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It is difficult for the conventional image compression method to achieve good compression effect in the underwater acoustic image (UWAI), because the UWAI has large amount of noise and low correlation between pixel points. In this paper, fractal coding is introduced into UWAI compression, and a fractal coding algorithm based on interest region is proposed according to the importance of different regions in the image. The application problems of traditional quadtree segmentation in UWAIs was solved by the range block segmentation method in the coding process which segmented the interest region into small size and the noninterest region into large size and balanced the compression ratio and the decoded image quality. This paper applies the classification, reduction codebook, and correlation coefficient matching strategy to narrow the search range of the range block in order to solve the problem of the long encoding time and the calculation amount of encoding process is greatly reduced. The experimental results show that the proposed algorithm improves the compression ratio and encoding speed while ensuring the image quality of important regions in the UWAI.

The UWAI refers to an image generated by imaging sonar according to the characteristics of the underwater target echo signal by means of acoustic wave detection. Due to the limitation of the underwater acoustic (UWA) channel and the storage capacity of the device [

Due to the particularity of UWAIs, many methods used for optical image compression cannot always achieve good results. The traditional image compression method is based on removing the correlation redundancy in the image. Due to the existence of noise, the correlation between the pixels of the UWAI is very poor. At the same time, limited by the entropy, the compression ratio of traditional image compression method is generally not high in the UWAI compression. Therefore, this paper applies the fractal coding based on the fractal theory and iterative function system to UWAI compression to improve the image compression performance. Fractal coding algorithm breaks the limitations of the information theory which is based on the widely existing self-similarity in images. The basic idea is to achieve high compression ratio by removing the structural redundancy through a set of compression transformations. Since Barnsley first applied fractal theory to image compression in 1988 [

In 1992, inspirited by Barnsley’s research, Jcaquin proposed fractal coding based on the local iterative function system [

The structure of this paper is as follows: the second section briefly introduces the principle of basic fractal coding; the third section focuses on the fractal coding algorithm based on region of interest and the correlation coefficient fractal coding algorithm is proposed; the simulation and experiment results are given in the fourth section; the fifth section comes the conclusion.

The basis fractal coding (BFC) is to find a set of compression transformations whose fixed points are similar with the original image. These sets of compression transformation are called the Iterated Function System (IFS). Jacquin proposed the Partial Iterative Function System (PIFS) and the basic fractal coding, inspired by IFS. The implementation of BFC algorithm is as follows.

When encoding, the image is first divided into a Range Block (R block) and a Domain Block (D Block). The R blocks do not overlap with each other, and the entire R blocks can form the original image. The D blocks can be generated by sliding a certain size window in the original image according to a preset step size which are allowed to have overlapping areas. To ensure the convergence of PIFS, the block size of D should be larger than that of R (usually the D block size is twice larger than the R block).

Supposing the size of the original image is M × M, the block size of R should be B × B and the block size of D block will be 2B × 2B. The sliding step is represents by

In order to match the D and R blocks, the D block needs to do the spatial contraction, and its size is scaled from 2B × 2B to B × B. Usually, the four-neighbor pixel averaging method is used for spatial contraction (as shown in Figure

Four neighborhood pixel average.

For each R blocks, it is necessary to find the closest block in the contracted D blocks to obtain the fractal code. According to PIFS, between the R block and the D block there is an affine similarity, which means that the R block is similar to the D block after the equidistant transformation (rotation, flipping, etc.). Jacquin simplified and summarized the isometric transformations, which is shown in Table

8 kinds of isometric transformations.

Index | Transformation name | Transformed pixel |
---|---|---|

1 | Identity transformation | |

2 | Axisymmetric reflection on the vertical axis | |

3 | Axisymmetric reflections on the horizontal | |

4 | Symmetric reflection on the main diagonal | |

5 | Symmetric reflection on the sub-diagonal | |

6 | 90° counterclockwise about the center | |

7 | 180° counterclockwise about the center | |

8 | 270° counterclockwise about the center | |

In the table,

After the entire

After the above process, for any

The matching error between

When searching in different

The procedure of the BFC is shown in Figure

The procedure of the BFC.

The fractal decoding process is relatively simple. By compression transformation, the decoded image can be applied to any image of the same size as the original image.

As can be seen from Section

Quadtree partitioning is similar to the tree structure in data structure. The original image can be regarded as the root of the tree, and the four fork points (corresponding to the four quadrant regions of the image respectively) are separated from the root node. Each of the fork points can select whether to further divide the four new subnodes according to certain rules (corresponding to four sub-regions of the image area corresponding to the intersection, respectively). The new subnode continues to split according to this rule, and when the segmented node reaches the maximum segmentation depth, the segmentation will stop. Then the entire image is divided into several subblocks with different sizes.

In practice, the gray-scale uniform criterion is generally used for the quadtree partitioning. When the block size of one image is larger than the minimum segment size, which means the difference between the maximum gray value and the minimum gray value is greater than a preset threshold, the block is further divided. Otherwise the block does not need to be split.

For different size image blocks generated after segmentation, the fractal code can be obtained by match searching in the corresponding codebooks using the basic fractal coding method. Therefore, the quality of the decoded image can be increased by dividing the portion of the image with a smaller difference in the pixel value by a larger size, thereby increasing the compression ratio and dividing the portion with a larger difference in the pixel value by a smaller size, thereby ensuring the decoding image quality.

Figures

Ordinary gray image quadtree segmentation: (a) original image Lena and (b) effect of quadtree segmentation.

UWAI quadtree segmentation: (a) original image ship and (b) effect of quadtree segmentation.

Considering that the main information of the UWAI is concentrated in the area where the target is located, the noisy background area does not need much attention. For this reason, different size segmentation is used for different important areas in the UWAIs in this paper. The important area in the image (hereinafter referred to as the region of interest) is divided by a small size, and a large size segmentation is adopted for the noninterest region. The specific segmentation process is as follows.

Denoising effect of different methods: (a) original image; (b) average filtering; (c) median filtering; (d) Butterworth low-pass filtering; (e) Gaussian low-pass filtering; (f) Wiener filtering.

① Use the canny operator for edge extraction on the denoised image.

② Morphological expansion is used to connect discontinuous target edge lines into closed lines.

③ The nontarget contour lines caused by interference are removed by morphological operation.

④ Fill the target contour area.

⑤ Morphological expansion is applied to expand the target area, and the expanded area is the required interest region for coding.

Figure

Extract results of interest region: (a) ship and (b) plane.

Segmentation effect of UWAI: (a) ship and (b) plane.

After the UWAI is segmented, R blocks of different sizes are generated. For each R block, it is necessary to search for the best matching block in its corresponding codebook to obtain a fractal code. According to the basic fractal coding proposed by Jacquin, the R block searches in all codebooks, which will cost a long time on encoding. Therefore, the search area of R block is reasonably reduced, and the matching process between R block and D block is optimized to reduce the calculation amount of encoding process and improve the encoding speed.

From formula (

As can be seen from (

When the variance of the R block is small, the matching error is accordingly small. Therefore, the R block is divided into two categories according to the variance: the R block whose variance is less than the preset threshold

Equation (

When searching for the best matching block of the R block, it is necessary to calculate the parameters according to (

For R block and D block, the correlation coefficient is represented by

This is available in formula (

Equation (

This means that if the R block matches the D block (

According to the above analysis, in the encoding procedure, for each R blocks, the correlation coefficient and the matching error of the first D block in the reduced codebook are calculated, respectively as

For a UWAI to be compressed, firstly extract the interest region. Then divides the interest region and the non-interest region into different sizes, and generates the codebooks with different size simultaneously. A reduced codebook is generated according to the threshold

(1) Preset the threshold

(2) According to the method proposed in Section

(3) According to the R block partition size, two codebooks of different sizes are respectively produced; and the reduced codebook is constructed according to the codebook threshold

(4) For smooth blocks (R blocks with variance less than), take the constant block as approximated, and the fractal code is directly output without searching.

(5) For nonsmooth blocks (R blocks with variance greater than or equal to

(6) Complete the encoding of all R blocks to generate an encoded file.

The specific steps of the encoding are shown in Figure

Specific steps of encoding based on the interest region algorithm.

(1) Read information such as the information of the quadtree partition, the position of the best matching block of the R block in different size codebooks, the equidistant transformation mode, the contrast factor, and the grayscale offset.

(2) Define three images Y_{1}, Y_{2}, and X having the same size with the original image, in which X is used to store the image generated by the iterative process and Y_{1} and Y_{2} are used to generate two codebooks with different sizes.

(3) Initialize Y_{1} and Y_{2}.

(4) For each R block in X, according to its fractal code

in which

(5) If the number of iterations reaches 8, go to step (6); otherwise, copy X to Y_{1}, Y_{2} and go to step (4).

(6) Output image X.

In order to verify the effectiveness of the algorithm, two UWAIs: ship and plane were used for the simulation experiment. The test image is shown in Figure

UWAIs: (a) ship and (b) plane.

① Experimental study of the parameter

Conversion curve of encoding performance with

Decode image comparison with different

② Experimental study of the parameter

Conversion curve of encoding performance with different

Experimental results comparison of different algorithms.

Algorithm | Image | |||||
---|---|---|---|---|---|---|

Ship | Plane | |||||

Encoding Time (s) | PSNR | Compression ratio | Encoding Time (s) | PSNR | Compression ratio | |

(dB) | (dB) | |||||

BFC (4 × 4) | 30.40 | 159.70 | 5.12 | 29.19 | 160.12 | 5.12 |

BFC (8 × 8) | 26.58 | 40.41 | 20.48 | 25.02 | 40.54 | 20.48 |

VBFC (4 × 4) | 29.80 | 17.71 | 5.12 | 28.41 | 17.31 | 5.12 |

VBFC (8 × 8) | 26.38 | 5.05 | 20.48 | 24.75 | 5.12 | 20.48 |

PSO (4 × 4) | 29.23 | 11.78 | 5.12 | 28.04 | 11.38 | 5.12 |

PSO (8 × 8) | 25.69 | 3.46 | 20.48 | 24.25 | 3.57 | 20.48 |

The proposed algorithm | 28.77 | 3.02 | 13.87 | 27.49 | 3.15 | 13.25 |

It can be seen from Table

Since most of the images are noninterest regions, this paper adopts a large size 8 × 8 segmentation for these parts. And for interest region, the small size 4 × 4 segmentation is adopted. Therefore, the compression of the algorithm in this paper is significantly improved compared with the basic 4 × 4 algorithm. In the quality of the decoded image, it can be seen from Figure

Decoding image of BFC, VBFC, PSO, and the proposed algorithm.

The original image

BFC (4 × 4)

BFC (8 × 8)

VBFC (4 × 4)

VBFC (8 × 8)

PSO (4 × 4)

PSO (8 × 8)

The proposed algorithm

The VBFC algorithm and the PSO algorithm use the method of variance approximation matching and particle swarm optimization to improve the encoding speed. It can be seen from the experimental results that the coding time of the VBFC and PSO algorithms decreases with the increase of the R block partition size, but even the PSO (8 × 8) algorithm with the smallest coding time is also longer than the encoding time of the proposed algorithm. This is mainly because the algorithm in this paper comprehensively adopts multiple strategies such as reduced codebook and fast search based on correlation coefficient, while VBFC algorithm and PSO algorithm only improve the match searching mode, and the calculation efficiency is not good than the proposed algorithm.

It can be seen from Figure

The proposed algorithm is also compared with the quadtree fractal algorithm. The quadtree fractal algorithm was first proposed by Fisher, but Fisher’s method needs to calculate the matching error of four subblocks in each block, and the matching process adopts the full search strategy which is the same as the BFC algorithm, resulting in a large amount of computation and long encoding time. Therefore, this paper chooses an improved quadtree fractal coding algorithm for comparison. The improved algorithm firstly performs quadtree decomposition on the image according to the gray uniformity criterion and then performs matching search on the decomposed R blocks of different sizes in the reduced codebook. The encoding efficiency is greatly improved compared with Fisher’s method.

The maximum segmentation size of the improved quadtree algorithm and the proposed algorithm are 8 × 8, and the minimum segmentation size is 4 × 4. As can be seen from Table

Comparison of improved quadtree algorithm with the proposed algorithm.

The number of 4 × 4 blocks | The number of 8 × 8 blocks | Encoding time | PSNR | Compression ratio | |
---|---|---|---|---|---|

Improved quadtree algorithm | 3996 | 25 | 186.35 | 30.18 | 5.53 |

| |||||

Proposed algorithm | 1128 | 742 | 3.02 | 28.77 | 13.87 |

In view of the particularity of UWAIs, this paper uses fractal coding based on partial similarity to compress the UAWI. In order to improve the encoding speed and compression ratio, this paper proposes a fractal coding algorithm based on interest region and correlation coefficient. The algorithm divides the interest region in the image into small size and divides the noninterest region into large size, which effectively increases the compression ratio and recovers the information of important regions well. At the encoding stage, the R block searching range is reduced by reducing the codebook and classification, and the inappropriate D block is pre-excluded according to the correlation coefficient between the R block and the D block, which greatly reduces the calculation amount of the encoding process. The simulation results verify that the proposed algorithm not only improves the UWAI compression ratio but also significantly reduces the encoding time, while at the same time ensuring the restoration quality of the interest region in the image.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

The authors acknowledge the project of the National Natural Science Foundation of China (Grant no. 61701487), the Innovation Foundation of Chinese Academy of Sciences (Grant no. CXJJ-17-M126), the Natural Science Foundation of Hainan Province (Grant no. 417211), the Young Talents’ Science and Technology Innovation Project of Hainan Association for Science and Technology (Grant no. QCXM201812), the National Key Research and Development Program of China (Grant no. 2016YFC1400100), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant no. XDA13030000), and the Fundamental Research Funds in Heilongjiang Provincial Department of Education (no. 135209239). The authors also thank the Technical Bureau of Qiqihar GYGG-201622.