CN107256571A - A kind of Fractal Dimension Estimation based on deep learning Yu adaptive differential box - Google Patents
A kind of Fractal Dimension Estimation based on deep learning Yu adaptive differential box Download PDFInfo
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Abstract
The invention discloses a kind of Fractal Dimension Estimation based on deep learning Yu adaptive differential box, belong to fractal image processing technology field；Comprise the following steps：1) row interpolation pretreatment is entered to initial small-sized image；2) the large scale low-resolution image for obtaining pretreatment is input in the good convolutional neural networks of pre-training, reconstructs large-sized high-definition picture, and the neutral net mainly includes feature extraction, Nonlinear Mapping and polymerization and rebuilds three convolutional layers；3) fractal dimension of large scale high-definition picture is estimated using adaptive differential box dimension；The method of the invention not only solves the problem of traditional box dimension accurately can not estimate fractal dimension under small-sized image window, and the introducing of adaptive differential box, also make it that the statistics of box number is more accurate；Compared with prior art, this method can keep the scaling consistency of image fractal dimension well simultaneously.
Description
Technical field
The invention belongs to fractal image processing technology field, and in particular to one kind is based on deep learning and adaptive differential box
Fractal Dimension Estimation.
Background technology
Fractal theory is widely used in digital image processing field as the new theory developed in recent years.Point
Shape dimension, in the main tool of image processing field, can not only measure the irregular journey of imaging surface as Fractal Theory Applications
Degree, and with the constant characteristic of change resolution holding.Therefore, fractal dimension becomes description imaging surface textural characteristics
An effective way, be widely used in the image processing fields such as graphical analysis, image simulation, pattern-recognition, Texture Segmentation
In.At present, substantial amounts of image fractal dimension computational methods are suggested and apply in fractal pattern process field.But,
More or less all there is certain defect in these methods.By taking difference box dimension as an example, the subject matter existed has some：
1) box number statistical is inaccurate.In difference box dimension, using the cuboid box of fixed size to gray scale
Curved surface is covered, and the position of box is also fixed, which results in enumeration problem occurred in some grids, finally
It cannot be guaranteed that completing the covering to whole image gray surface using the box of minimal amount.
2) fractal dimension of small-sized image can not accurately be estimated.Texture recognition, image point are being carried out using fractal dimension
Cut etc. in image processing process, generally require whole gray level image being mapped to Cancers Fractional Dimension Feature figure.In order to as far as possible
Ground reflects the grain details information in the range of image local, usually requires that the corresponding neighborhood window of each pixel as far as possible
It is small, estimate the fractal dimension of central pixel point for example with size for 3 × 3 or 5 × 5 neighborhood window.But, fractal dimension
Computational methods realized mostly by way of multiple dimensioned statistics, it is therefore desirable to enough statistics.But in small size
Enough multiple dimensioned statistics can not be obtained under window, so that image fractal dimension can not generally be estimated under small neighbourhood window
Meter or estimated result are inaccurate.
The content of the invention
, can it is an object of the invention to provide a kind of Fractal Dimension Estimation based on deep learning Yu adaptive differential box
It is difficult to estimate with the fractal dimension for overcoming small-sized image and the problem of box number statistical is inaccurate.
A kind of image fractal dimension method of estimation, comprises the following steps：
Step 1, initial small-sized image is pre-processed, be amplified image；
Step 2, using super-resolution convolutional neural networks pretreated enlarged drawing is rebuild, obtain more initial
The image of small-sized image more large scale and higher resolution；If image size is expressed as M × M；
Step 3, the fractal dimension of the image obtained using adaptive differential box dimension to step 3 estimated, specifically
For：
On S31, the gray surface regarded the image that step 2 is obtained as in three dimensions, gray surface each point coordinates for (x,
Y, z), wherein, x, y represent the original pixel planes coordinate of image, and z-axis represents image intensity value；
S32, pixel planes are divided into grid, wherein, size of mesh opening is represented with s × s；Based on each grid, from net
Lattice border starts to set up cuboid upwards along z-axis, determines the gray value I of the bottom intersection point of cuboid and gray surfaceminAnd
The gray value I of the top intersection point of cuboid and gray surfacemax, then write music according to obtaining covering the corresponding ash in the net region
The box quantity in face：Ni sThe box quantity of i-th of grid is represented, i=1,2 ..., n, n represents image
Upper number of grid；The box quantity and value of all net regions under current grid size is so calculated, is obtained in the grid chi
The minimum box quantity N that very little lower covering whole image needss；
S33, constantly change size of mesh opening, according to S32 method, obtain the box quantity under different demarcation yardstick；Its
In, the division yardstick of grid is r=s/M；For the grid under each division yardstick, the logarithm value of each box quantity is calculated
logNsAnd 1/r logarithm value log (1/r)；With logN in two-dimensional coordinate systemsFor ordinate, log (1/r) is abscissa, is painted
Coordinate points (log (1/r), logN gone out under each division yardsticks), least square linear fit is carried out to all points, obtained
The slope of straight line is the fractal dimension D of image.
Preferably, initial pictures are amplified with pretreatment using bi-cubic interpolation method.
Preferably, in the step 2, being weighed using super-resolution convolutional neural networks to pretreated enlarged drawing
The process built is：
Convolution algorithm is carried out to pretreated image using a series of different wave filters first, obtains corresponding low point
Resolution characteristic pattern；
Then it is high-resolution features figure by convolution algorithm Nonlinear Mapping by low resolution characteristic pattern；
Processing is finally averaged to high-resolution features figure, reconstruction obtains large scale high-definition picture.
Compared with prior art, the invention has the advantages that：
1) present invention is amplified processing using deep learning algorithm for reconstructing to initial small-sized image window, it is ensured that point
Shape dimension can obtain enough statistics in calculating process, solve traditional box dimension under small-sized image window
The problem of fractal dimension can not accurately be estimated, and compared with other image interpolation amplification methods, this method can be protected well
Hold the scaling consistency of image fractal dimension.
2) use of adaptive differential box so that covering of the box to gradation of image curved surface is even closer, is more nearly box
The essence that dimension is defined, so that the statistics of box number is more accurate, substantially increases the computational accuracy of box counting dimension.
Brief description of the drawings
Fig. 1 is the flow chart of the embodiment of the present invention；
Fig. 2 is the structure chart of convolutional neural networks of the present invention；
Fig. 3 is the image rebuild under different amplification, wherein, Fig. 3 (a) is original image；Fig. 3 (b) multiplication factors n=
2；Fig. 3 (c) multiplication factors n=4；
Fig. 4 is the four width test images that embodiment is used, and Fig. 4 (a) is the completely black color image of fractal dimension theoretical value 2；
Fig. 4 (b) is the chessboard table images of fractal dimension theoretical value 3；Fig. 4 (c) and Fig. 4 (d) is two width figures in Brodatz texture searchings
As D26 and D47.
Fig. 5 is the principle schematic of difference box dimension, and wherein Fig. 5 (a) is the principle signal of conventional differential box dimension
Figure；Fig. 5 (b) is the principle schematic of adaptive differential box dimension of the present invention.
Embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.
As shown in figure 1, the invention provides a kind of fractal dimension estimation side based on deep learning Yu adaptive differential box
Method, the process that implements of this method comprises the following steps：
1) initial pictures are pre-processed.Processing is amplified to the initial small-sized image of input using bi-cubic interpolation method,
Export corresponding large scale low-resolution image.What multiplication factor was estimated according to image fractal dimension is actually needed to determine.
2) deep learning is rebuild.The large scale low-resolution image that this step mainly obtains pretreatment is input to pre-training
In good super-resolution convolutional neural networks, large-sized high-definition picture is reconstructed.The neutral net used is mainly wrapped
Include feature extraction, Nonlinear Mapping and polymerization and rebuild three convolutional layers, network structure is as shown in Figure 2.Wherein, feature extraction master
Convolution algorithm is carried out to pretreated image using a series of different wave filters, obtain corresponding low resolution feature
Figure；Nonlinear Mapping be by low resolution characteristic pattern by convolution algorithm Nonlinear Mapping be high-resolution features figure；Polymerization weight
Build and mainly realized by averaging processing to high-resolution features figure.The neutral net is using mean square deviation as cost function knot
The backpropagation of standardization and stochastic gradient descent method are trained optimization.As shown in figure 3, Fig. 3 (a) is initial small size figure
Picture；Reconstruction image when Fig. 3 (b) and Fig. 3 (c) is multiplication factor n=2 and n=4 respectively.
3) fractal dimension is estimated, is specially：
S31, the image for the M × M sizes for obtaining step 2 are regarded as each on the gray surface in three dimensions, gray surface
Point coordinates is (x, y, z), wherein, x, y represent the original pixel planes coordinate of image, and z-axis represents image intensity value；
S32, pixel planes are divided into the grid that the size of non-overlapping copies is s × s, based on each grid, from grid
Border starts to set up cuboid upwards along z-axis, determines the gray value I of the bottom intersection point of cuboid and gray surfaceminAnd it is long
The gray value I of the top intersection point of cube and gray surfacemax, you can obtain covering the corresponding gray surface in the net region
Box quantity：Ni sThe box quantity of i-th of grid is represented, i=1,2 ..., n, n represents that image is surfed the Net
Lattice quantity；So calculate each box quantity and value for dividing all net regions under yardstickObtain in the grid
The minimum box quantity N that whole image needs is covered under sizes；
S33, constantly change size of mesh opening, according to S32 method, obtain the box quantity under different demarcation yardstick；Its
In, the division yardstick of grid is r=s/M, the different size of mesh opening of different demarcation yardstick correspondence；For under each division yardstick
Grid, calculate the logarithm value logN of each box quantitysAnd 1/r logarithm value log (1/r)；In two-dimensional coordinate system with
logNsFor ordinate, log (1/r) is abscissa, draws coordinate points (log (1/r), logN under each division yardsticks), to institute
Least square linear fit is carried out a little, and the slope of obtained straight line is the fractal dimension D of image：
It should be noted that conventional differential box dimension is covered using fixed-size cuboid box to gray surface
Cover, and the position of box is also fixed on corresponding grid, as shown in Fig. 5 (a), the gray scale of gray surface in each grid
Maxima and minima is respectively fallen in corresponding box, passes through box Counting Formula：
It can obtain covering the box number in the grid required for gray surface.
Wherein, ceil (...) is flow in upper plenum, and n is box number.It can be seen that covering the ash in the grid
Write music face need 4 cuboid box, still, which part box includes a great number of elements beyond gray surface, intuitively
Show as box and not compact is covered to gray surface, and then the estimated accuracy of fractal dimension is impacted.
The present invention is covered using adaptive cuboid box to gray surface, shown in such as Fig. 5 (b).Each net
Gray level I in lattice between the gray scale maxima and minima of gray surfacemax-Imin+ 1 is that ash can write music in grid coverage
The height h of the whole cuboid in face.Corresponding box Counting Formula is as follows：
In adaptive differential box dimension, the height of cuboid box can become with fluctuating for gray surface
Change, can so make covering of the box to gradation of image curved surface compacter, while also complying with the general principle of box counting dimension, the party
Method be not confined to integer count to the statistics of box number, but has been expanded to fraction counting, so that box number
Statistics is more accurate, substantially increases the computational accuracy of box counting dimension.
In order to verify the effect of this method, four width test images (being designated as A, B, C, D) are have chosen, such as Fig. 4 (a)-(d) institutes
Show.The present embodiment, which has altogether, has carried out two groups of contrast experiments：1) using image A, B as test image, this method and tradition are utilized respectively
Difference box dimension (DBC) estimates the fractal dimension of image, as a result as shown in table 1；2) using image B, C, D as test image, point
Image progress 2,3,4 times are not put using traditional images interpolation method (by taking bi-cubic interpolation as an example) and deep learning algorithm for reconstructing
Greatly, the fractal dimension of image is estimated in conjunction with adaptive differential box dimension, as a result as shown in table 2.
The image fractal dimension that the two methods of table 1 are calculated
Fractal dimension of the two methods of table 2 in different amplification hypograph
As shown in table 1, two methods are all consistent to image A result of calculation with theoretical value, and the method for the invention is to figure
As B result of calculation is also consistent with theoretical value, and conventional differential box dimension (DBC) is to image B result of calculation and theoretical value
There is deviation, the fractal dimension that this is also demonstrated estimated by this method is more accurate；As shown in table 2, point obtained by two methods
Shape dimension has all reduced with the increase of image magnification, wherein, point shape that the method based on bi-cubic interpolation is obtained
Dimension increases reduced amplitude with multiplication factor and reduced apparently higher than the method based on deep learning algorithm for reconstructing, and the latter
Amplitude can be ignored substantially, this also demonstrates the scaling consistency of image fractal dimension from side.
In summary, presently preferred embodiments of the present invention is these are only, is not intended to limit the scope of the present invention.
Within the spirit and principles of the invention, any modification, equivalent substitution and improvements made etc., should be included in the present invention's
Within protection domain.
Claims (3)
1. a kind of image fractal dimension method of estimation, it is characterised in that comprise the following steps：
Step 1, initial small-sized image is pre-processed, be amplified image；
Step 2, using super-resolution convolutional neural networks pretreated enlarged drawing is rebuild, obtain relatively initial small chi
The image of very little image more large scale and higher resolution；If image size is expressed as M × M；
Step 3, the fractal dimension of the image obtained using adaptive differential box dimension to step 3 are estimated, are specially：
On S31, the gray surface regarded the image that step 2 is obtained as in three dimensions, gray surface each point coordinates for (x, y,
Z), wherein, x, y represent the original pixel planes coordinate of image, and z-axis represents image intensity value；
S32, pixel planes are divided into grid, wherein, size of mesh opening is represented with s × s；Based on each grid, from Grid Edge
Boundary starts to set up cuboid upwards along z-axis, determines the gray value I of the bottom intersection point of cuboid and gray surfaceminAnd it is rectangular
The gray value I of the top intersection point of body and gray surfacemax, then according to obtaining covering the corresponding gray surface in the net region
Box quantity：Ni sThe box quantity of i-th of grid is represented, i=1,2 ..., n, n represents that image is surfed the Net
Lattice quantity；The box quantity and value of all net regions under current grid size is so calculated, is obtained under the size of mesh opening
Cover the minimum box quantity N that whole image needss；
S33, constantly change size of mesh opening, according to S32 method, obtain the box quantity under different demarcation yardstick；Wherein, net
The division yardstick of lattice is r=s/M；For the grid under each division yardstick, the logarithm value logN of each box quantity is calculateds
And 1/r logarithm value log (1/r)；With logN in two-dimensional coordinate systemsFor ordinate, log (1/r) is abscissa, is drawn each
Coordinate points (log (1/r), logN under individual division yardsticks), least square linear fit, obtained straight line are carried out to all points
Slope be image fractal dimension D.
2. a kind of image fractal dimension method of estimation as claimed in claim 1, it is characterised in that in the step 1, using double
Cube interpolation method is amplified pretreatment to initial pictures.
3. a kind of image fractal dimension method of estimation as claimed in claim 1, it is characterised in that in the step 2, using super
The process that resolution ratio convolutional neural networks are rebuild to pretreated enlarged drawing is：
Convolution algorithm is carried out to pretreated image using a series of different wave filters first, corresponding low resolution is obtained
Characteristic pattern；
Then it is high-resolution features figure by convolution algorithm Nonlinear Mapping by low resolution characteristic pattern；
Processing is finally averaged to high-resolution features figure, reconstruction obtains large scale high-definition picture.
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Cited By (6)
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| CN108804848A (en) * | 2018-06-22 | 2018-11-13 | 西南石油大学 | A kind of computational methods of log box counting dimension |
| CN110135464A (en) * | 2019-04-18 | 2019-08-16 | 深兰科技（上海）有限公司 | A kind of image processing method, device, electronic equipment and storage medium |
| CN110751657A (en) * | 2019-09-26 | 2020-02-04 | 湖北工业大学 | Image three-dimensional fractal dimension calculation method based on triangular coverage |
| CN112560933A (en) * | 2020-12-10 | 2021-03-26 | 中邮信息科技(北京)有限公司 | Model training method and device, electronic equipment and medium |
| CN116912178A (en) * | 2023-06-26 | 2023-10-20 | 成都理工大学 | Method for identifying trace on surface of wire |
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Application publication date: 20171017 |