CN101282475A - Finite element conversion method for image and picture compression encode - Google Patents

Abstract

A method for image transformation and image coding based on finite element, (1) disintegrating the image with multiresolution by finite element, the image signal is used as node base and micro base of the finite element. The finite element node base Phi(x) can be general finite base, spline function base and C-B spline base, micro base in orthogonal space of the finite element can be acquired by the above formula. (2) coding modulus of the disintegrated node base by arithmetic or Hofmann, coding method for the micro base can be selected from zero-tree coding (EZW), hierarchical trees (SPIHT) algorithm coding, embedded optimal truncation coding or other improved coding methods.

Description

The finite element converter technique and the image compression encoding of image

The present invention relates to a kind of image compression encoding method of using the finite element converter technique, or rather, relate to a kind of image transform and image compression encoding method.

Be used to communicate by letter and the digital image compression technology of storage comprises compressed encoding method by moving image panel of expert (MPEG) or joint image expert group (JPEG) standard, wherein have and use discrete cosine transform coding, huffman coding and based on the coding method of wavelet transformation.

Common image compression earlier with image transform, adopts different compressed encodings according to different conversion.

Popular in the world image conversion method mainly contains cosine transform (DCT) and wavelet transformation at present.

Method for compressing image based on dct transform is behind dct transform, by removing HFS, carries out image encoding and stay low frequency part, thereby realizes image compression, and its major defect is to produce blocking artifact.

Method for compressing image based on wavelet transformation is that image is through utilizing the characteristics of wavelet transformation behind the wavelet transformation, wavelet coefficient is gathered methods such as (SPIHT) encodes, embedded optimum blocks (EBCOT) coding with zero tree (EZW) coding, multistage tree encodes, improve compression ratio so greatly, and do not had blocking artifact.Major defect is that image must be through scanning repeatedly, coding take a large amount of time.

In order to overcome above-mentioned these shortcomings and limitation, the present invention has introduced the finite element converter technique, the sweep time during with the minimizing image encoding.One object of the present invention is, a kind of image compression method efficiently that uses the finite element converter technique is provided.

The method may further comprise the steps: input picture is carried out the finite element conversion obtain finite element node base and micro-base system number; Adopt then the coefficient of the node base of finite element with huffman coding or arithmetic coding, and the coefficient of trace base is set (EZW) coding with zero, multistage tree set (SPIHT) coding (SPIHT), embedded optimum block (EBCOT) coding, or by their improved coding method.

Concrete as follows of finite element converter technique:

(1) selects the finite element node base

And with the node base translation

Picture signal is decomposed to become

During the conversion of numerical imaging finite element, the numerical value of each pixel of numerical imaging can be regarded the node base coefficient of lowermost layer as, also can use the coefficient that least square method is obtained the node base of image finite element conversion lowermost layer.

(2) 1/S times of space of structure finite element

And its orthogonal complement space

F ^T＝{ψ ₁(x/S)，ψ ₂(x/S)，…ψ _S-1(x/S-i)，(x/S-i)，ψ ₂(x/S-i)，…，ψ _S-1(x/S-i)i＝1，2，…}

Signal decomposition is become:

:

$a_i^1=\underset{j}{\mathrm{\Σ}}{f}_{i,j}{a}_j^0;i=\mathrm{1,2},\·\·\·$

$b_i^{1,j}=\underset{j}{\mathrm{\Σ}}{g}_{i,j}^k{a}_j^0,i=\mathrm{1,2},\·\·\·,k=\mathrm{1,2},\·\·\·S-1---\left(2\right)$

(3) by that analogy, signal can be decomposed into:

$=\·\·\·$

Above coefficient a _i ^k, b _i ^{K, j}Can try to achieve with formula (2) recursion.

Since image be the two dimension, can do line translation earlier, after do rank transformation or do rank transformation earlier, after do line translation.

Above-mentioned finite element node base can be a spline function, and the finite element function base as also can being can also adopt C-B batten base, and S can be 2,3,4,5.Finite element is decomposed can do recursion decomposition several times, and S can be different in each time.

Finite element orthogonal complement space function base can be asked with the following method:

Obtain h thus _j ^kThereby, get finite element orthogonal complement space function base ψ _k(Sx).

Coefficient increases progressively the f in the apply-official formula (2) _{I, j}, g _{I, j} ^kCan ask with the orthogonal finite element method method, also can utilize the spatial translation symmetry directly to try to achieve approximation.

Image is through coefficient a after the conversion _j ^kDirectly applied arithmetic is encoded or huffman coding, coefficient b _i ^{K, j}, k=1,2 can be with adopting zero tree (EZW) coding, and multistage tree set (SPIHT) coding (SPIHT), embedded optimum block (EBCOT) coding.

Because S can be 2,3,4,5 etc., the finite element conversion is usually as long as do once, or secondary decomposes, and need do two, three times, four times and decomposes and needn't resemble wavelet transformation, thereby reduce time of scanning.

Claims (7)

1. method for compressing image, after it is characterized in that using the finite element conversion, the coefficient of finite element node base is with arithmetic coding or huffman coding, the coefficient of its trace base is used and is adopted zero tree (EZW) coding, multistage tree set (SPIHT) coding (SPIHT), embedded optimum block (EBCOT) coding or its improved coding method.

2. according to claim 1, during the finite element conversion, finite element node base function

Can adopt general finite element function base, can also adopt C-B batten base, batten base (once, secondary, three times).The trace base can be used

i＝1，2，…；k＝1，2，…，S-1

Try to achieve, interval [T, T] is the domain of definition of trace base.During the conversion of numerical imaging finite element, the numerical value of each pixel of numerical imaging can be regarded the node base coefficient of finite element conversion lowermost layer as, and the coefficient of the node base of image finite element conversion lowermost layer also can be used the method for approaching and obtain.

3. according to claim 1, the analogizing relation and can use the orthogonal finite element method method and try to achieve of limited conversion coefficient, but also the property symmetrically and evenly of application space is directly got approximate trying to achieve.

4. according to claim 1, during the finite element conversion, the micro-base of finite element can be 1,2, and 3,4, i.e. S=2,3,4,5 etc.

5. according to claim 1, the finite element conversion can be decomposed with multilayer, and the number of the trace base of each layer can be different.

6. according to claim 1, during image transform, image edge processing can be used symmetry approach, or continuation method.

7. according to claim 1, by the image compression behind the coding is to utilize the coefficient of the trace base of finite element node base and finite element to encode, the coefficient of finite element node base is with arithmetic coding or huffman coding, the coding method of trace base can be adopted zero tree (EZW) coding, multistage tree set (SPIHT) coding (SPIHT), embedded optimum block (EBCOT) coding or its improved coding method.