CN105426916A - Image similarity calculation method - Google Patents

Abstract

The invention discloses an image similarity calculation method. The method comprises: (1) extracting texture features of two to-be-compared images and calculating texture feature similarity of the two to-be-compared images; (2) calculating feature similarity of Riemannian manifolds of the two to-be-compared images; and (3) performing weighted calculation on comprehensive similarity of the two to-be-compared images by utilizing results in the steps (1) and (2). According to the method, the texture features of the images are extracted with Shearlet wavelet transformation and the similarity of the images is measured by using the similarity of the Riemannian manifolds and the difference between textures to realize comprehensive measurement of the similarity of the images, thereby effectively improving the accuracy and recall level of image retrieval.

Description

Image similarity calculation method

Technical field

The present invention relates to image retrieval technologies field, particularly relate to a kind of measure of image similarity.

Background technology

Image ratio has more obtained a large amount of concern of image procossing and computer vision field, because it is the core ingredient of multiple application, and such as Object identifying, stereoscopic vision, image interpolation, image denoising, and exemplar-based image repair etc.Common methods is the Similarity Measure between the overall two width images of definition one, namely compares and obtains a little to the bag that neighbouring neighbours are formed from two width images.We think the image generally defined in Riemann manifold.Popular appearance like this, such as, is defined in R ⁿimage, give the suitable tolerance be defined on image.

Textural characteristics is one of key character of image, and it can reflect the regularity of distribution of neighborhood territory pixel gray scale, wherein wavelet analysis be a kind of brand-new time, frequency analysis, be the time scale analytical approach of signal.Increasing research in recent years concentrates on how to carry out analyzing image texture by wavelet transformation.

The characteristic similarity that Riemann is popular: two width images are defined in respectively Riemann popular on, then the similarity of two width images be exactly in fact in movement images by certain a bit centered by the popular Euclidean distance of the Riemann of subimage.

Textural characteristics similarity: textural characteristics is one of key character of image, and it can reflect the regularity of distribution of neighborhood territory pixel gray scale, wherein wavelet analysis be a kind of brand-new time, frequency analysis, be the time scale analytical approach of signal.Increasing research in recent years concentrates on how to carry out analyzing image texture by wavelet transformation, utilizes the texture feature vector of analysis of texture to have good effect to calculate textural characteristics similarity.But it is not high based on the accuracy rate of the image retrieval of two kinds of Similarity Measure in prior art.

Summary of the invention

The present invention proposes a kind of and shape similarity computing method of combined with texture feature popular based on Riemann, utilize weighting to carry out comprehensive similarity description, and then obtain shape similarity.

A kind of image similarity calculation method, is characterized in that, comprising:

(1) textural characteristics of two width images to be compared is extracted respectively, and the textural characteristics similarity both calculating;

(2) characteristic similarity of the Riemann manifold of two width images to be compared is calculated;

(3) comprehensive similarity of the result weighted calculation of step (1), step (2) two width images to be compared is utilized.

Image texture reflection be a kind of partial structurtes feature of image, the energy distribution based on frequency domain can differentiate the basic assumption of texture, adopts wavelet transformation texture feature extraction in step (1).

The present invention adopts small wave converting method to forward image texture to transform domain by wave filter or bank of filters, then applied energy criterion texture feature extraction [MukundanR; RamakrishnanKRMomentFunctionsinImageAnalysis-TheoryandAp plications1998].

Adopt wavelet transformation texture feature extraction, its reason is texture is narrow band signal, and different texture generally has different centre frequencies and bandwidth.Wave filter will input texture image I (x, y) and carry out convolution with shearlet small echo, can obtain the subband of different directions and yardstick.

The textural characteristics similarity of two width images to be compared:

$S_{texture}=norm({\left({\mathrm{\Σ}}_{i=1}^n{\left|f_{Q_i}-f_{I_i}\right|}^2\right)}^{1/2}$

Wherein f _qand f _ithe texture feature vector of two width images to be compared (image Q and image I) respectively; I is proper vector number.

Be given two image u based on the Similarity Measure that Riemann is popular, define respective image area in v and (suppose R ²for the sake of simplicity), comparison point (x, y ∈ R is respectively thought ²) the simplest method of neighbours to compare be use Euclidean distance comparison point x, y two neighbours.

This formula gives a clear and definite comparison, supposes that image area is Euclidean plane, this method is extensive be applied in a lot of document based on bag comparative approach.

And final comprehensive similarity calculating sets Q as image to be checked, I is the sub-picture in image library, uses the similarity of their contents of weighted feature distance metric.

Described comprehensive similarity S (Q, I)=ω _zs _manifold(Q, I)+ω _ts _texture(Q, I);

Wherein use S _lmanifoldand S _texturerepresent the characteristic similarity that the Riemann of two width images to be compared and image Q and image I is popular and textural characteristics similarity respectively;

ω _zand ω _tbe two adjustable weights, and meet ω _z+ ω _t=1.

Described comprehensive similarity can be expressed as the weighted sum of two similarities, and the value of S is less, be then considered as more similar.ω _zand ω _tselection be determine according to the contribution degree of corresponding ingredient, can utilize based on weight-coefficient compromise, be referred to as again the method that Similarity Measure upgrades, it is the object that the weight coefficient suitably adjusted in range formula according to feedback information reaches Optimized Matching result.

For simplicity, during original state, described ω _z=ω _t=0.5.

As preferably, ω _zand ω _tbe configured to preset value, by the result for retrieval calculated, analyze each amount of the characteristic similarity of textural characteristics similarity and Riemann manifold, and optimize ω by feedback iteration _zand ω _t.

The present invention adopts Gabor wavelet to convert texture feature extraction, utilization is defined in the popular similarity calculating two width images of Riemann, and the similarity of the similarity simultaneously calculated by textural characteristics and the popular upper calculating of Riemann is weighted and obtains final comprehensive similarity.Experimental result shows, in literary composition, algorithm complex is little, and retrieval accuracy is high, has good retrieval performance.

Embodiment

Below in conjunction with specific embodiment, the present invention is described in detail.

The present embodiment image similarity calculation method, comprises the steps:

(1) for two width images to be compared, carry out texture feature extraction respectively, calculate textural characteristics similarity.

The present embodiment adopts wavelet transformation texture feature extraction, and its reason is texture is narrow band signal, and different texture generally has different centre frequencies and bandwidth.Wave filter will input texture image I (x, y) and carry out convolution with shearlet small echo, can obtain the subband of different directions and yardstick.

If the size of I (x, y) is M × N, then the image exported through Shearlet wavelet decomposition is

I _mn(x，y)＝I(x，y)*ψ _mn(x，y)(1)

Wherein, ψ _mn(x, y) carries out yardstick to Shearlet wavelet basis function ψ (x, y) to stretch and the little wave system that formed after rotational transform, can be expressed as

ψ _mn(x，y)＝a ^-mψ(x′，y′)，a>1，m，n∈Z(2)

Wherein, x '=a ^-m(xcos θ+ysin θ), y '=a ^-m(ycos θ-xsin θ),

θ=n π/k, k are direction numbers, a ^-mit is scale factor.Then the basis function of two-dimentional Shearlet ripple may be defined as

$\mathrm{\ψ}(x,y)=\frac{1}{2{\mathrm{\π\σ}}_x{\mathrm{\σ}}_y}\exp \[-\frac{1}{2}(\frac{x^2}{{\mathrm{\σ}}_x^2}+\frac{y^2}{{\mathrm{\σ}}_y^2})+2\mathrm{\π}\mathrm{\ω}x---\left(3\right)$

Wherein, ψ (x, y) is through the Gaussian function of complex sinusoid FUNCTION MODULATION;

σ _xand σ _ybe respectively the variance of Shearlet ripple basis function along x-axis and y-axis direction;

Frequency centered by ω.

Here, Shearlet wavelet basis function is the bandpass filter of frequency centered by (ω, 0).The average μ calculated by formula (1) _mnwith standard variance σ _mncan as the textural characteristics of image, its expression formula is

${\mathrm{\μ}}_{mn}={\mathrm{\Σ}}_{x=1}^M{\mathrm{\Σ}}_{y=1}^N\left|I_{mn}(x,y)\right|/\left(MN\right)---\left(4\right)$

${\mathrm{\σ}}_{mn}={\[{\mathrm{\Σ}}_{x=1}^M{\mathrm{\Σ}}_{y=1}^N{\left(\right|I_{mn}\left(x,y\right)-{\mathrm{\μ}}_{mn}\left|\right)}^2/\left(MN\right)\]}^{1/2}---\left(5\right)$

Proper vector can be expressed as: f (μ ₀₀, σ ₀₀; μ ₀₁, σ ₀₁; ).

When direction number and scale parameter value are respectively 6 and 4, conspicuousness is the highest.

Two width images to be compared are image Q and image I respectively, and corresponding texture feature vector is respectively f _qand f _i.

S _texturerepresent the textural characteristics similarity of image Q and image I

$S_{texture}(Q,I)=norm({\left({\mathrm{\Σ}}_{i=1}^n{\left|f_{Q_i}-f_{I_i}\right|}^2\right)}^{1/2}$

Wherein f _qand f _ithe texture feature vector of two width images to be compared (image Q and image I) respectively; I is proper vector number.

(2) characteristic similarity of the Riemann manifold of two width images to be compared (image Q and image I) is calculated.

Given two image u, define respective image area and (suppose R in v ²for the sake of simplicity), we think comparison point (x, y ∈ R respectively ²) neighbours.It is use Euclidean distance comparison point x, y two neighbours that the simplest method compares.That is, let us definition

$D(t,x,y)={\∫}_{R^2}{g}_t\left(h\right){\left(u\right(x+h)-v(y+h\left)\right)}^{2}dh---\left(7\right)$

Wherein, g _tbe a given window function, suppose it is the Gaussian function of variable t, h is defined in R ²on coordinate figure.This formula gives a clear and definite comparison, supposes that image area is Euclidean plane, this method is extensive be applied in a lot of document based on bag comparative approach.

The present invention compares by the image similarity being defined in Riemann manifold the similarity that formula (as the plane of delineation given an anisotropy metric, similar structures tensor) comes between computed image.Need to solve one with x, the y degeneration PDE as variable, PDE equation is as follows:

$\frac{\∂D}{\∂t}={\mathrm{\Δ}}_{x}D+2Tr\left({D_{xy}}^{2}D\right)+{\mathrm{\Δ}}_{y}D---\left(8\right)$

Wherein D is Euclidean distance;

Δ _xd is the differential of D in x direction;

Δ _yd is D differential in y-direction;

Tr is the quadratic sum of diagonal of a matrix;

D _xyrepresent that D is to the partial derivative of xy.

This may be the simplest situation of linear PDE of the multiple dimensioned comparison of expression two image bags.Note, in formula (7), t reflects the size for the image block compared.When to be defined in Riemann manifold epigraph bag compare, the method from axiomatization is a lot.The multiple dimensioned image similarity based on Riemann's Epidemic analysis compares, and one need be provided to flow shape M _iwith corresponding metric G _i, and the priori link between two image Riemanns are popular.Concrete method for solving can see [VadimFedorov, PabloArias, RidaSadek, GabrieleFacciolo, andColomaBallester.LinearMultiscaleAnalysisofSimilaritie sbetweenImagesonRiemannianManifolds:PracticalFormulaandA ffineCovariantMetrics.SIAMJ.IMAGINGSCIENCESVol.8, No.3, pp.2021 – 2069].

(3) comprehensive similarity calculates

If image Q is image to be checked, image I is the sub-picture in image library, uses the similarity of their contents of weighted feature distance metric.

Use S _manifoldand S _texturerepresent the characteristic similarity that the Riemann of image Q and image I is popular and textural characteristics similarity respectively, both can be expressed as comprehensive similarity similarity

$\begin{array}{c}S(Q,I)={\mathrm{\ω}}_z{S}_{manifold}(Q,I)+{\mathrm{\ω}}_t{S}_{texture}(Q,I)\\ ={\mathrm{\ω}}_z{S}_{manifold}(Q,I)+{\mathrm{\ω}}_{t}norm({\left({\mathrm{\Σ}}_{i=1}^n{\left|f_{Q_i}-f_{I_i}\right|}^2\right)}^{1/2}\end{array},$

Wherein, ω _zand ω _tbe two adjustable weights, and meet ω _z+ ω _t=1.

The value of S is less, be then considered as more similar.ω _zand ω _tselection be determine according to the contribution degree of corresponding ingredient, can utilize based on weight-coefficient compromise, be referred to as again the method that Similarity Measure upgrades, it is that the weight coefficient suitably adjusted in range formula according to feedback information reaches the object of Optimized Matching result.

First, weight is configured to some preset values, by the result for retrieval calculated, for the situation meeting user's requirement, analyze their each component, the weights large to contribution degree increase, to contribution degree little just reduce weights, after feedback iteration, weight just can close to optimal value.For the sake of simplicity, suppose that each part judges to have equal contribution degree to similarity, therefore, get ω _z=ω _t=0.5.

Claims (6)

1. an image similarity calculation method, is characterized in that, comprising:

(1) textural characteristics of two width images to be compared is extracted respectively, and the textural characteristics similarity both calculating;

(2) characteristic similarity of the Riemann manifold of two width images to be compared is calculated;

(3) comprehensive similarity of the result weighted calculation of step (1), step (2) two width images to be compared is utilized.

2. image similarity calculation method as claimed in claim 1, is characterized in that, the textural characteristics similarity of two width images to be compared:

$S_{texture}=norm({\left({\mathrm{\Σ}}_{i=1}^n{\left|f_{Q_i}-f_{I_i}\right|}^2\right)}^{1/2}$

Wherein f _qand f _ithe texture feature vector of two width images to be compared respectively; I is proper vector number.

3. image similarity calculation method as claimed in claim 2, is characterized in that, described comprehensive similarity S (Q, I)=ω _zs _manifold(Q, I)+ω _ts _texture(Q, I);

Wherein use S _lmanifoldand S _texturerepresent the characteristic similarity that the Riemann of two width images to be compared and image Q and image I is popular and textural characteristics similarity respectively;

ω _zand ω _tbe two adjustable weights, and meet ω _z+ ω _t=1.

4. image similarity calculation method as claimed in claim 3, is characterized in that, adopts wavelet transformation texture feature extraction in step (1).

5. image similarity calculation method as claimed in claim 4, is characterized in that, described ω _z=ω _t=0.5.

6. image similarity calculation method as claimed in claim 5, is characterized in that, ω _zand ω _tbe configured to preset value, by the result for retrieval calculated, analyze each amount of the characteristic similarity of textural characteristics similarity and Riemann manifold, and optimize ω by feedback iteration _zand ω _t.