) values for different methods.

Fig. 14. FSIM (dB) values for different methods.

(AIICA) [20], “High Level Synthesis for Retiming Stochastic VLSI signal Processing Architectures” (HLSRSVS) [21] and “VLSI Implementation of a Cost-Efficient Near-Lossless CFA Image Compressor [22]. The complexfor Wireless Capsule Endoscopy”  (VICENLCFAIC)  ity of the proposed work is O x × n2 where ␳x is the number of fractal patterns involved. Then, we present the comparison of Peak Signal to Noise Ratio for the proposed method (NLICPFTI) with the existing methods AIICA [20], HLSRSVS [21], VICENLCFAIC [22] and the results are shown in Fig. 11 and Table 9. In Table 9, we find that the NLICPFTI shows better PSNR for all the dataset. In Table 10 and Fig. 12, we also find that NLICPFTI gives best EPSNR for all the dataset when compared to the other techniques. Based on the most recent research works, the medical image compression techniques can reach around 30–50 dB of PSNR for the high com-

pression ratios. The PSNR value can be increased by reducing the compression ratio – which will affect the compressed file size significantly. SSIM is applied to a square fractal with the size of 4 × 4 pixels that moves pixel by pixel horizontally and vertically covering all the rows and columns of the image, starting from top-left corner of the image. In Table 11 and Fig. 13, we show that the proposed technique gives better SSIM among the other techniques. The feature based similarity index is more in the MRI images and the experimental results also demonstrate that the FSIM of the proposed techniques has better performance than FSIM on all the datasets for other methods as shown in Table 12 and Fig. 14. The PSNR also gets better as the compression ratio is more. The Compression ratio is also very high for the NLICPFTI method as shown in Table 13 and Fig. 15.

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Fig. 15. Compression ratios for different methods.

5. Conclusion In this paper, a new image compression algorithm based on NLICPFTI has been proposed to improve the compression efficiency. The compression ratio is doubled with the proposed method when compared with AIICA method. PSNR ratio is increased by 1.43 times when compared with HLSRSVS. EPSNR is increased by 1.84 times when compared with VICENLCFAIC. SSIM is increased by 1.17 times when compared with VICENLCFAIC method. Finally FSIM is also increased by 1.1 times when compared with HLSRSVS method. The proposed algorithm is suitable for applications, which requires high compression percentage with better PSNR, EPSNR, SSIM and FSIM index. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] A.E. Jacquin, Image coding based on a fractal theory of iterated contractive image transformations, IEEE Trans. Image Process. 1 (1) (1992) 18–30. [2] B. Ramamurthi, A. Gersho, Classified vector quantization of images, IEEE Trans. Commun. 34 (11) (1986) 1105–1115. [3] Y. Fisher, E. Jacobs, R. Boss, Fractal image compression using iterated transforms, in: Image and Text Compression, Springer, 1992, pp. 35–61. [4] D.E. Golberg, Genetic Algorithms in Search, Optimization, and Machine Learning, 1989, Addion Wesley, 1989, p. 102. [5] J. Kennedy, Particle swarm optimization, in: Encyclopedia of Machine Learning, Springer, 2011, pp. 760–766. [6] Y. Zhao, B. Yuan, A new affine transformation: its theory and application to image coding, IEEE Trans. Circuits Syst. Video Technol. 8 (3) (1998) 269–274.

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