CN107240132B - A method of fractal dimension is calculated using gray level co-occurrence matrixes - Google Patents
A method of fractal dimension is calculated using gray level co-occurrence matrixes Download PDFInfo
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Abstract
The present invention provides a kind of method for calculating fractal dimension using gray level co-occurrence matrixes, it uses different grey level quantization grades to construct gray level co-occurrence matrixes, and then extracts the three textural characteristics parameters of contrast, entropy, inverse difference moment of gray level image in different grey level quantization grades；Using obvious fractal characteristic phenomenon existing between textural characteristics parameter and grey level quantization grade, the fractal dimension of image is calculated.The present invention is a kind of new method realizing the fractal dimension of surface topography and calculating, with it is easy to operate, convenient for programming realization, numerous advantages such as image rotation invariance, the grayscale information of image simply and is effectively combined with spatial information, it is advantageously implemented analyzing image texture, has found a new direction for fractal dimension calculation method.
Description
Technical field
The invention belongs to fractal geometries and texture analysis field, and in particular to a kind of to utilize gray level co-occurrence matrixes meter
The method for calculating fractal dimension.
Background technique
Texture is that a kind of common existing basic inherent attribute, the spatial distribution attribute for characterizing image pixel are special in image
Sign often shows as the approximate aligned transfer of regional area mode with macroscopic view.Texture analysis is that the important of computer vision technique is ground
Study carefully hot spot, appoints many research fields such as surface quality evaluation, pattern-recognition, geology, medicine, artificial intelligence.It is close
Year, domestic and foreign scholars create many new analyses or shift means extract effective textural characteristics, such as gray level co-occurrence matrixes, certainly
Correlation function algorithm, fractal theory, Markov random field theory, wavelet theory etc., so that the research to texture feature extraction becomes
Must be in riotous profusion colorful, new approaches are provided for more subtly progress image texture classification and analysis.
Gray level co-occurrence matrixes occupy leading position in the statistical analysis technique of texture, can preferably describe texture
Randomness and detail.Haralick proposed gray level co-occurrence matrixes in 1973 in a creative way, by the gray scale of Landsat image
Information is converted into texture information.Based on the method for gray level co-occurrence matrixes texture feature extraction, texture accuracy height, applicability are described
It is good, it is the important foundation for the local mode and queueing discipline for analyzing image texture.Ohanian et al. to fractal characteristic, GLCM,
The classification performance of the texture characteristic extracting methods such as MRF and Gabor filtering is assessed, and GLCM is suitable for the relatively thin of irregular arrangement
Texture, fractal method are suitable for self-similarity texture.Based on gray level co-occurrence matrixes can extract contrast, correlation, inverse difference moment,
Totally 14 feature vectors such as entropy, covariance, energy.Ulaby et al. thinks this 4 spies of contrast, inverse difference moment, correlation, energy
Correlation between sign is weaker, and is able to achieve higher Texture classification precision.Baraldi A, Parmiggiani F et al. think
Contrast and entropy are most important two features.
Point shape belongs to the fractal geometry in modern mathematics, was proposed, recognizes in 1975 by U.S. mathematician Mandelbrot
It is showed and certain whole similitude for the local characteristics of form, structure, information, function, energy etc. in time-space domain.FRACTAL DIMENSION
Number is to describe the scrambling of complicated shape, an important feature of spacial validity and measurement.Fractal dimension is
It is appointed extensively in key areas such as analyzing image texture, signal processings.Pentland etc. thinks point shape and image grayscale information
Between there are corresponding connection relationship, can use the fractal dimension of image-region to describe the texture features of image-region.Such as
The inherent law of what characterization rough surface morphology is characterized in the hot issue of Machinery Processing Surface Quality evaluation.Common roughness
Ra is difficult to show the random behavior and minutia of rough surface morphology comprehensively, therefore fractal theory has been widely used in table
The identification of the feature of facial contour curve and surface topography.Currently, the estimation side of many fractal dimensions has been proposed in domestic and foreign scholars
Method.Often mainly there are size method, package topology, divider method, structure function method, spectrum with calculation method to the fractal dimension of complex curve
Dimension method, covariance-weighted method etc..Three-dimensional spatial information is utilized for the common evaluation method of the fractal dimension of rough surface
(elevation) or image color information mainly has projection warps, cube cladding process, three-dimensional structure function method, differential box dimension method
Deng.
But the evaluation method of above-mentioned fractal dimension has the following problems:
Currently, the calculating between any different fractal dimension calculation method, to the fractal dimension of same width imaging surface
As a result without same result.The fractal characteristic of different fractal dimension calculation methods is mostly judged using related coefficient cor
Conspicuousness and stability.The fractal characteristic on special three-dimensional appearance surface, there is presently no find document to find standard surface
Its accuracy is examined, is and traditional differential box counting comparative analysis.
It is all to solve respectively, i.e., first using projection warps, cube cladding process, three-dimensional structure function method, differential box dimension
Method etc. calculates fractal dimension, also needs in addition to use gray level co-occurrence matrixes statistical shape texture eigenvalue, workload is very big.
Summary of the invention
The present invention provides a kind of method for calculating fractal dimension using gray level co-occurrence matrixes, is point shape for realizing surface topography
The grayscale information of image simply and is effectively combined with spatial information, is conducive to reality by a kind of new method that dimension calculates
Existing analyzing image texture has found a new direction for fractal dimension calculation method.
The method for calculating fractal dimension using gray level co-occurrence matrixes of the invention comprising following steps:
Step 1, the grinding skin texture of work piece is acquired, obtains optical imagery, and the optical imagery is converted into
Gray level image；
Step 2, the gray level co-occurrence matrixes that the gray level image is constructed using different grey level quantization grades, from the gray scale symbiosis
The textural characteristics parameter on work piece surface is extracted in matrix, wherein textural characteristics parameter includes: contrast, entropy and inverse difference moment；
Step 3, any one textural characteristics parameter is taken into logarithm with corresponding grey level quantization grade, and with least square method
Linear fit is carried out to two logarithms, extracts the slope of fitting a straight line；
Step 4, fractal dimension is calculated:
Fractal dimension is calculated using contrast, if slope is k1, fractal dimension D1, then D1=(k1+0.0553)/1.0234；
Fractal dimension is calculated using entropy, if slope is k2, fractal dimension D2, then D2=(1.4547-k2)/0.4827；
Fractal dimension is calculated using inverse difference moment, if slope is k3, fractal dimension D3, then D3=(1.1326-k3)/0.8288。
Further, the grinding skin of work piece is acquired in the step 1 with 160 enlargement ratios using optical microscopy
Texture obtains optical imagery；And the optical imagery is converted by gray level image using matlab software image handling implement case.
Further, grayscale image is generated using function graycomatrix ready-made in matlab software in the step 2
The gray level co-occurrence matrixes P of picture.
Further, the preparation method of textural characteristics is as follows in the step 2:
Wherein, CON is contrast, and ENT is entropy, and IDM is inverse difference moment, and i, j are natural number, and P (i, j) is gray scale symbiosis square
It is located at the element of the i-th row jth column in battle array.
Further, used in the step 3 the polyfit function of matlab software with least square method to (log (r),
Log (M)) linear fit is carried out, the slope of fitting a straight line is extracted, it is any textural characteristics parameter that wherein M, which is to estimate,；R is ruler
Degree, is grey level quantization grade.
The present invention have the characteristics that it is following and the utility model has the advantages that
(1) present invention firstly provides fractal dimension is calculated based on gray level co-occurrence matrixes, the prior art is all fractal dimension
The method that textural characteristics are considered as two kinds of independent analysis image textures, i.e., different Expressive Features are calculated with based on gray level co-occurrence matrixes
Surface different characteristic is described in amount.
(2) it is based on above-mentioned initiative thinking, the present invention constructs relationship between gray level co-occurrence matrixes and fractal dimension.It is based on
Gray level co-occurrence matrixes calculate fractal dimension realization, can using gray level co-occurrence matrixes Same Way simultaneously calculate contrast, entropy,
The workload of calculating is greatly saved in the texture eigenvalues such as inverse difference moment and fractal dimension.
(3) present invention constructs gray level co-occurrence matrixes using different grey level quantization grades, and then extracts image in different gray scales
Three textural characteristics parameters of contrast, entropy, inverse difference moment in the case of quantized level.By textural characteristics parameter and grey level quantization grade it
Between there are fractal characteristic phenomenons, calculate the fractal dimension of image.This method is easy to operate, realizes convenient for programming.
(4) present invention is guaranteed in calculating process using the textural characteristics average value of 0 °, 45 °, 90 °, 135 ° four direction
The rotational invariance feature of image texture characteristic extracting method.
Detailed description of the invention
Fig. 1 is implementation procedure of the invention；
Fig. 2 is grinding surface gray level image；
Fig. 3 is variation of the contrast C ON with grey level quantization grade；
Fig. 4 is variation of the entropy ENT with grey level quantization grade；
Fig. 5 is variation of the inverse difference moment IDM with grey level quantization grade；
Fig. 6 is the log-log coordinate axis figure of texture eigenvalue and grey level quantization grade；
Fig. 7 is the covering box number of differential box counting calculating method with the variation of box size.
Fig. 8 is the log-log coordinate axis figure for covering box number and box size.
Specific embodiment
Below by specific embodiment and attached drawing, technical solution of the present invention is described in further detail.
The purpose of the present invention is realizing a kind of fractal dimension calculation method of new finished surface texture, work is preferably measured
The systematicness and complexity of part finished surface texture preferably characterize and identification mechanical processing quality.Shape and image grayscale is divided to believe
There are substantial connections between breath.Gray level co-occurrence matrixes can preferably describe the randomness and detail of texture, be image texture point
The important foundation of analysis.The textural characteristics parameters such as contrast, entropy, the inverse difference moment extracted based on gray level co-occurrence matrixes can be preferably anti-
Reflect the local mode and queueing discipline of image texture.To same width gray level image, if the grey level quantization grade that selection is different, will obtain
Different gray level co-occurrence matrixes and texture eigenvalue.It has been investigated that three contrast, entropy, inverse difference moment textural characteristics are with gray scale
There are apparent fractal characteristics for the changing rule of quantized level.Therefore, the present invention proposes a kind of to divide using gray level co-occurrence matrixes
The new method that shape dimension calculates.
The present invention provides a kind of method for calculating fractal dimension using gray level co-occurrence matrixes, uses gray level co-occurrence matrixes meter
The fractal dimension of work piece surface texture is calculated, the machined surface texture with microcrystal fused alumina wheel grinding 20CrMnTi steel is
Example, implementation procedure are as shown in Figure 1, comprising the following steps:
Step 1: image type is converted, i.e., optical imagery is converted into gray level image.
Wherein, optical imagery is obtained with the grinding skin texture of 160 enlargement ratios acquisition workpiece using optical microscopy.
And the optical imagery is converted by gray level image using matlab software image handling implement case.
Fig. 2 is the gray level image of 20CrMnTi steel grinding skin texture.
Step 2: construct the gray level co-occurrence matrixes of the gray level image using different size of grey level quantization grade, from described
This 4 textural characteristics parameters of the contrast C ON, entropy ENT, inverse difference moment IDM of work piece surface are extracted in gray level co-occurrence matrixes respectively.
Wherein, the gray level co-occurrence matrixes of gray level image are generated using function graycomatrix ready-made in matlab software
P, and then contrast C ON, entropy ENT, inverse difference moment IDM textural characteristics parameter are calculated, if i, j are natural number, P (i, j) is gray scale
It is located at the element of the i-th row jth column in co-occurrence matrix, then the calculation formula of textural characteristics is successively as follows
Difference is obtained if step-length d, the grey level quantization grade Ng of selection are different with generation direction θ to same width gray level image
Gray level co-occurrence matrixes, and then influence the calculated result of textural characteristics parameter.If step-length d size is selected as 5, grey level quantization grade
Ng is successively taken as 16 × i respectively, wherein i=1, and 2,3 .., 14, construct gray level co-occurrence matrixes P.In order to guarantee image texture characteristic
Rotational invariance, the textural characteristics average value of 0 °, 45 °, 90 °, 135 ° four direction can be sought.It is vertical sit with texture eigenvalue
Mark, grey level quantization grade are abscissa, and Fig. 3~Fig. 5 is followed successively by the contrast C ON, entropy ENT, inverse difference moment IDM of finished surface in Fig. 2
With the changing rule of grey level quantization grade Ng.
Step 3: calculating the fractal dimension of image texture.
Can any comparative selection degree CON, entropy ENT, a textural characteristics parameter in inverse difference moment IDM for image texture
Fractal dimension calculates.It, can be by this textural characteristics parameter when selecting a certain item textural characteristics parameter to be used to calculate fractal dimension
As M is estimated, using grey level quantization grade Ng as scale r.If a, b are constant, C is characterized scale coefficient, when will estimate M and scale
When r takes logarithm respectively, then there is relational expression is
Log (M)=log (C)+(aD+b) log (r) (4)
When selection is used to calculate fractal dimension with a certain item textural characteristics parameter, using the polyfit of matlab software
Function carries out linear fit to (log (r), log (M)) with least square method, extracts the slope k of fitting a straight line.Then its FRACTAL DIMENSION
Counting D is
D=(k-b)/a (5)
When carrying out linear fit to (log (r), log (M)) using least square method, related coefficient Cor index may be selected
Quality is calculated for evaluating fractal dimension.Related coefficient is bigger, then fractal dimension calculates that quality is better, and this method is better suited for point
The calculating of shape dimension.If Cov (log (r), log (M)) is log (r), the covariance of log (M), D (log (r)), D (log (M))
Distinguish log (r), the variance of log (M), then the calculation formula of related coefficient cor is
Different grey level quantization grades in above-mentioned second step are respectively asked for into logarithm with its one-to-one texture eigenvalue respectively.
Fig. 6 is the double logarithmic chart of contrast C ON, entropy ENT, inverse difference moment IDM and grey level quantization grade.The slope k of Fig. 6 can be extracted respectively
With related coefficient cor, as shown in table 1
Logistic fit slope and related coefficient when 1 different texture feature of table
In order to further confirm that above-mentioned use contrast C ON, entropy ENT, this four textural characteristics of inverse difference moment IDM are measured with ash
The method for changing grade variation calculates the feasibility of fractal dimension.It is carried out pair here, traditional differential box counting calculation method can be used
Compare argument and analysis.Fractal characteristic is extracted using differential box counting calculation method for Fig. 2.Fig. 7 is covering grid number N and grid side
Relationship between long d.Fig. 8 be differential box counting in cover grid number logarithm log (N) and grid side length logarithm log (d) it
Between relationship.It is also possible to which the slope k for calculating Fig. 8 is -2.3491, related coefficient cor is -0.9981.It is found that box counting dimension
D0It is 2.3491.Because the related coefficient absolute value ratio of differential box counting calculation method utilizes contrast, 3 entropy, inverse difference moment lines
Small when reason feature calculation, i.e. linear fit degree is weaker, so the gray level co-occurrence matrixes based on different compression gray levels extract
The fractal characteristic of textural characteristics process is more significant than traditional differential box counting, the stabilization of the Calculated Values of Fractal Dimensions of this method
Property is more preferable than traditional differential box counting.
The box counting dimension of the finished surface gray level image different to 60 width has carried out calculating analysis, additionally using described above
Fitting when method calculates separately out using contrast C ON, entropy ENT, this four textural characteristics calculating fractal dimensions of inverse difference moment IDM
Slope k.60 groups of calculated results are subjected to ascending order arrangement according to the size of differential box counting, as shown in table 2.
The calculated result of 2 60 width image of table
Use the polyfit function of matlab software with least square method to (D0, k) and linear fit is carried out, solve a, b
Value, can extrapolate box counting dimension D as a result,0With linear relationship when different texture feature between fit slope k.Calculated result such as table 3
It is shown.
3 fit slope of table and related coefficient
When calculating fractal dimension using contrast C ON, when the fit slope of (log (Ng), log (CON)) is k1When, then
Fractal dimension D1For
D1=(k1+0.0553)/1.0234 (7)
When calculating fractal dimension using entropy ENT, when the fit slope of (log (Ng), log (ENT)) is k2When, then divide shape
Dimension D2For
D2=(1.4547-k2)/0.4827 (8)
When calculating fractal dimension using inverse difference moment IDM, when the fit slope of (log (Ng), log (IDM)) is k3When, then
Fractal dimension D3For
D3=(1.1326-k3)/0.8288 (9)
Therefore, when calculating fractal dimension based on gray level co-occurrence matrixes, contrast C ON, entropy ENT, inverse difference moment is respectively adopted
Result when this 3 textural characteristics of IDM calculate the fractal dimension of Fig. 2 is followed successively by 2.3954,2.4002,2.3931.
Claims (5)
1. a kind of method for calculating fractal dimension using gray level co-occurrence matrixes, which comprises the following steps:
Step 1, the grinding skin texture of work piece is acquired, obtains optical imagery, and the optical imagery is converted into gray scale
Image；
Step 2, the gray level co-occurrence matrixes that the gray level image is constructed using different grey level quantization grades, from the gray level co-occurrence matrixes
The middle textural characteristics parameter for extracting work piece surface, wherein textural characteristics parameter includes: contrast, entropy and inverse difference moment；
Step 3, any one textural characteristics parameter is taken into logarithm with corresponding different grey level quantization grades, and with least square method
Linear fit is carried out to the logarithm taken, obtains data point by this method, and extracts the slope of fitting a straight line using data point；
Step 4, fractal dimension is calculated:
Fractal dimension is calculated using contrast, if slope is k1, fractal dimension D1, then D1=(k1+0.0553)/1.0234；
Fractal dimension is calculated using entropy, if slope is k2, fractal dimension D2, then D2=(1.4547-k2)/0.4827；
Fractal dimension is calculated using inverse difference moment, if slope is k3, fractal dimension D3, then D3=(1.1326-k3)/0.8288。
2. the method for calculating fractal dimension using gray level co-occurrence matrixes as described in claim 1, which is characterized in that the step
Optical imagery is obtained with the grinding skin texture of 160 enlargement ratios acquisition work piece using optical microscopy in 1；And it uses
The optical imagery is converted into gray level image by matlab software image handling implement case.
3. the method for calculating fractal dimension using gray level co-occurrence matrixes as described in claim 1, which is characterized in that the step
The gray level co-occurrence matrixes P of gray level image is generated in 2 using function graycomatrix ready-made in matlab software.
4. the method for calculating fractal dimension using gray level co-occurrence matrixes as claimed in claim 3, which is characterized in that the step
The preparation method of textural characteristics is as follows in 2:
Wherein, CON is contrast, and ENT is entropy, and IDM is inverse difference moment, and i, j are natural number, and P (i, j) is in gray level co-occurrence matrixes
Positioned at the element of the i-th row jth column.
5. the method for calculating fractal dimension using gray level co-occurrence matrixes as described in claim 1, which is characterized in that the step
It uses the polyfit function of matlab software to carry out linear fit to (log (r), log (M)) with least square method in 3, extracts
The slope of fitting a straight line, it is any textural characteristics parameter that wherein M, which is to estimate,；R is scale, is grey level quantization grade.
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| CN109191423B (en) * | 2018-07-18 | 2019-07-02 | 中国矿业大学 | A kind of porous media Permeability Prediction method based on machine image intelligence learning |
| CN110472304A (en) * | 2019-07-26 | 2019-11-19 | 水利部水土保持监测中心 | Basin topography fractal dimension quantization method based on " window technique " |
| CN110532511A (en) * | 2019-07-26 | 2019-12-03 | 四川师范大学 | It is a kind of based on gray scale-order co-occurrence matrix rotary inertia powder concentration measurement method |
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