CN107256571A - A kind of Fractal Dimension Estimation based on deep learning Yu adaptive differential box - Google Patents

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

A Fractal Dimension Estimation Method Based on Deep Learning and Adaptive Difference Box

technical field

The invention belongs to the technical field of fractal image processing, and in particular relates to a fractal dimension estimation method based on deep learning and an adaptive difference box.

Background technique

As a new theory developed in recent years, fractal theory is widely used in the field of digital image processing. As the main tool of fractal theory applied in the field of image processing, fractal dimension can not only measure the degree of irregularity of image surface, but also has the characteristic of keeping invariant with the change of resolution. Therefore, fractal dimension has become an effective way to describe image surface texture features, and is widely used in image processing fields such as image analysis, image simulation, pattern recognition, and texture segmentation. At present, a large number of image fractal dimension calculation methods have been proposed and applied in the field of fractal image processing. However, these methods more or less have certain defects. Taking the difference box counting method as an example, the main problems are as follows:

1) The statistics of the number of boxes are inaccurate. In the differential box counting method, a fixed-size cubic box is used to cover the grayscale surface, and the position of the box is also fixed, which leads to overcounting problems in some grids, and ultimately cannot guarantee the use of the minimum number of The box completes the coverage of the entire grayscale surface of the image.

2) The fractal dimension of small-sized images cannot be accurately estimated. In image processing such as texture recognition and image segmentation using fractal dimension, it is often necessary to map the entire grayscale image to a fractal dimension feature map. In order to reflect the texture details in the local area of the image as much as possible, the neighborhood window corresponding to each pixel is usually required to be as small as possible, for example, a neighborhood window with a size of 3×3 or 5×5 is used to estimate the center The fractal dimension of the pixel. However, most of the calculation methods of fractal dimension are realized by means of multi-scale statistics, so enough statistical data are needed. However, sufficient multi-scale statistical data cannot be obtained under a small window size, so that the image fractal dimension cannot be estimated or the estimation result is inaccurate under a small neighborhood window.

Contents of the invention

The purpose of the present invention is to provide a fractal dimension estimation method based on deep learning and adaptive difference boxes, which can overcome the problems of difficulty in estimating the fractal dimension of small-sized images and inaccurate statistics of the number of boxes.

An image fractal dimension estimation method, comprising the steps of:

Step 1. Preprocessing the initial small-size image to obtain an enlarged image;

Step 2. Using a super-resolution convolutional neural network to reconstruct the preprocessed enlarged image to obtain an image with a larger size and higher resolution than the initial small-size image; let the image size be expressed as M×M;

Step 3, using the adaptive difference box counting method to estimate the fractal dimension of the image obtained in step 3, specifically:

S31, regard the image obtained in step 2 as a gray-scale surface in three-dimensional space, and the coordinates of each point on the gray-scale surface are (x, y, z), where x, y represent the original pixel plane coordinates of the image, and the z axis represents Image gray value;

S32. Divide the pixel plane into grids, wherein the grid size is represented by s×s; based on each grid, a cuboid is established from the grid boundary along the z-axis, and the lowest intersection point between the cuboid and the gray surface is determined. The gray value I _min of and the gray value I _max of the uppermost intersection point between the cuboid and the gray surface, according to the number of boxes covering the gray surface corresponding to the grid area: N ⁱ _s represents the number of boxes in the i-th grid, i=1,2,...,n,n represents the number of grids on the image; calculate the sum of the number of boxes in all grid areas under the current grid size, and get The minimum number of boxes N _s required to cover the entire image under the grid size;

S33. Constantly change the grid size, and obtain the number of boxes under different division scales according to the method of S32; wherein, the division scale of the grid is r=s/M; for each grid under each division scale, calculate each box The logarithmic value logN _s of the quantity and the logarithmic value log(1/r) of 1/r; in the two-dimensional coordinate system, take logN _s as the ordinate and log(1/r) as the abscissa, and draw the Coordinate points (log(1/r), logN _s ), perform least square linear fitting on all points, and the slope of the obtained line is the fractal dimension D of the image.

Preferably, the initial image is enlarged and preprocessed by adopting a bi-cubic interpolation method.

Preferably, in the step 2, the process of reconstructing the preprocessed enlarged image using a super-resolution convolutional neural network is as follows:

First, a series of different filters are used to perform convolution operations on the preprocessed image to obtain the corresponding low-resolution feature map;

Then the low-resolution feature map is nonlinearly mapped to a high-resolution feature map through a convolution operation;

Finally, the high-resolution feature map is averaged to reconstruct a large-scale high-resolution image.

Compared with the prior art, the present invention has the following advantages:

1) The present invention uses a deep learning reconstruction algorithm to enlarge the initial small-size image window, which ensures that the fractal dimension can obtain sufficient statistical data during the calculation process, and solves the problem that the traditional box counting method cannot be accurately estimated under a small-size image window The difficulty of fractal dimension, and compared with other image interpolation and enlargement methods, this method can well maintain the scaling invariance of image fractal dimension.

2) The adoption of the adaptive difference box makes the box cover the gray surface of the image more closely, which is closer to the essence of the definition of the box dimension, thus making the statistics of the box number more accurate and greatly improving the calculation accuracy of the box dimension.

Description of drawings

Fig. 1 is the flowchart of the embodiment of the present invention;

Fig. 2 is the structural diagram of convolutional neural network described in the present invention;

Fig. 3 is the image reconstructed under different magnifications, wherein, Fig. 3 (a) is original image; Fig. 3 (b) magnification n=2; Fig. 3 (c) magnification n=4;

Fig. 4 is four pieces of test images that embodiment adopts, and Fig. 4 (a) is the whole black image that fractal dimension theoretical value is 2; Fig. 4 (b) is the checkerboard image that fractal dimension theoretical value is 3; Fig. 4 ( c) and Figure 4(d) are two images D26 and D47 in the Brodatz texture library.

Fig. 5 is a schematic diagram of the principle of the differential box counting method, wherein Fig. 5 (a) is a schematic diagram of the principle of the traditional differential box counting method; Fig. 5 (b) is a schematic diagram of the principle of the adaptive differential box counting method of the present invention.

detailed description

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

As shown in Figure 1, the present invention provides a method for estimating fractal dimension based on deep learning and adaptive difference box, the specific implementation process of the method includes the following steps:

1) Initial image preprocessing. The bicubic interpolation method is used to enlarge the input initial small-size image, and output the corresponding large-size low-resolution image. The magnification factor is determined according to the actual needs of image fractal dimension estimation.

2) Deep learning reconstruction. This step mainly inputs the pre-processed large-size low-resolution image into the pre-trained super-resolution convolutional neural network to reconstruct a large-size high-resolution image. The neural network used mainly includes three convolutional layers of feature extraction, nonlinear mapping and aggregation reconstruction. The network structure diagram is shown in Figure 2. Among them, feature extraction mainly uses a series of different filters to perform convolution operations on preprocessed images to obtain corresponding low-resolution feature maps; nonlinear mapping is to nonlinearly map low-resolution feature maps through convolution operations into High-resolution feature maps; aggregation reconstruction is mainly achieved by averaging the high-resolution feature maps. The neural network uses the mean square error as the cost function combined with the standard backpropagation and stochastic gradient descent method for training optimization. As shown in Figure 3, Figure 3(a) is the initial small-scale image; Figure 3(b) and Figure 3(c) are the reconstructed images at magnifications n=2 and n=4, respectively.

3) Fractal dimension estimation, specifically:

S31, regard the image of M×M size obtained in step 2 as a gray-scale curved surface in three-dimensional space, and the coordinates of each point on the gray-scale curved surface are (x, y, z), wherein x, y represent the original pixel plane of the image Coordinates, the z-axis represents the gray value of the image;

S32. Divide the pixel plane into non-overlapping grids with a size of s×s. Based on each grid, build a cuboid starting from the grid boundary along the z-axis, and determine the intersection point of the cuboid and the gray surface at the bottom. The grayscale value I _min and the grayscale value _Imax of the uppermost intersection point between the cuboid and the grayscale surface can be used to obtain the number of boxes covering the grayscale surface corresponding to the grid area: N ⁱ _s represents the number of boxes in the i-th grid, i=1,2,...,n,n represents the number of grids on the image; thus calculate the sum of the number of boxes in all grid areas under each division scale Obtain the minimum number of boxes N _s required to cover the entire image under the grid size;

S33. Constantly change the grid size, according to the method of S32, to obtain the number of boxes under different division scales; wherein, the division scale of the grid is r=s/M, and different division scales correspond to different grid sizes; for each Divide the grid under the scale, and calculate the logarithmic value logN _s of the number of boxes and the logarithmic value log(1/r) of 1/r; in the two-dimensional coordinate system, logN _s is the vertical coordinate, and log(1/r) is The abscissa draws the coordinate points (log(1/r), logN _s ) under each division scale, and performs least square linear fitting on all points, and the slope of the obtained straight line is the fractal dimension D of the image:

It should be noted that the traditional differential box counting method uses a fixed-sized cubic box to cover the grayscale surface, and the position of the box is also fixed on the corresponding grid, as shown in Figure 5(a), each grid The gray maximum and minimum values of the inner gray surface fall in the corresponding boxes respectively, through the box counting formula:

The number of boxes needed to cover the grayscale surface in the grid can be obtained.

Among them, ceil(…) is the upper integer function, and n is the number of boxes. It can be seen from the figure that four cubic boxes are required to cover the gray-scale surface in the grid. However, some of the boxes contain a large number of elements other than the gray-scale surface, which intuitively shows that the coverage of the gray-scale surface by the box is not compact. Then it affects the estimation accuracy of fractal dimension.

The present invention uses an adaptive cuboid box to cover the grayscale surface, as shown in Figure 5(b). The gray level I _max -I _min +1 between the gray maximum value and the minimum value of the gray surface in each grid is the height h of the entire cuboid that can cover the gray surface in the grid. The corresponding box count formula is as follows:

In the adaptive difference box counting method, the height of the cuboid box can change with the fluctuation of the gray surface, which can make the box cover the gray surface of the image more compact, and also conform to the basic principle of the box dimension. The statistics of the number of boxes is not limited to integer counting, but expanded to fractional counting, which makes the statistics of the number of boxes more accurate and greatly improves the calculation accuracy of the box dimension.

In order to verify the effect of this method, four test images (denoted as A, B, C, D) are selected, as shown in Fig. 4(a)-(d). The present embodiment has carried out two groups of comparison experiments altogether: 1) with image A, B as test image, utilize this method and traditional difference box counting method (DBC) to estimate the fractal dimension of image respectively, the result is as shown in table 1; 2 )Taking images B, C, and D as test images, use traditional image interpolation method (taking bicubic interpolation as an example) and deep learning reconstruction algorithm to enlarge the image by 2, 3, and 4 times respectively, and then combine the adaptive difference box counting method The fractal dimension of the image is estimated, and the results are shown in Table 2.

Table 1 Image fractal dimensions calculated by two methods

Table 2 The fractal dimensions of the image under different magnifications by the two methods

As shown in table 1, two kinds of methods all agree with theoretical value to the calculation result of image A, and the calculation result of image B of the method of the present invention also agrees with theoretical value, and traditional differential box counting method (DBC) is to image B The calculated results deviate from the theoretical value, which also verifies that the fractal dimension estimated by this method is more accurate; as shown in Table 2, the fractal dimension obtained by the two methods increases with the increase of the image magnification. Among them, the fractal dimension obtained by the method based on bi-cubic interpolation decreases significantly with the increase of the magnification factor than the method based on the deep learning reconstruction algorithm, and the reduction rate of the latter is basically negligible. This also verifies the scaling invariance of the image fractal dimension from the side.

To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

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 surface_minAnd it is rectangular The gray value I of the top intersection point of body and gray surface_max, 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 needs_s；

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 calculated_s And 1/r logarithm value log (1/r)；With logN in two-dimensional coordinate system_sFor ordinate, log (1/r) is abscissa, is drawn each Coordinate points (log (1/r), logN under individual division yardstick_s), 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.