CN101080008A - A multi-description coding method based on alternate function system - Google Patents

A multi-description coding method based on alternate function system Download PDF

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CN101080008A
CN101080008A CN 200710099533 CN200710099533A CN101080008A CN 101080008 A CN101080008 A CN 101080008A CN 200710099533 CN200710099533 CN 200710099533 CN 200710099533 A CN200710099533 A CN 200710099533A CN 101080008 A CN101080008 A CN 101080008A
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function system
iterated function
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fractal
description coding
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赵耀
张志远
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Beijing Jiaotong University
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Abstract

This invention discloses a multi-description coding method based on an iterative function system, which applies a tessellated segment mode to divide an iterated function system to several parts taken as descriptions to be transmitted at the coding terminal, when receiving only one path of description information, it applies a fractal extrapolation method to resume the un-received information and re-structure an iterative function system and finally repeatedly iterates the received iterative function system to get decoded images.

Description

A kind of multi-description coding method based on iterated function system
Technical field
The present invention relates to a kind of image multi-description coding-decoding method, in particular, relate to a kind of multi-description coding-decoding method, belong to the image encoding and decoding technique field based on iterated function system.
Background technology
Fractal image coding is the method for compressing image of a kind of thinking novelty of growing up in nearly ten years, compares with other comparatively ripe compress technique, has lot of advantages such as high compression ratio, resolution independence.It has utilized the fixpoint theory in the mathematics, attempts to describe entire image with a function (family), claims that this function (family) is an iterated function system.Be essentially different with orthogonal transform coding in the past; When decoding, by the arbitrary resolution image being carried out the iterated transform of limited number of time, no matter initial pictures how, can both converge to decoded picture.Barnsley and Sloan have proposed this thought the earliest, and nineteen ninety Jacquin has designed the fractal image coding device based on the square division of first practicality, and have caused people to this field keen interest and concern widely.
In fractal image coding, original image finally can be divided into the sub-piece of two classes, the sub-piece of codomain that is non-overlapping copies is coding unit and allows the sub-piece of the partly overlapping domain of definition, each coding unit all obtains best being similar to by the conversion of the sub-piece of certain domain of definition, be that approximate error is that collage error minimizes, storage or transmit the coefficient of all conversion as the position of scale factor, brightness translation, the sub-piece of the domain of definition etc., is promptly finished the coding to entire image.
1, iterated function system: an iterated function system (IFS) comprises that (X, d), and ω is shone upon in a series of deflation that is defined in this space to a complete metric space n: X → X, stringent factor is respectively S n, n=1,2, L, N.Usually IFS is expressed as { X: ω n, n=1,2, L, N}, convergence factor is S=max{S nN=1,2, L, N.
2, the fixed point theorem of iterated function system: make { X: ω n, n=1,2, L, N} are the iterated function system with stringent factor S, conversion W:H (X) → H (X) is defined as W ( B ) = ∪ n = 1 N ω n ( B ) ,  B ∈ H (X), W is the deflation mapping on the complete metric space { H (X), h (d) } so, and stringent factor is S, i.e.  B, C ∈ H (X), have h (W (B), W (C))≤Sgh (B, C); And has unique fixed point A = W ( A ) = ∪ n = 1 N ω n ( A ) , and can obtain by following formula, ∀ B ∈ H ( X ) , A = lim n → ∞ W n ( B ) .
3, the collage theorem of iterated function system: make that (X is a complete metric space d), makes B ∈ H (X), and a TFS is selected, { X: ω in given ε 〉=0 n, n=1,2, L, N} has stringent factor S, and 0≤S＜1 makes h ( B , ∪ n = 1 N ω n ( B ) ) ≤ ϵ , wherein h (d) is for Hausdoff estimates, so h (B, A)≤ε/(1-s), wherein A is the fixed point of this IFS, simultaneously for all B ∈ H (X), has following relation h ( B , A ) = ( 1 - S ) - 1 gh ( B , ∪ n = 1 N ω n ( B ) ) .
Along with the develop rapidly of the Internet and wireless mobile communications, multimedia service shared proportion in service grows with each passing day, but it is bringing people's life conveniently simultaneously, and the network congestion problem that the real-time network data transmission occurs also becomes increasingly conspicuous.In internet communication, loss of data and delay are one of common situations, and in the radio multimedium data communication, because deep fading's channel may cause transfer of data to be made mistakes or loss of data, thereby cause receiving terminal not to be correctly decoded.Therefore the picture quality that how to solve generation therefrom in image and the video signal transmission problem that seriously descends has become in recent years an important subject, and multiple description codedly begun to receive publicity as a kind of optional solution, because multiple description coded is to be a plurality of independently code streams with signal decomposition, and transmit, thereby can be in the robustness of enhancing signal under the high compression efficiency by different channels.
Multiple description coded thought is to be proposed as an information-theoretical problem by people such as Gersho in IEEE Shannon Theory Workshop meeting in 1979 the earliest.Subsequently, this thought is applied to audio frequency, in the coding transmission of image and video.
1, multiple description coded basic framework: establish X and Represent information source to be transmitted and reconstruction signal respectively,
Figure A20071009953300072
Expression
Figure A20071009953300073
With respect to the distortion value of X, R iThe expression code check.The multiple description coded a plurality of codec { C of design that are meant i, i=1,2, L, M} makes:
I, each C iRate distortion function f (R i, D i) satisfy to provisioning request;
Ii, any one above C iCombination gained distortion function D must be less than min{D i;
Iii, (C 1, C 2, L, C M) distortion function obtain global optimum.
Here, any one C iCan independently decode.
For the multi-description coding-decoding device of two descriptions, its structure as shown in Figure 1, the channel at decoder 1 and decoder 2 places is called the limit channel, decoder 0 place channel is called center channel.If have only the signal of a channel correctly to be transferred to receiving terminal, then the distortion value of reconstruction signal is greater than the Min. distortion value; If the signal of two channels receives that all then one of them signal can be used to strengthen another signal, with the higher-quality reconstructed value that obtains.
2, the classification of conventional images multi-description coding method
At present the multi-description coding method of image mainly be divided into based on quantize, based on conversion with based on multiple description coded three classes of spatial spread.
(1), based on the multi-description coding-decoding method that quantizes: based on the multiple description coded of quantification is the quantization function that needs a complexity of design, be used for information source is carried out the quantification of different accuracy, its basic thought is the big step-length of quantification carry out to(for) single description, and a plurality of descriptions then can obtain meticulous quantification when mutually combining.Mainly be divided into based on scalar quantization multiple description [Y.Tanya based on the multiple description method that quantizes, W.Berger and E.M.Reingold, " index assignment of the multichannel communication when wrong the generation " Electrical and Electronic engineering association information theory journal, the 48th volume, the 10th phase, the 2656-2668 page or leaf, 2002.] [S.D.Servetto, K.kamchandran and V.Vaishampayan, " based on the image encoding of many descriptions small echo " Electrical and Electronic engineering association image processing journal, the 9th volume, the 5th phase, 2002.] and based on many describing methods of vector quantization [V.A.Vaishampayan, N.J.A.Sloane and S.D.Servetto, " the multiple description method with vector quantization of trellis code book: design and analyze " Electrical and Electronic engineering association information theory journal, the 48th volume, the 5th phase, 1718-1734 page or leaf, 2001.]
(2), based on the multi-description coding-decoding method of conversion: multiple description coded its basic thought based on conversion is will introduce the correlation of controlled quantity through the coefficient after the orthogonal transform again by specific correlating transforms, so that the data of losing can approximate evaluation obtain [Y.Wang from the data that other receive, M.T.Orchanr and V.Vaishampayan, Electrical and Electronic engineering association frame is handled journal " to use the multi-description coding method of point to the correlation conversion ", the 10th volume, the 3rd phase, the 351-366 page or leaf, 2001.]
(3), based on the multi-description coding-decoding method of spatial spread: the common ground of various multiple description codings based on spatial spread is: by orthogonal transform with K dimensional signal spatial spread to L dimension (L 〉=K), carry out sub-sampling again.If L 〉=N * K (N for describe number) then according to sampling theorem, each description can recover original signal [D.Chung and Y.Wang separately, " use " the video technique journal of Electrical and Electronic engineering association circuit and system based on the signal decomposition of lapped orthogonal transform and many descriptions image encoding of method for reconstructing, the 9th volume, the 6th phase, the 895-908 page or leaf, 1999.]
Existing multi-description coding method is based on quantification, conversion and spatial spread.Up to the present also there are not the methods of describing to be based on fractal image more.Fractal coding has lot of advantages such as high compression ratio, resolution independence.
Summary of the invention
The objective of the invention is to propose a kind of many descriptions method for encoding images based on iterated function system.The objective of the invention is to be achieved through the following technical solutions: a kind of multi-description coding method based on iterated function system is characterized in that it comprises:
(1), tries to achieve the preordering method of the iterated function system of figure;
(2), use predetermined dividing method that the iterated function system of trying to achieve is cut apart;
(3), the part of using predetermined restoration methods that iterated function system is lost is recovered;
(4), use predetermined method to classify to the sub-piece of each codomain;
(5), reconstruct iterated function system, this system of iteration obtains decoded picture.
The present invention design based on many descriptions method for encoding images of iterated function system with the initial data demultiplexing.The present invention makes full use of fractal image and removes the map information that the characteristic of the correlation of adjacent block mapping in the similitude of different scale and the fractal image recovers to lose piece, obtains encoding and decoding performance preferably and stronger Channel Transmission robustness.
During coding, piece image at first passes through fractal image coding, and image can be split into the sub-piece of mutually disjoint codomain, for cutting apart the good sub-piece of codomain, adopts tessellated mode that it is distributed into two groups.One tunnel transmission code stream of describing has been formed in the mapping of the sub-piece correspondence of every group codomain, is referred to as main description.Meanwhile, the sub-piece of each codomain is classified, be divided three classes: cross grain, vertically texture and tilted direction texture according to the texture trend.Classified information as the relevant information that increases along with main description is transmitted together.
During decoding, when the two-way descriptor can both receive, the range block map information that uses two-way to describe constructed an iterated function system.When only receiving one tunnel descriptor, use and receive the range block map information and the classified information of description, adopt the method for fractal extrapolation to recover the map information of not receiving description, rebuild out an iterated function system in conjunction with the map information of receiving.Through iteration, can obtain decoded picture preferably.
Advantage of the present invention: no matter the many descriptions method for encoding images based on iterated function system that the present invention is designed is on the objective measurement of compression performance, and still recovering has all had the raising of certain degree in the subjective assessment of picture quality.Iff receiving one tunnel raising that can obtain 0.5-3dB when describing; When the two-way description is received simultaneously, the raising of 2-6dB is arranged than the method for reference.
Meanwhile, the advantage of fractal image has been inherited in coding method of the present invention fully, and situation about taking place for packet loss has more robustness.Can see that the classical way of the speed ratio reference of image quality decrease was slow when loss rate increased.The present invention can better enhancing signal robustness.
Description of drawings
The structure chart that Fig. 1 describes for double-channel;
Fig. 2 is multiple description coded device and the decoder frame model that the present invention is based on iterated function system, and wherein (a) is encoder; (b) decoder;
Fig. 3 mainly describes the generation schematic diagram for the present invention;
Fig. 4 is the block diagram of relevant information production process of the present invention;
Fig. 5 is the schematic diagram of the fractal Extrapolation method of the present invention;
When Fig. 6 was all black picture for first iterative image, 8 iteration of fractal decoding are figure as a result;
Fig. 7 is the present invention and reference method raising relatively, and situation about receiving when wherein (a) is for the two-way information of same is (b) for only receiving the situation of one tunnel information;
Fig. 8 is a robustness result schematic diagram of the present invention, and wherein (a) is test pattern Lena; (b) be test pattern Boat.
Embodiment
Below in conjunction with the drawings and specific embodiments the present invention is further described.
Important module specific explanations shown in Figure 2 is as follows:
1, producing multichannel describes
As shown in Figure 3, through behind the fractal image, image is divided into the sub-piece of mutually disjoint codomain, for cutting apart the good sub-piece of codomain, adopt tessellated distribution method, be divided into two groups, every group as one tunnel description, the benefit of Fen Peiing is like this: decide all there is another group in range block around it range block for any one in each group, utilize the correlation of fractal transformation between image block, can better recover to lose the map information of piece.The pairing mapping of these range blocks has constituted the code stream that every road is described, and is referred to as main description (P iI=1,2).Light piece is one group among Fig. 3, and dark piece is another group.So main description 1 (P has been formed in the mapping of dark piece correspondence 1), main description 2 (P have been formed in the mapping of light piece piece correspondence 2).
For each range block, adopt the trend of its texture of methods analyst of gradient decline, each range block is divided three classes: cross grain piece, vertical texture block, cross grain piece.Claim that classified information is relevant information C iI=1,2.As shown in Figure 4.
2, fractal Extrapolation method
When one tunnel descriptor was lost, the map information of receiving was half of original iterated function system as shown in Figure 5, and second half map information is described and lost along with losing one the tunnel, therefore, and the map information that adopts the method for fractal extrapolation to recover to lose.
The key skills of the fractal Extrapolation method that this method is used is: the map information of use adjacent block estimates to lose the map information of sub-piece.Utilize relevant information to determine to use which adjacent block to estimate.The foundation of doing like this is: the texture of image generally all is the continuity with trend, and for example, if a sub-piece is a cross grain, the sub-piece on the left side of this height piece or the right side is that the probability of cross grain will be very big so.
Black block is the range block of losing in a tunnel among Fig. 5, and fractal Extrapolation method just is to use the mapping of its neighborhood piece correspondence and relevant information to recover its corresponding map information.Suppose from relevant information, can know that the textural characteristics of black block is a cross grain, from its horizontal neighborhood, find a range block, use its map information black of extrapolating to lose the map information of piece with cross grain, neighborhood piece correspondence be mapped as ω j, the corresponding sub-piece of the domain of definition is D i,
Figure A20071009953300121
Be the mapping of losing piece that estimates, other is S jAnd O jBe ω jIn parameter, so the method for fractal extrapolation can be expressed as following equation;
Figure A20071009953300122
As can be seen, what estimate loses the piece map information for to have identical texture to move towards the corresponding map information of neighborhood piece with it from formula, but its corresponding domain of definition piece then is the adjacent domain of definition piece that has identical texture trend with the domain of definition piece of selected neighborhood piece.
3, entropy coding
In our method, adopted the entropy coding of arithmetic coding as iterated function system and relevant information, further compress iterated function system and relevant information.
4, center pathway decoding and wing decoding
If have one the tunnel to describe and to lose, the method that adopts fractal extrapolation so recovers to lose the map information in one tunnel description from the road map information of describing that obtains and relevant information.Behind the map information that obtains all domain of definition pieces, just can reconstruct an iterated function system.All do not have to lose if two-way is described, so just can directly use main description to set up iterated function system.By the definition of iterated function system and character as can be known, the resulting iterated function system IFS of this method tightens, and its attractor can obtain by the continuous iterated transform to the arbitrary initial image.From the mathematics angle of strictness, need that iteration is countless repeatedly just to obtain attractor.But in actual application, only need can restrain behind the iteration limited number of time N, carrying out the N+1 iteration, the quality of image is slight variation.Generally speaking, N=8.As shown in Figure 6.
When table 1 initial pictures was all black picture, 8 iteration are the PSNR value of correspondence as a result
Iterations N
1 2 3 4 5 6 7 8
PSNR (dB) 10.46 14.77 19.00 23.90 27.77 29.84 30.61 30.80
As seen from the above table, after the decoded picture iteration 8 times, the quality of image has changed hardly.
By last, the encoder specific implementation method shown in Fig. 2 (a) based on iterated function system:
(1). for piece image, at first pass through fractal image, this image has been divided into the sub-piece of codomain of non-overlapping copies, and the size of the sub-piece of codomain is got 4 * 4,8 * 8,16 * 16 (pixel) usually according to the difference of code check.The sub-piece of each codomain can be in the hope of corresponding mapping;
(2). for cutting apart the good sub-piece of codomain, it is divided into two groups by tessellated distribution method, and the mapping of the sub-piece correspondence of codomain simultaneously also is divided into two groups as shown in Figure 4 accordingly.The mapping of each group is as the one tunnel main descriptor transmission of describing;
(3). adopt the method for texture analysis, the sub-piece of each codomain is classified, it is among the map1 that record sort information, classified information are recorded in classified information figure;
(4). each road is described, adopted the method for fractal extrapolation to estimate the map information that lacks the range block correspondence;
(5). for the map information that estimates, adopt
Figure A20071009953300131
Calculate the collage error of this information, and, this error and preset threshold (tol) are made comparisons,, illustrate that the mapping of estimating is effective if less than given threshold value, if greater than given threshold value, illustrate that the mapping of estimating is invalid, note this information among the map2: if mapping effectively establishes 1 on the correspondence position in map2 at piece label information figure, otherwise, establish 0.Simultaneously the classified information of this range block among the map1 is deleted.Related information transmission during map1 and map2 describe as each road, threshold value tol generally gets 4-6;
(6). adopt arithmetic coding method, with map information, map1 and map2 further carry out entropy coding, form the code stream that will transmit or store at last.
Multiple description encoding implement body implementation method shown in Fig. 2 (b) based on iterated function system:
(1). for the code stream that obtains, data are carried out entropy decoding and de-quantization.And judge that can obtain several roads describes, describe, change (2), describe, change (4) if having to one the tunnel if obtain two-way;
(2). judge whether packet loss is arranged,, change (3), all be estimated, change then (3) otherwise change the map information of (5) handling up to all packet loss if do not have;
(3). the main descriptor that two-way is described proposes, and reconstructs an iterated function system, changes (7);
(4). packet loss is used as in the road description that will lose, so change for each package informatin of losing
(5), breath all estimates if all bags are broken one's promise, and rebuilds an iterated function system and changes (7);
(5). check map2, confirm the validity of fractal extrapolation, if invalid, in iterative process, adopt the method for two-wire shape interpolation to recover this piece, if effectively change (6);
(6). check map1, recover the texture trend of this piece, adopt the method for fractal extrapolation to estimate the map information of this piece;
(7). the iterated function system that iterative approximation comes out obtains decoded picture.

Claims (10)

1, a kind of multi-description coding method based on iterated function system is characterized in that it comprises:
(1), tries to achieve the preordering method of the iterated function system of figure;
(2), use predetermined dividing method that the iterated function system of trying to achieve is cut apart;
(3), the part of using predetermined restoration methods that iterated function system is lost is recovered;
(4), use predetermined method to classify to the sub-piece of each codomain;
(5), reconstruct iterated function system, this system of iteration obtains decoded picture.
2, a kind of multi-description coding method according to claim 1 based on iterated function system, it is characterized in that: the above-mentioned predetermined method of asking iterated function system is to use the method for fractal image; Or the above-mentioned predetermined method of cutting apart iterated function system is to use tessellated dividing method; Or the above-mentioned predetermined restoration methods restoration methods that is fractal extrapolation.
3, according to claim 1, a kind of multi-description coding method of 2, it is characterized in that also comprising based on iterated function system:
For the iterated function system on each road, its parameter adopts the lossless compress mode of the coding that counts further to encode.
4, a kind of multi-description coding method based on iterated function system according to claim 1 is characterized in that: for the sub-piece of each codomain, the method for using gradient to descend is divided three classes it: cross grain, vertically texture and diagonal texture;
g 0 = 1 N ( N - 1 ) ( Σ y = 0 N - 1 Σ x = 0 N - 2 | I ( x , y ) - I ( x + 1 , y ) | )
g 1 = 1 N ( N - 1 ) ( Σ y = 0 N - 2 Σ x = 0 N - 1 | I ( x , y + 1 ) - I ( x , y ) | )
g 2 = 1 N ( N - 1 ) ( Σ y = 0 N - 2 Σ x = 0 N - 2 | I ( x + 1 , y + 1 ) - I ( x , y ) | )
g＝max(g 0，g 1，g 2)，
If g=g 0, this piece is a cross grain, if g=g 1, then this piece is vertical texture, if g=g 2, then this piece is the diagonal texture.
5, a kind of multi-description coding method according to claim 2 based on iterated function system, it is characterized in that: the restoration methods of described fractal extrapolation, also comprise, the mapping of losing piece of using fractal Extrapolation method to recover, use given method to judge its validity, if effectively then use this mapping,, then use specific interpolation method to recover this piece if invalid; Or for the mapping of the domain of definition piece that uses fractal Extrapolation method to recover
Figure A2007100995330003C2
, calculate its collage error
Figure A2007100995330003C3
, itself and given threshold value are compared, if greater than given threshold value then invalid, if less than given threshold value then be considered as effectively.
6, a kind of multi-description coding method based on iterated function system according to claim 2 is characterized in that: the restoration methods of described fractal extrapolation, for specific interpolation method, employing be two-wire shape interpolation method.
7, according to claim 5,6 described a kind of multi-description coding methods based on iterated function system, it is characterized in that: the restoration methods of described fractal extrapolation also comprises:
Adopt a form to store classified information, whether another form is stored the fractal extrapolated mapping of this piece effective.
8, a kind of multi-description coding method according to claim 7 based on iterated function system, it is characterized in that: the restoration methods of described fractal extrapolation, two forms all adopt the Methods for Coding that counts to do further compression, and each form uses the algorithm of ZIG-ZAG that two dimension is become one dimension.
9, a kind of multi-description coding method based on iterated function system according to claim 1 is characterized in that: in when decoding, can use arbitrarily image as the initial pictures of iteration; Or,, stop iteration when the MSE value of the result images of adjacent twice iteration the time less than given threshold value in when decoding.
10, for realizing the described a kind of multi-description coding method of claim 1, it is characterized in that: an encoder of the realization that uses a computer and a decoder of its correspondence based on iterated function system.
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