CN105741253A - Enhancement estimation method of image fractal feature on the basis of merge replication - Google Patents

Abstract

The invention discloses an enhanced estimation method for image fractal features based on merged copying. The original image is merged and copied for n times, and the newly formed texture image is larger in size, which is convenient for multi-scale statistics; the box counting method is taken as an example, for To achieve multi-scale coverage, it is necessary to divide the image into grids at different scales; if the image scale is increased by merging and copying, the submultiple of the enlarged image size can be used as the grid size to ensure that the multi-scale statistics have sufficient Data; since the fractal characteristics of the mirror image and the original image are consistent, it can be considered that the complexity of the new texture image formed by the combination of the original image and its mirror image arrangement only includes the complexity of the original image and the complex changes formed by the image arrangement. And the complexity of permutation and combination increases with the increase of the number of merging and copying, the fractal characteristics of the image are enhanced with the increase of the number of merging and copying, and the fractal dimension of the image will also increase.

Description

An Enhanced Estimation Method of Image Fractal Features Based on Merge and Copy

technical field

The invention belongs to the technical field of fractal image processing, and in particular relates to an enhanced estimation method of image classification features based on merged replication.

Background technique

Fractal theory was born in the late 1970s and early 1980s. It is an emerging discipline for the study of irregular graphics and chaotic motion. The natural connection between fractal theory and images has established its application in image processing, and the fractal characteristics of images have also attracted the attention of a large number of image researchers. Many natural scenes in nature can be described by fractal models, such as sky, ocean and ground. As for the surface and spatial structure of man-made objects, there are inherent differences with the characteristic laws described by fractal models. Therefore, fractal features can be used as the measure of artificial target detection. As the core tool of fractal application in the field of image processing, fractal features can not only measure the irregularity of the image surface, but also have the invariance of multi-scale and multi-resolution changes, which is consistent with the perception of human vision on the texture roughness of the image surface . To sum up, fractal features become an effective way to describe image surface features. Common image fractal features in research include fractal dimension, Hurst exponent, fractal intercept feature, etc. The present invention mainly takes fractal dimension as an example to enhance and estimate the fractal feature.

In the field of fractal image processing such as shape analysis, pattern recognition, and texture segmentation based on fractal dimension, the entire algorithm process is mostly to take neighborhood windows for each pixel point of the image, or directly divide the image into equal-sized windows, and use The fractal dimension calculation method such as the box counting method estimates the fractal dimension of the image sub-block in the window, and performs further shape analysis, pattern recognition, texture segmentation, etc. on the image according to the calculated fractal dimension. For the above algorithm flow, there are two main problems.

First of all, it is a question of window size selection. In order to reflect the complexity of the local changes in the image and detect the local details of the image, the window size is usually required to be as small as possible. However, since the fractal dimension is mostly calculated by multi-scale coverage, its calculation is a statistical process. If the window size is too small, it will not be possible to obtain enough sets of statistical data, so that the fractal dimension cannot be calculated or the calculation results are not enough. precise.

Second, there is the issue of algorithm sensitivity. Due to the fractal theory itself has the characteristic of scale statistics, the algorithm is inherently less sensitive to image changes, and the fractal dimension will change significantly only when the image changes sufficiently. This also causes the fractal dimension of some image details to be indistinguishable from the background area during actual image processing, which is not conducive to image processing such as shape analysis, pattern recognition, and texture segmentation.

Contents of the invention

In view of this, the purpose of the present invention is to provide a method that can enhance and estimate the fractal features of images, which solves the problem that the fractal features of small-scale images are difficult to estimate and the extracted image fractal features are not obvious. The size of the image is enlarged to facilitate the estimation of the fractal characteristics of the image, and the fractal characteristics of the enlarged image are enhanced compared with the original image.

A method for enhancing estimation of image fractal features based on merging and copying, comprising the steps of:

The first step is to determine the original image to be estimated;

In the second step, the original image determined in the first step is respectively subjected to horizontal mirroring, vertical mirroring and diagonal mirroring;

In the third step, the original image and its horizontal mirror image, vertical mirror image and diagonal mirror image are arranged and combined according to the corresponding mirror position, and the image enlarged to twice the size is obtained, which is the first merged and copied image;

The fourth step is to determine the number of merging n according to the actual needs of image fractal dimension estimation and sensitivity requirements;

Perform horizontal mirroring, vertical mirroring, and diagonal mirroring processing on the image after the first merged copy, and arrange and combine the image after the first merged copy with its horizontal mirror, vertical mirror, and diagonal mirror according to the corresponding mirror position, Obtain the image after the second merging and copying; and so on, finally obtain an image whose size is enlarged by 2 ⁿ times, which is the image after the nth merging and copying;

The fifth step is to calculate the fractal feature of the image after the n-th merging and copying, which is the estimation of the fractal feature of the original image to be estimated.

Preferably, the merge replication times n is 2-4.

Preferably, a box counting method is used for fractal feature estimation: the combined and copied image is regarded as a three-dimensional surface, and the z-axis represents the gray level of the image; a three-dimensional box is constructed with a scale r and covers the entire image surface, and the minimum box required for statistical coverage Number N _r ; by changing the scale r of the covering box, calculate the number N _r of boxes required to cover the entire image surface at different scales r, according to the definition of the box counting dimension:

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}}\frac{{\mathrm{<span\; class="notranslate">\; logN</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

The least squares linear fitting is performed on the distribution points (log(1/r), log(N _r )) in the logarithmic coordinate system corresponding to the formula (1), and the slope of the fitted line obtained is the fractal of the image dimension.

Preferably, the fractal feature estimation is performed using the blanket method.

Preferably, the fractal feature estimation is performed using the fractal Brownian model method.

The present invention has following beneficial effect:

Using the image processing method of n times merging and copying the original image will obtain a texture image based on the arrangement and combination of the original image whose size is enlarged by 2 ⁿ times. On the one hand, the newly formed texture image has a larger size, which is convenient for multi-scale statistics. Taking the box counting method as an example, in order to achieve multi-scale coverage, the image needs to be divided into grids at different scales. If the image scale is increased by merging and copying, the submultiple of the enlarged image size can be used as the grid size to ensure sufficient data for multi-scale statistics.

On the other hand, since the fractal characteristics of the mirror image and the original image are consistent, it can be considered that the complexity of the new texture image formed by the combination of the original image and its mirror image arrangement only includes the complexity of the original image and the complexity of the image arrangement. Changes, and the complexity of permutations and combinations increases with the increase in the number of merged replications. In short, as the fractal characteristics of the image are enhanced with the increase of the number of merged replications, the fractal dimension of the image will also increase.

To sum up, the merge and copy method can be used to enhance the estimated fractal features of images, and this method is beneficial to realize image processing such as shape analysis, pattern recognition, and texture segmentation based on fractal features.

Description of drawings

Fig. 1 (a) is the original image window selected in pixel-based fractal feature estimation; Fig. 1 (b) is the original image window selected in region-based fractal feature estimation;

Fig. 2 (a) is the original image determined in the method of the present invention; Fig. 2 (b) is the horizontal mirror image of original image; Fig. 2 (c) is the vertical mirror image of original image; Fig. 2 (d) is original image The diagonal mirror image of ;

Fig. 3 is the result synoptic diagram that adopts different times of merging and duplicating, wherein, in Fig. 3 (a), the times of merging and duplication n=1; Among Fig. 3 (b), the times of merging and duplication n=2; Among Fig. 3 (c), the times of merging and duplication n = 3;

Figure 4 is two sets of detection images in Brodatz texture library, Figure 4(a) and Figure 4(b) are D64 and D65 images respectively; Figure 4(c) and Figure 4(d) are D95 and D96 images respectively.

detailed description

The present invention will be described in detail below with reference to the accompanying drawings and examples.

Here we mainly take the fractal feature of fractal dimension as an example to illustrate the proposed method.

The technical scheme of the method is: firstly, the original image or the image window is mirrored and copied, specifically including horizontal mirroring, vertical mirroring and diagonal mirroring. The reason for mirror copying is mainly to consider that mirroring the image will not change the complexity of the image, that is, the fractal characteristics of the mirror image and the original image are consistent. Merge the obtained mirror copy image with the original image according to the corresponding mirror positions to form a new image doubled in size. The main consideration of merging according to the mirror position is to minimize the large mutation of each block image during splicing, ensure the continuity of the merged image, and avoid the step change at the splicing point from destroying the fractal characteristics of the original image. Similarly, the enlarged image can continue to be merged and copied, and the size of the image increases with the increase of the number of merged copies; the fractal dimension of the enlarged image is calculated using the box counting method, and the calculation result can be used to estimate the fractal of the original image dimension.

The first step is to determine the original image window. As shown in Figure 1, whether it is a pixel-based fractal feature estimation algorithm or a region-based fractal feature estimation algorithm, it is first necessary to determine the image window required for the actual calculation of the algorithm. Here it is assumed that the determined original image window size is M×N, and the fractal feature to be estimated is the fractal dimension.

The second step is mirror copying. Assuming that the grayscale representation of the M×N original image is G ₀ (x,y), the mirror image of the original image is as follows:

Horizontal mirroring: G _H (x,y)=G ₀ (M-x+1,y);

Vertical mirroring: G _V (x,y)=G ₀ (x,N-y+1);

Diagonal mirror image: G _D (x, y) = G ₀ (M-x+1, N-y+1);

As shown in Figure 2, the original image can be mirrored horizontally, vertically and diagonally through mirror copying. At this time, the fractal characteristics of each mirror image and the original image are consistent, and the fractal dimension is also the same.

The third step is image merging. Arranging and combining the original image with its horizontal mirror image, vertical mirror image and diagonal mirror image according to the corresponding mirror positions, an image whose size is doubled can be obtained, expressed as:

$\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left|\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\end{array}\right|$

The fourth step is to determine the number n of merged replications. Finally determine the number of merging n according to the actual dimension estimation requirements and sensitivity requirements; perform horizontal mirroring, vertical mirroring and diagonal mirroring processing on the image after the first merging and copying, and combine the image after the first merging and copying with The horizontal mirror image, vertical mirror image and diagonal mirror image are arranged and combined according to the corresponding mirror positions to obtain the image after the second merged copy; and so on, the final image with a size enlarged by 2 ⁿ times is finally obtained, which is the image after the nth merged copy Image; the result of texture image enhanced by fractal feature is shown in Figure 3. According to the experiment in Figure 4, it is more reasonable to suggest that the number of merged replications n be 2 to 4.

The fifth step is to estimate the fractal characteristics. Here, the box counting method commonly used to calculate the fractal dimension, which is a fractal feature, is introduced as an example. The merged and copied image is regarded as a three-dimensional surface, and the z-axis represents the gray level of the image. Construct a three-dimensional box with scale r and cover the entire image surface, and count the minimum number N _r of boxes required for coverage. By changing the scale r of the covering box, calculate the number N _r of boxes required to cover the image at different scales r, according to the definition of the box counting dimension

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}}\frac{{\mathrm{<span\; class="notranslate">\; logN</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}$

In the logarithmic coordinate system, by performing least square linear fitting on these distribution points (log(1/r), log(N _r )), the slope of the fitted line obtained is the fractal dimension of the image .

Fractal feature estimation can also be carried out by blanket method, fractal Brownian model and other methods.

Since merging and copying will enhance the fractal characteristics of the image, the calculation result of the fractal dimension of the image after merging and copying will increase based on the fractal dimension of the original image. This result can be used to estimate the fractal dimension of the original image and be applied to shape analysis and pattern recognition. , texture segmentation and other image processing.

In order to verify the effect of merging and copying on the fractal dimension of the image, here we select two groups of images D64 and D65, D95 and D96 from the Brodatz texture library, as shown in Figure 4. Each set of images consists of two texture images of different complexity. The effect of the proposed method is verified by comparing the fractal dimension calculated from the images before and after merging and copying. Table 1 shows the fractal dimension results calculated by the box counting method for the selected four images.

Table 1 Calculation results of image fractal dimension

It can be found from Table 1 that the calculation result of the fractal dimension of each test image will increase with the increase of the number of window merging and copying. Comparing the two texture images D64 and D65 in a single group, it can be found that because the texture of D65 is more complex, the calculated fractal dimension is always greater than that of D64 under different times of merging and copying. Similarly, the fractal dimension of D95 is always greater than that of D96. The experimental results show that the fractal dimension of the image does increase with the increase of the merge and copy times, and the fractal dimension of the image with a larger fractal dimension is still larger after the merge and copy. However, it is worth noting that the difference in fractal dimension of two images in the same group gradually decreases with the increase of the number of merged replications. A reasonable explanation is that the complexity of permutations and combinations will increase with the increase in the number of merged copies, while the complexity of the original image and its mirror image remains unchanged, so the increase in the number of copies will cause the complexity of permutations and combinations to increase. The complexity of the image contributes more, which weakens the influence of the difference in the fractal characteristics of the original image. This coincides with the second beneficial effect mentioned. Based on the above experiments, the number n of merging and copying should be controlled at 2 to 4 times, which can not only ensure that the multi-scale statistics of small-scale images have sufficient data, but also ensure that the fractal characteristics of the merged images still have sufficient differences.

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 (5)

1. a kind of enhanced estimation method based on the image fractal feature of merging and copying, it is characterized in that, comprises the steps: The first step is to determine the original image to be estimated; In the second step, the original image determined in the first step is respectively subjected to horizontal mirroring, vertical mirroring and diagonal mirroring; In the third step, the original image and its horizontal mirror image, vertical mirror image and diagonal mirror image are arranged and combined according to the corresponding mirror position, and the image enlarged to twice the size is obtained, which is the first merged and copied image; The fourth step is to determine the number of merging n according to the actual needs of image fractal dimension estimation and sensitivity requirements; Perform horizontal mirroring, vertical mirroring, and diagonal mirroring processing on the image after the first merged copy, and arrange and combine the image after the first merged copy with its horizontal mirror, vertical mirror, and diagonal mirror according to the corresponding mirror position, Obtain the image after the second merging and copying; and so on, finally obtain an image whose size is enlarged by 2 ⁿ times, which is the image after the nth merging and copying; The fifth step is to calculate the fractal feature of the image after the n-th merging and copying, which is the estimation of the fractal feature of the original image to be estimated. 2. A method for enhancing estimation of image fractal features based on merging and copying as claimed in claim 1, wherein the number of times n of merging and copying is 2-4. 3. a kind of enhancement estimation method based on the image fractal feature of merging and copying as claimed in claim 1, it is characterized in that, adopt box counting method to carry out fractal feature estimation: the image after merging and copying is regarded as three-dimensional surface, z axis represents Image grayscale; construct a three-dimensional box with scale r and cover the entire image surface, and count the minimum number of boxes N _r required for coverage; by changing the scale r of the covered box, calculate the number of boxes required to cover the entire image surface at different scales r The number N _r , according to the definition of the box count dimension: $\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; lim</span>}}\frac{\mathrm{<span\; class="notranslate">\; log</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ The least squares linear fitting is performed on the distribution points (log(1/r), log(N _r )) in the logarithmic coordinate system corresponding to the formula (1), and the slope of the fitted line obtained is the fractal of the image dimension. 4. a kind of enhanced estimation method based on the image fractal feature of merging and copying as claimed in claim 1, is characterized in that, adopts blanket method to carry out fractal feature estimation. 5. a kind of method for enhancing estimation based on the image fractal feature of merging and copying as claimed in claim 1, is characterized in that, adopts fractal Brown model method to carry out fractal feature estimation.