CN1545323A - Image compression coding method using rectangle block filling code word to reduce space redundancy - Google Patents

Abstract

The invention is an image compressing and coding method using rectangle to fill code words in order to reduce space redundancy. Firstly, fill some subset SNJ of the subgraph sets SN with rectangle blocks from big to small ones until the SNJ is full of rectangle blocks, and mark these blocks; then making Huffman coding on all the subgraphs's SNJ data, to obtain the final compression data. Generally, this processing is made on the subsets with wavelet coefficients' amplitude is near zero, and it makes routine processing on the other wavelet coefficients. It can largely save operational quantity and obtain high data compression.

Description

Use rectangular block to fill the image compression encoding method that code word reduces spatial redundancy

Technical field

The invention belongs to the Image Compression field, be specifically related to a kind of rectangular block that utilizes and fill the image compression encoding method that code word reduces spatial redundancy.

Background technology

1, the statistical property of image and attribute

Generally speaking, when having the image encoding of M * N pixel, the data symbol sequence of pixel count is thought of as statistics independently.According to the discrete memoryless source cryptoprinciple, his entropy is ^[1]

$H\left(X\right)=\frac{1}{\mathrm{MN}}\underset{j=1}{\overset{\mathrm{MN}}{\mathrm{\Σ}}}\underset{i=1}{\overset{L}{\mathrm{\Σ}}}P\left(x_{i,j}\right){\log }_2\left(\frac{1}{P\left(x_{i,j}\right)}\right)\≤{\log }_{2}L---\left(1\right)$

Here, p (x _i) be the distribution function of pixel intensity, L is the hierarchy number and the i=1 of pixel intensity ..., L.During to block encoding, the data symbol of several pixels joins together to encode, and their combination entropy must be not more than entropy sum separately, promptly

$H(X_1,...X_K)\≤\underset{k=1}{\overset{K}{\mathrm{\Σ}}}H\left(X_k\right)---\left(2\right)$

If be not to add up independently between pixel, promptly there is certain correlation between them, at this moment following formula is got the strict sign of inequality.

In fact, nearly all image pixel data is not to add up independently, their brightness space distribution function p (x _i) be subjected to the physical characteristic constraint of the device of scanner-recorder spare and demonstration, equally also be subjected to the attribute constraint of image self.

The physical characteristic of device of considering scanner-recorder spare and demonstration can be regarded image as be made up of a series of spots set during to the influencing of image attributes, each in these spots, and its brightness has following two-dimentional Gaussian Profile pattern ^[2]

$p_i(x_i,y_i)=e^{-({x_i}^2+{y_i}^2)}=e^{-r_i^2}---\left(3\right)$

Here x _i, y _iBe respectively level and vertical range apart from i spot center, r _iIt is radius.If, be R from spot centre distance _i, his brightness drops to the distance of a half of spot center brightness, and the distribution function of spot intensity can be write as

$p_i\left(r_i\right)=2^{-{(r_i/R_i)}^2}$

Like this, to influence relation as follows for the brightness of other pixels around the brightness of a certain pixel K was subjected in the image

$D_n=I_n+\underset{m=0,m\≠n}{\overset{M}{\mathrm{\Σ}}}{I}_m{p}_m\left(r_{m-n}\right)---\left(4\right)$

I in the formula _nBe the brightness of n spot, second portion is the influence of neighbor to n spot, wherein I _mBe the brightness of m spot, r _M-nBe that m spot is to the distance between n spot.

The Luminance Distribution of most of images determined by the content of image, and Lena image for example has different Luminance Distribution on his face and health.Can consider that piece image is to be set up jointly by the sub collective drawing of different attribute, encodes respectively according to the set of different attribute subgraph ^[3]But the subgraph set that also has identical attribute in the searching image, and, can obtain very low view data code word like this with the Search Results back coding of classifying.Yet, dissimilar images is difficult to find the general classification and the low rate encoding method of attribute.

2, the transformed mappings of image

Mapping is the important means in the image Compression process, and commonly used have a discrete cosine transform (DCT) ^[4]And wavelet transformation ^[5]Deng.The DCT algorithm is divided into grouping set such as 8 * 8 or 16 * 16 with the pixel of image, behind dct transform, the low frequency component of image concentrates on the upper right corner, high fdrequency component is then in the lower left corner, carry out the compression that huffman coding can obtain view data behind the coefficient quantization to mapping, but he has lost the detail section of image.Not data compression effect of dct transform itself, he has just done a mapping that time domain arrives frequency domain, has changed discrete cosine transform coefficient and has distributed and structure, provides facility for further carrying out data compression process.Wavelet transformation is another transform method commonly used, and when image Compression was used, he was mapped to two-dimensional quadrature wavelet decomposition image set with two dimensional image.Shown in Fig. 1 b, four number of sub images in this two-dimensional space, have been comprised, i.e. the high-frequency information of the high-frequency information of the high-frequency information of image low frequency information, image level direction, image vertical direction and image diagonal direction.As identical with DCT, the of mapping own do not compress view data, but he has carried out reconstruct to decomposing the wavelet subband coefficients of images distribution, and shown in the wavelet coefficient distribution histogram of Fig. 1 c, wavelet coefficient is assembled near zero.He brings benefit to compressing to handle according to the picture characteristics after the mapping.

List of references:

1.John?G.proakis，“Digital?Communications，Fourth?Edition”[M]McGraw-Hill?Education?Co.pp90.

2.Kenneth?R.Castleman，“Digital?Image?Processing”[M]Prentice?Hall?International，Inc.pp41

3. " the subregion compress technique of medical ultrasonic dynamic image " Fudan Journal [J] 1999 such as bright, the Song Jun of Shao Qian, Ye Xiaodong, vol.38 (3) P331-336

4. " principle of data compression and application " Electronic Industry Press, Wu Le south [M] 1995

5.Charles?K.Chui“An?Introduction?to?Wavelets”[M]Academic?Press，Inc.

6. all beautiful, Luo Jianshu etc. " the zero searching fractal image coding [J] of combined with wavelet transformed ". Chinese image graphics journal, 2001.

7. grandson's nine sweet smell, yellow intelligent. " based on the Wavelet image coding [J] of zero tree, pyramid lattice shape vector quantization ". Chinese image graphics journal, 2001.

Summary of the invention

The objective of the invention is to propose a kind of very big data compression that both can obtain, can save the image compression encoding method of computing workload again.

The image compression encoding method that the present invention proposes is a kind of method of carrying out image compression encoding based on wavelet transformation.

Through wavelet transformation, obtain four subgraphs of two-dimentional exploded view picture, his image attributes and former figure have basic change, the present wavelet coefficient of its mark sheet gathers near null in a large number, shown in Fig. 1 b, c, this adopts bit-planes to classify to carry out low rate encoding and has created condition decomposing picture to us.

To the wavelet coefficient two dimensional image of Fig. 1 b, can regard the set of a series of different amplitude wavelet coefficients as shown in Figure 2 as:

S＝{…?S _-i?…?S ₀?…?S _i?…} (5)

In the formula ... S _-iS ₀S _iExpression wavelet coefficient amplitude is 0, ± 1 ... the set of bit-planes subgraph.As shown in Figure 3, he is that the wavelet coefficient amplitude is the subgraph S set of i _iWherein comprised at diverse location, difform subclass S _Ij, j=1 ..., these sub collective drawing with same alike result have been set up jointly into S _iSubgraph set, i.e. S _Ij∈ S _i, j=1 ..., same S _Ij∈ S, i=0, ± 1 ... j=1 ...For the subgraph S set _iIn each subgraph S _IjCan describe with multiple mathematical method, as to subgraph S _IjThe two-dimentional huffman coding based on rim detection, somatotype coding etc., can obtain low bit rate coding like this.But, it is to be noted because subgraph S _IjNumber is bigger, has the S of same alike result to searching _iSubgraph set and to subgraph S _IjDescription bring huge operand.In order to simplify calculating process, the present invention proposes a kind of new image compression encoding method, adopt rectangular block to fill code word exactly and come subgraph S _IjBe described.Specifically, for the subgraph S set _N(be S _iIn certain subgraph of determining set) in a certain subclass S _Nj, adopt the rectangular block code word to fill (promptly filling zero), fill descending carrying out, up to filling up whole subclass; Then rectangular block is identified.The sign of all these rectangular blocks is this subclass S _NjDescription.

Illustrate the inventive method below.As shown in Figure 3, at a sub-set of graphs S _NIn a subgraph S is arranged _Nj, at S _NjIn the wavelet coefficient amplitude of 129 pixels be N all, at S _NjExtra-regional wavelet coefficient amplitude is other values.At this moment, filling number of codewords as rectangular block is 16, to S _NjDescription as shown in table 1 be 69 bits, and initial data is 1032 bits.

Table 1. rectangular block is filled code word to S _NjDescription desired data amount

The code word bits number

(the code word number of types is that piece is counted bit number graph data bit to the code word type

16)

Bit-planes 9 9/

9×9 ＜4 1 ＜4 648

Square

2×4 ＜4 3 ＜12 192

Shape

4×1 ＜4 3 ＜12 96

Piece

Fill out 2 * 2＜41＜4 32

Fill

2×1 ＜4 1 ＜4 16

Sign indicating number

1×2 ＜4 2 ＜8 32

Word

1×1 ＜4 4 ＜16 32

Total bit number＜69 1032

As seen fill code word to S with rectangular block _NjDescription can save very big data volume, the multiple of the data volume of saving depends on S _NjThe size of area and rectangular block are filled code word type and number.Through after the above-mentioned processing, to the subgraph S of all bit-planes _IjData are carried out huffman coding, obtain final packed data.Said method is equally applicable to two-dimensional image sequence, and obtains better effect.

Because the amplitude range of wavelet coefficient enlarges behind the wavelet transformation, this makes the bit-planes number of subsets of classifying by coefficient amplitude increase, and whole like this calculation operations amount is bigger.But by the mapping of wavelet transformation, wavelet coefficient is assembled near zero, promptly decomposes the wavelet subband coefficients of images amplitude and accumulates in { S near zero part _-xS _-1S ₀S ₁S ₂S _XOn the subclass, and (100-X) that account for whole wavelet coefficient is more than the %.Therefore, the present invention can only carry out above-mentioned computing (promptly the bit-planes to these amplitudes adopts the word arithmetic of rectangular block filler code) to them, and the bit-planes wavelet coefficient of other amplitudes is carried out the huffman coding computing according to a conventional method.It is enough that general X gets 4-10.For example shown in Figure 1, the wavelet coefficient amplitude is accounting for more than 90% (x=10) between-10～10, i.e. S _90%={ S _-10S _-1S ₀S ₁S ₂S ₁₀.As only to S _90%Carry out above-mentioned computing, and the wavelet coefficient of the bit-planes of other amplitudes is carried out the huffman coding computing according to a conventional method, then can obtain very big data compression simultaneously again saving operand greatly.Wavelet coefficient after handling is carried out the compressed encoding that huffman coding has been finished entire image again.

Description of drawings

Fig. 1 is the wavelet transformation and the corresponding wavelet coefficient amplitude distribution of Lena image, and wherein Fig. 1 (a) is the Lena image, and Fig. 1 (b) is wavelet decomposition image and structure, and Fig. 1 (c) is the wavelet coefficient amplitude histogram.

Fig. 2 is for waiting bit plane subclass S _i

Fig. 3 is subgraph S _NiRectangular block filler code WD.

Fig. 4 is the S of two-dimensional wavelet transformation subband component ₀, S _iSubclass and, wherein Fig. 4 (a) is S ₀Subclass, Fig. 4 (b) is S ₁Subclass, Fig. 4 (c) is S ₀' subclass.

Fig. 5 is that 3 D wavelet transformation subband component and rectangular block are filled code word, and wherein Fig. 5 (a) is three layers of wavelet decomposition of 3-D view, and Fig. 5 (b) is the 3-D view wavelet decomposition, and Fig. 5 (c) fills code word for the three-dimensional rectangle piece.

Embodiment

Further describe the present invention below by compressed encoding experimental example based on two peacekeeping two-dimensional image sequence of small echo.

(1) compressed encoding of two dimensional image experiment

Get Lena and Barbara image, picture format is 512 * 512 * 8bit, carries out wavelet transformation:

$\left(W_{\mathrm{\Ψ}}f\right)(a,b)=|a{|}^{-1/2}\underset{R}{\∫}f\left(t\right)\stackrel{\‾}{\mathrm{\Ψ}\left(\frac{t-b}{a}\right)}\mathrm{dt}---\left(6\right)$

F (x) ∈ L wherein ²(IR), by wavelet mother function Ψ (x) be by translation and the flexible family of functions that generates

${\mathrm{\Ψ}}_{\mathrm{ab}}\left(x\right)=|a{|}^{-1/2}\mathrm{\Ψ}\left(\frac{x-b}{a}\right)---\left(7\right)$

A, b are respectively flexible and shift factor, a, b ∈ L in the formula ²(IR), a ≠ 0, Ψ (x) satisfies the admissibility condition

$C_{\mathrm{\&Psi;}}=\underset{-\&infin;}{\overset{+\&infin;}{\&Integral;}}\frac{|\widehat{\mathrm{\&Psi;}}\left(w\right){|}^2}{\left|w\right|}\mathrm{dw}<\&infin;---\left(8\right)$

In conversion, adopt dyadic wavelet:

Ψ _j，k(x)＝2 ^j/2Ψ(2 ^jx-k)， j，k∈Z (9)

When realizing, adopt qualified limited long impulse response filter (FIR) commonly used to realize to discrete one dimension digital signal { C _n ⁰} _{N ∈ Z}Wavelet transformation

$C_k^{j-1}=\underset{n}{\mathrm{\&Sigma;}}{\stackrel{\&OverBar;}{h}}_{2k-n}{C}_n^j---\left(10\right)$

$d_k^{j-1}=\underset{n}{\mathrm{\&Sigma;}}{\stackrel{\&OverBar;}{g}}_{2k-n}{C}_n^j---\left(11\right)$

Reconstruction formula is:

$C_n^j=\underset{k}{\mathrm{\&Sigma;}}{h}_{n-2k}{C}_k^{j-1}+\underset{k}{\mathrm{\&Sigma;}}{g}_{n-2k}{d}_k^{j-1}---\left(12\right)$

Wherein, C _k ^J-1, d _k ^J-1Be respectively the low frequency component of reflection integral image and the high fdrequency component of reflection image detail part.

By respectively the one-dimensional transform of row and column being finished the two-dimensional wavelet transformation of image.The decomposition of the luminance component of image after through three layers of wavelet transformation, the result is shown in Fig. 2 and Fig. 1 b.

The histogram distribution of the wavelet coefficient after the conversion is shown in Fig. 1 c.S ₀The wavelet coefficient on plane accounts for 45% of whole number of coefficients, if comprise S ₁And S _-1Subclass, the wavelet coefficient number accounts for more than 75% of whole coefficient sets.Simple for computing, this paper is with S _(5,5)={ S _-5S _-1S ₀S ₁S ₅In all subclass be merged into zero subclass S ' ₀, shown in Fig. 4 c, then to S ' ₀Subclass carries out handling as the rectangular block code word zero filling method of Fig. 3 ^[6], and the wavelet coefficient of the bit-planes of other amplitudes is carried out the huffman coding computing according to a conventional method.During processing, at first with S ' ₀Have wavelet coefficient pixel adjacent, zero amplitude on the subclass and form a subgraph S ' _0j, at S ' ₀Several subgraphs S ' can be arranged on the subclass _0j, i.e. j=1,2 ...Adopt 1 * 1,2 * 2,3 * 3 ..., N * N rectangular block is filled the code word type and is carried out S ' ₀All S ' on the subclass _0jFill, as shown in Figure 3, the descending rectangular block of filling is one by one filled code word, up to S ' _0jFill up ^[6], like this rectangular block filler code WD of Tian Chonging S ' _0jThese rectangular blocks filling code words will be carried out the huffman coding compression with the wavelet coefficient of other bit-planes subclass then, and compression result is as shown in table 2.

The rectangular block code word zero filling method experimental result and the comparison of table 2 Lena image

Compression method PSNR (dB) compression ratio

(doubly)

Rectangular block code word zero filling method 29.08 43.29

Conventional huffman coding method 29.08 7.02

Zero searching fractal image coding method ^[7]28.61 33.6

Zero tree, pyramid lattice shape vector quantization coding method 29.0 42.6

^[8]

Table 2 shows, under identical PSNR condition, the relatively more conventional huffman coding method of the Image Data Compression of the inventive method is high a lot, and computational complexity just slightly increases.With zero searching fractal image coding method, zero tree, pyramid lattice shape vector quantization coding method are compared, and the image compression performance of rectangular block code word zero filling method is higher, and computational complexity wants much simple.

(2) compressed encoding of two-dimensional image sequence experiment

Get one section medical ultrasonic video image, picture format is 640 * 480 * 8bit, totally 256 frames and two sections Miss America and Salesman normal video image, and picture format is 352 * 288 * 8bit, every section 112 frame.The luminance component of its image three layers of wavelet transformation through vertical, level and time three directions are decomposed, and shown in Fig. 5 a, wherein directions X is represented column direction, Y direction indication line direction, Z direction indication time-axis direction.He is an X three dimensions, shown in the left figure of Fig. 5 b, he is the three dimensional representation of two-dimensional image sequence low frequency component after small echo once decomposes, and white portion is the null value wavelet coefficient after the conversion, other wavelet coefficients flock together, and as seen have a large amount of spatial redundancies therein.Shown in the right figure of Fig. 5 b, it is the three dimensional representation that small echo once decomposes the back diagonal components, and as seen wavelet coefficient is almost nil therein.It also can change into the three-dimensional bit set that waits wavelet coefficient after the conversion.Similar to the situation of two dimension, the present invention is only to three-dimensional S ' ₀Subclass (S _(5,5)) carry out the processing of rectangle cube block codewords zero filling method, adopt 1 * 1 * 1,2 * 2 * 2,3 * 3 * 3 during processing ..., N * N * N rectangle cube piece is filled code word and is carried out S ' ₀Each S ' on the subclass _0jFill, carry out the huffman coding compression with other bit-planes subclass then, experimental result is as shown in table 3.

Table 3 two-dimensional image sequence rectangle cube block codewords zero filling method coding

Video image title picture size and frame number mean P SNR (dB) compression ratio

Medical ultrasonic 640 * 480 * 256 34.538 79.04

Miss?America 352×288×112 36.02 170.16

Salesman 352×288×112 36.02 83.90

According to Shannon theory, the information source redundancy comes from the correlation of information source itself and the inhomogeneities of source symbol probability distribution.If can make full use of this two characteristics, just can realize efficient compression to the information source data.Wavelet transformation is mapped to two-dimensional quadrature wavelet decomposition image set with two dimensional image, not view data not being compressed of mapping itself, but he has carried out reconstruct to decomposing the wavelet subband coefficients of images distribution, makes wavelet coefficient assemble near zero, and this provides convenience for various compression methods.Eliminating the information redundancy of map image, is the main target of various image compression encoding methods, and as zero tree, pyramid lattice shape vector quantization coding method, it utilizes in the wavelet transformation process the residual self-similarity of each subgraph to encode, and has obtained effect.But his calculation of complex, operand is big, and uncomfortable Real Time Compression is used.The rectangular block code word zero filling method that the present invention proposes, made full use of the spatial redundancy of the two-dimensional quadrature wavelet decomposition image set that wavelet transformation obtains, the adjacent symbol that will have same alike result is combined, and alternative with a new symbol (rectangular block code word zero filling method code word), reduced the spatial redundancy that shines upon the exploded view picture effectively.And the code word number of types that he increased seldom, and the code book data volume size that produces during to huffman coding does not have big influence.Rectangular block code word zero filling method has very high compression efficiency, and his computing is simple, is very suitable for the Real Time Compression of image.

Rectangular block code word zero filling method is based on the information space redundancy of eliminating the adjacent-symbol with same alike result, and it also can combine with the method that adopts other contraction principles, obtains higher picture compression efficiency.

Claims (4)

1, a kind of rectangular block that uses is filled the image compression encoding method that code word reduces spatial redundancy, establishes S={ ... S _-iS ₀S _iBe the set of a series of different amplitude wavelet coefficients, wherein ... S _-iS ₀S _iExpression wavelet coefficient amplitude is 0, ± 1 ... ± i ... bit-planes subgraph set, S _IjBe S _iMiddle diverse location, difform subclass, j=1,2 ..., S _NBe S _iIn the set of certain concrete subgraph, it is characterized in that for subclass S _IjAdopt the rectangular block code word to fill, fill descending carrying out, up to filling up whole subclass S _Nj, and rectangular block identified; Then, the sub-graph data of all bit-planes is carried out huffman coding, obtain final packed data.

2, image compression encoding method according to claim 1 is characterized in that only antithetical phrase set of graphs { S _-xS ₀S _xIn S _iAdopt the rectangular block code word to fill computing, and the WAVELET SYSTEMS of the bit-planes of other amplitude is carried out the computing of Huffman system sign indicating number according to a conventional method, getting X is 4-10.

3, image compression encoding method according to claim 2 is characterized in that X is taken as 5, and note S _(5,5)={ S _-5S _-1S ₀S ₁S ₂S ₅In the zero subclass that is merged into of all subclass be S ₀', S ₀' be two-dimensional space, adopt 1 * 1,2 * 2,, 3 * 3 ..., N * N rectangular block is filled code word to S ₀' S on the subclass _0j' fill, carry out the huffman coding compression with other bit-planes subclass then.

4, image compression encoding method according to claim 2 is characterized in that getting X=5 for two-dimensional image sequence, and note S _(5,5)={ S _-5S _-1S ₀S ₁S ₂S ₅In the zero subclass that is merged into of all subclass be S ₀', S ₀' be three dimensions, adopt 1 * 1 * 1,2 * 2 * 2,3 * 3 * 3 ... the rectangle cubic block code word of N * N * N is to S ₀' S on the subclass _0j' fill, carry out the huffman coding compression with other bit-planes subclass then.

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