CN107240132A - A kind of method that utilization gray level co-occurrence matrixes calculate fractal dimension - Google Patents
A kind of method that utilization gray level co-occurrence matrixes calculate fractal dimension Download PDFInfo
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Abstract
The present invention provides a kind of method that utilization gray level co-occurrence matrixes calculate fractal dimension, it uses different grey level quantizations levels to build gray level co-occurrence matrixes, and then extracts contrast of the gray level image in the case of different grey level quantizations level, entropy, unfavourable balance away from three textural characteristics parameters；Using the obvious fractal characteristic phenomenon existed between textural characteristics parameter and grey level quantization level, the fractal dimension of image is calculated.The present invention is to realize a kind of new method that the fractal dimension of surface topography is calculated, with it is simple to operate, be easy to numerous advantages such as programming realization, image rotation consistency, the half-tone information of image and spatial information is simple and be effectively combined, analyzing image texture is advantageously implemented, is that fractal dimension computational methods have found a new direction.
Description
Technical field
The invention belongs to fractal geometry and texture analysis field, and in particular to one kind utilizes gray level co-occurrence matrixes meter
The method for calculating fractal dimension.
Background technology
Texture is a kind of basic inherent attribute commonly existed in image, and the spatial distribution attribute for characterizing image pixel is special
Levy, often show as the approximate aligned transfer of regional area pattern and macroscopic view.Texture analysis is that the important of computer vision technique is ground
Study carefully focus, appoint many research fields such as surface quality evaluation, pattern-recognition, geology, medical science, artificial intelligence.It is near
Year, domestic and foreign scholars create many new analyses or shift meanses and extract effective textural characteristics, such as gray level co-occurrence matrixes, from
Correlation function algorithm, fractal theory, Markov random field theory, wavelet theory etc. so that the research to texture feature extraction becomes
Obtain in riotous profusion colorful, new approaches are provided more subtly to carry out 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 a creative way in 1973, 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, the degree of accuracy of description texture is high, applicability
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 estimated, and GLCM is applied to the thinner of irregular arrangement
Texture, fractal method is applied to self-similarity texture.Based on gray level co-occurrence matrixes can extract contrast, correlation, unfavourable balance away from,
Totally 14 characteristic vectors such as entropy, covariance, energy.Ulaby et al. thinks this 4 spies of contrast, unfavourable balance square, correlation, energy
Correlation between levying is weaker, and can realize higher Texture classification precision.Baraldi A, Parmiggiani F et al. think
Contrast and entropy are most important two features.
The fractal geometry that point shape belongs in modern mathematics, was proposed in 1975 by U.S. mathematician Mandelbrot, recognizes
Showed for the local characteristicses of form, structure, information, function, energy etc. in time-space domain and certain overall similitude.FRACTAL DIMENSION
Number is the scrambling of description complicated shape, a key character of spacial validity with measuring.Fractal dimension is
Appointed extensively in key areas such as analyzing image texture, signal transactings.Pentland etc. thinks point shape and gradation of image information
Between there is corresponding contact relation, it is possible to use the fractal dimension of image-region describes the texture features of image-region.Such as
The inherent law what characterizes rough surface morphology is characterized in the hot issue that Machinery Processing Surface Quality is evaluated.Conventional roughness
Ra is difficult to the random behavior and minutia of performance rough surface morphology comprehensively, therefore fractal theory has been widely used in table
The feature recognition of facial contour curve and surface topography.At present, 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 computational methods to the fractal dimension of complex curve
Dimension method, covariance-weighted method etc..Three-dimensional spatial information is make use of for the conventional evaluation method of the fractal dimension of rough surface
(elevation) or image color information, mainly there is projection warps, cube cladding process, three-dimensional structure function method, differential box dimension method
Deng.
But there is problems with the evaluation method of above-mentioned fractal dimension：
At present, between any different fractal dimension computational methods, the calculating to the fractal dimension of same width imaging surface
As a result without same result.The fractal characteristic of different fractal dimension computational methods is mostly judged using coefficient correlation 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.
All it is 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 to use gray level co-occurrence matrixes statistical shape texture eigenvalue in addition, workload is very big.
The content of the invention
The present invention provides a kind of method that utilization gray level co-occurrence matrixes calculate fractal dimension, is point shape for realizing surface topography
A kind of new method that dimension is calculated, the half-tone information of image and spatial information simply and are effectively combined by it, are conducive to reality
Existing analyzing image texture, is that fractal dimension computational methods have found a new direction.
The method that the utilization gray level co-occurrence matrixes of the present invention calculate fractal dimension, it comprises the following steps：
Step 1, the grinding skin texture of work piece is gathered, optical imagery is obtained, and the optical imagery is converted into
Gray level image；
Step 2, the gray level co-occurrence matrixes of the gray level image are built using different grey level quantizations level, 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 unfavourable balance away from；
Step 3, any one textural characteristics parameter is taken the logarithm with corresponding grey level quantization level, and with least square method
Linear fit is carried out to two logarithms, the slope of fitting a straight line is extracted；
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；
Using unfavourable balance away from fractal dimension is calculated, if slope is k3, fractal dimension D3, then D3=(1.1326-k3)/0.8288。
Further, the grinding skin of work piece is gathered in the step 1 with 160 enlargement ratios using light microscope
Texture, obtains optical imagery；And the optical imagery is converted into by gray level image using matlab software image handling implement casees.
Further, function graycomatrix generation gray-scale maps ready-made in matlab softwares are used 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 unfavourable balance away from i, j are natural number, and P (i, j) is gray scale symbiosis square
It is located at the element that the i-th row jth is arranged in battle array.
Further, used in the step 3 the polyfit functions of matlab softwares with least square method to (log (r),
Log (M)) linear fit is carried out, the slope of fitting a straight line is extracted, wherein M, to estimate, is any textural characteristics parameter；R is chi
Degree, is grey level quantization level.
The characteristics of present invention has following and beneficial effect：
(1) present invention firstly provides fractal dimension is calculated based on gray level co-occurrence matrixes, prior art is all fractal dimension
With calculating the method that textural characteristics are considered as two kinds of independent analysis image textures, i.e., different Expressive Features based on gray level co-occurrence matrixes
Surface different characteristic is described in amount.
(2) above-mentioned initiative thinking is based on, the present invention constructs relation 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,
Unfavourable balance away from etc. texture eigenvalue and fractal dimension, greatly save the workload of calculating.
(3) present invention builds gray level co-occurrence matrixes using different grey level quantization levels, and then extracts image in different gray scales
Contrast, entropy, unfavourable balance in the case of quantized level is away from three textural characteristics parameters.Pass through textural characteristics parameter and grey level quantization level
Between there is fractal characteristic phenomenon, calculate the fractal dimension of image.This method is simple to operate, is easy to programming realization.
(4) present invention is in calculating process, using the textural characteristics average value of 0 °, 45 °, 90 °, 135 ° four direction, it is ensured that
The rotational invariance feature of image texture characteristic extracting method.
Brief description of the drawings
Fig. 1 is implementation procedure of the invention；
Fig. 2 is grinding surface gray level image；
Fig. 3 is changes of the contrast C ON with grey level quantization level；
Fig. 4 is changes of the entropy ENT with grey level quantization level；
Fig. 5 is unfavourable balance away from changes of the IDM with grey level quantization level；
Fig. 6 is the log-log coordinate axle figure of texture eigenvalue and grey level quantization level；
Fig. 7 covers change of the box number with box size for differential box counting calculating method.
Fig. 8 is covering box number and the log-log coordinate axle figure of box size.
Embodiment
Below by specific embodiment and accompanying drawing, technical scheme is described in further detail.
The purpose of the present invention is to realize a kind of fractal dimension computational methods of new finished surface texture, preferably weighs work
The systematicness and complexity of part finished surface texture, are preferably characterized and identification mechanical processing quality.Shape is divided to believe with gradation of image
There is substantial connection 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.Based on gray level co-occurrence matrixes extract contrast, entropy, unfavourable balance away from etc. textural characteristics parameter can be preferably anti-
Reflect the local mode and queueing discipline of image texture.To same width gray level image, if the different grey level quantization level of selection, will be obtained
Different gray level co-occurrence matrixes and texture eigenvalue.It has been investigated that, contrast, entropy, unfavourable balance are away from three textural characteristics with gray scale
There is obvious fractal characteristic in the changing rule of quantized level.Therefore, the present invention proposes that one kind is divided using gray level co-occurrence matrixes
The new method that shape dimension is calculated.
The present invention provides a kind of method that utilization gray level co-occurrence matrixes calculate fractal dimension, and it uses gray level co-occurrence matrixes meter
Calculate work piece surface texture fractal dimension, using the machined surface texture of microcrystal fused alumina wheel grinding 20CrMnTi steel as
Example, implementation procedure is as shown in figure 1, comprise the following steps：
The first step：Image type is changed, i.e., optical imagery is converted into gray level image.
Wherein, the grinding skin texture of workpiece is gathered with 160 enlargement ratios using light microscope, optical imagery is obtained.
And the optical imagery is converted into by gray level image using matlab software image handling implement casees.
Fig. 2 is the gray level image of 20CrMnTi steel grinding skin textures.
Second step：The gray level co-occurrence matrixes of the gray level image are built using different size of grey level quantization level, from described
The contrast C ON, entropy ENT, unfavourable balance of work piece surface are extracted in gray level co-occurrence matrixes respectively away from this 4 textural characteristics parameters of IDM.
Wherein, the gray level co-occurrence matrixes of gray level image are generated using function graycomatrix ready-made in matlab softwares
P, and then contrast C ON, entropy ENT, unfavourable balance are calculated away from IDM textural characteristics parameters, if i, j are natural number, P (i, j) is gray scale
It is located at the element that the i-th row jth is arranged in co-occurrence matrix, then the calculation formula of textural characteristics is as follows successively
To same width gray level image, if the step-length d of selection, grey level quantization level Ng are different with generation direction θ, difference is obtained
Gray level co-occurrence matrixes, and then have influence on the result of calculation of textural characteristics parameter.If the selection of step-length d sizes is 5, grey level quantization level
Ng is taken as 16 × i, wherein i=1,2,3 .., 14, structure gray level co-occurrence matrixes P respectively successively.In order to ensure image texture characteristic
Rotational invariance, the textural characteristics average value of 0 °, 45 °, 90 °, 135 ° four direction can be sought.Using texture eigenvalue as vertical seat
Mark, grey level quantization level is abscissa, and Fig. 3~Fig. 5 is followed successively by the contrast C ON, entropy ENT, unfavourable balance of finished surface in Fig. 2 away from IDM
With grey level quantization level Ng changing rule.
3rd step：Calculate the fractal dimension of image texture.
Arbitrarily comparative selection degree CON, entropy ENT, unfavourable balance it can be used for image texture away from a textural characteristics parameter in IDM
Fractal dimension is calculated., 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, yardstick r is used as using grey level quantization level Ng.If a, b are constant, C is characterized scale coefficient, when will estimate M and yardstick
When r respectively takes the logarithm, 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 softwares
Function carries out linear fit with least square method to (log (r), log (M)), 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, coefficient correlation Cor indexs may be selected
Quality is calculated for evaluating fractal dimension.Coefficient correlation 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), log (M) covariance, D (log (r)), D (log (M))
Respectively log (r), log (M) variance, then coefficient correlation cor calculation formula be
Different grey level quantizations level in above-mentioned second step is each taken the logarithm respectively with its one-to-one texture eigenvalue.
Fig. 6 is the double logarithmic chart of contrast C ON, entropy ENT, unfavourable balance away from IDM and grey level quantization level.Fig. 6 slope k can be extracted respectively
With coefficient correlation cor, as shown in table 1
Logistic fit slope and coefficient correlation during 1 different texture feature of table
In order to further confirm that above-mentioned use contrast C ON, entropy ENT, unfavourable balance are measured away from this four textural characteristics of IDM with ash
The method for changing level change calculates the feasibility of fractal dimension.Here, can be using traditional differential box counting computational methods progress pair
Compare argument and analysis.For Fig. 2 fractal characteristic is extracted using differential box counting computational methods.Fig. 7 is covering grid number N and grid side
Relation between long d.Fig. 8 be logarithm log (N) and the grid length of side of covering grid number in differential box counting logarithm log (d) it
Between relation.It is also possible to which the slope k for calculating Fig. 8 is -2.3491, coefficient correlation cor is -0.9981.Understand, box counting dimension
D0For 2.3491.Because the coefficient correlation absolute value Billy of differential box counting computational methods is with contrast, entropy, unfavourable balance away from 3 lines
Manage small during feature calculation, i.e. linear fit degree is weaker, so the gray level co-occurrence matrixes based on different compression gray levels are extracted
The fractal characteristic of textural characteristics process is more notable 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
Method calculates using contrast C ON, entropy ENT, unfavourable balance fitting during away from this four textural characteristics calculating fractal dimensions of IDM respectively
Slope k.60 groups of result of calculations are subjected to ascending order arrangement according to the size of differential box counting, as shown in table 2.
The result of calculation of the width image of table 2 60
Use the polyfit functions of matlab softwares with least square method to (D0, linear fit k) is carried out, a, b is solved
Value, thus, can extrapolate box counting dimension D0Linear relationship during with different texture feature between fit slope k.Result of calculation such as table 3
It is shown.
The fit slope of table 3 and coefficient correlation
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 away from IDM using unfavourable balance, when the fit slope of (log (Ng), log (IDM)) is k3When, then
Fractal dimension D3For
D3=(1.1326-k3)/0.8288 (9)
Therefore, when based on gray level co-occurrence matrixes calculate fractal dimension when, be respectively adopted contrast C ON, entropy ENT, unfavourable balance away from
Result when this 3 textural characteristics of IDM calculate Fig. 2 fractal dimension is followed successively by 2.3954,2.4002,2.3931.
Claims (5)
1. a kind of method that utilization gray level co-occurrence matrixes calculate fractal dimension, it is characterised in that comprise the following steps：
Step 1, the grinding skin texture of work piece is gathered, optical imagery is obtained, and the optical imagery is converted into gray scale
Image；
Step 2, the gray level co-occurrence matrixes of the gray level image are built using different grey level quantizations level, 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 unfavourable balance away from；
Step 3, any one textural characteristics parameter is taken the logarithm with corresponding grey level quantization level, and with least square method to two
Individual logarithm carries out linear fit, 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；
Using unfavourable balance away from fractal dimension is calculated, if slope is k3, fractal dimension D3, then D3=(1.1326-k3)/0.8288。
2. the method for fractal dimension is calculated using gray level co-occurrence matrixes as claimed in claim 1, it is characterised in that the step
Gather the grinding skin texture of work piece in 1 with 160 enlargement ratios using light microscope, obtain optical imagery；And use
The optical imagery is converted into gray level image by matlab software image handling implement casees.
3. the method for fractal dimension is calculated using gray level co-occurrence matrixes as claimed in claim 1, it is characterised in that the step
Function graycomatrix ready-made in matlab softwares is used to generate the gray level co-occurrence matrixes P of gray level image in 2.
4. the method for fractal dimension is calculated using gray level co-occurrence matrixes as claimed in claim 3, it is characterised in that the step
The preparation method of textural characteristics is as follows in 2：
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Wherein, CON is contrast, and ENT is entropy, and IDM is unfavourable balance away from i, j are natural number, and P (i, j) is in gray level co-occurrence matrixes
The element arranged positioned at the i-th row jth.
5. the method for fractal dimension is calculated using gray level co-occurrence matrixes as claimed in claim 1, it is characterised in that the step
Use the polyfit functions of matlab softwares to carry out linear fit to (log (r), log (M)) with least square method in 3, extract
The slope of fitting a straight line, wherein M, to estimate, are any textural characteristics parameters；R is yardstick, is grey level quantization level.
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| CN108509702A (en) * | 2018-03-21 | 2018-09-07 | 武汉理工大学 | Soil erosion optimal spatial scale selection model and its computational methods |
| CN108562727A (en) * | 2018-04-24 | 2018-09-21 | 武汉科技大学 | A kind of evaluation method of asphalt surface texture polishing behavior |
| CN109191423A (en) * | 2018-07-18 | 2019-01-11 | 中国矿业大学 | A kind of porous media Permeability Prediction method based on machine image intelligence learning |
| WO2020015086A1 (en) * | 2018-07-18 | 2020-01-23 | 中国矿业大学 | Porous medium permeability prediction method based on intelligent machine image 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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