CN103886614A - Image edge detection method based on network node fractal dimensions - Google Patents

Abstract

The invention discloses an image edge detection method based on network node fractal dimensions and belongs to the technical field of computer vision and image processing. The image edge detection method comprises the following steps of converting RGB images into an undirected weighting network; 2 calculating fractal dimensions of all of nodes in the network; 3 recognizing the image edges according to local fractal dimensions of all of nodes in the network. The image edge detection method has the advantages that the noise wave resisting capacity is good, the edge detection can be still effectively performed on images including strong-noise-wave images, the signal to noise ratio is high; the gradient background distinguishing capacity is good, the edge detection can be effectively performed on images including gradient backgrounds, the signal to noise ratio is high; the method has good effect on analog images or real images.

Description

The method for detecting image edge of node fractal dimension Network Based

Technical field

The invention belongs to computer vision and technical field of image processing, relate to a kind of method for detecting image edge of node fractal dimension Network Based.

Background technology

Edge is one of most important feature of image, the place of correspondence image gray scale acute variation.Along with the development of infotech, rim detection becomes a basic content in image processing and computer vision.The object of rim detection is that in discriminating digit image, bright spot changes obvious point, all has application in the various fields of image processing, it is usually used in fields such as figure is cut apart, object identification, feature extraction.Image Edge-Detection has reduced data volume significantly, and has rejected and can think and incoherent information retained the important structure attribute of image.

Have many methods for rim detection, their overwhelming majority can be divided into two classes: the class based on search and the class based on zero point.Method based on search is that the minimum and maximum value by finding in image first order derivative is carried out detection boundaries, the normally direction in gradient maximum by boundary alignment.Search based on gray scale is one of widespread use of these class methods, but because edge and the ripple of making an uproar are all corresponding with gray scale acute variation place, thus the edge detection method based on search type to the ripple sensitivity of making an uproar, thereby to the Image Edge-Detection poor effect that contains the ripple of making an uproar.

Method based on zero point is to find border zero point by finding image second order derivative.Algorithm conventional in the method is Canny operator, has provided the index of evaluation edge detection performance quality: 1, good signal to noise ratio (S/N ratio), and the probability that is judged to be marginal point by non-marginal point is low, and the probability that marginal point is judged to non-marginal point is low; 2, high positioning performance, the marginal point detecting will be as far as possible at the center of actual edge; 3, only there is unique response at single edge, and to produce the probability of multiple responses low at single edge, and false response edge should obtain maximum the inhibition.Nonetheless, still there are some problems in Canny: contain gradual change background or analog image when making an uproar ripple by force at image, Canny can not find correct image border.In addition, wavelet transformation is suggested and widespread use as the edge detection method of image, and its most important being characterised in that can be carried out partial transformation to space (time) and frequency.

Summary of the invention

In view of this, the object of the invention is to for a little less than the anti-noise wave energy power existing in conventional images edge detection method, to the problem such as the rim detection that contains gradual change background image is not in place, a kind of method for detecting image edge of node fractal dimension Network Based has been proposed, the method is according to three indexs of rim detection performance quality, adopt the node fractal dimension edge detection method that image is converted to network, make no matter the rim detection of image is all to have good detection effect in simulation or true picture.

For achieving the above object, the invention provides following technical scheme:

A method for detecting image edge for node fractal dimension Network Based, comprises the following steps: step 1: RGB image is converted to undirected weighting network; Step 2: the fractal dimension of each node in computational grid; Step 3: according to local dimension's recognition image edge of each node in network.

Further, in step 1, image pixel is considered as to network node, with limit connection layout, as neighbor, the weight on limit obtains by the calculating of the rgb value of paired node.

Further, in step 1, specifically comprise: replace image pixel, tectonic network G=(V, E, W with node), V represents node, and E represents limit (being connected into pairs neighbor), and W represents the weight w on limit _k, utilize following formula to calculate w _k:

$w_k=\frac{\left|\right|R_{\mathrm{ij}}-R_{\mathrm{mn}}\left|\right|}{\mathrm{MAX}\left(R\right)}$

Wherein: w _krepresent the weight on k article of limit, R _ijrepresent to be positioned at the rgb value of the capable j row of image i place pixel.

Further, in step 2, the box based on hausdorff covers local dimension's theory and box covering algorithm, utilizes following formula to calculate respectively the fractal dimension of each node V:

$d_i=-\underset{l\→0}{\lim }\frac{1n{d}_i\left(l\right)}{1\mathrm{nl}}$

Wherein, d _irepresent node V _inode fractal dimension, l increases progressively until equal network diameter or d to add one form _i(l) no longer reduce along with the increase of l.

Further, in step 3, according to the each node fractal dimension obtaining, utilize the fractal dimension of following formula computational grid G:

D＝{d ₁,d ₂,d ₃,...,d _n}。

Further, in step 3, according to the fractal dimension of network G, by judging that the node fractal dimension at edge is significantly less than other node dimension, and the node dimension at edge is in all environment, though color difference, brightness difference, all can be identified, thereby realize, the edge of image be detected.

Beneficial effect of the present invention is: 1, anti-noise wave energy power is strong, to still effectively carrying out rim detection containing the ripple image of making an uproar by force, has higher signal to noise ratio (S/N ratio).2, strong to the resolving ability of gradual change background, can effectively carry out rim detection to the image containing gradual change background, there is higher signal to noise ratio (S/N ratio).3, no matter be at analog image or really in image, all have good effect.

Accompanying drawing explanation

In order to make object of the present invention, technical scheme and beneficial effect clearer, the invention provides following accompanying drawing and describe:

Fig. 1 is the schematic flow sheet of the method for the invention;

Fig. 2 is concrete steps decomposing schematic representation;

Fig. 3 is that box covering operator is applied to complex network schematic diagram;

Fig. 4 is the structure of picture network.

Embodiment

Cover people's application at complex network to it such as local dimension's theory and Song according to the box of Hausdorff, can realize this method calculating for node dimension in network, step is as follows:

The first step: given network G ₁with the box that is of a size of l, can obtain a new network G ₂, the satisfied node i being connected and j are apart from d _ijbe not less than l.

Second step: according to the coloring principle in gray scale theory, by network G ₂in be directly connected saving different colours.After painted completing, produce new network G ₃.

The 3rd step: network G ₃in every kind of color represent different boxes, can calculate box number N _b(l) minimum value.

The size l of box must be no more than network diameter.For fractal complex network, N _b(l) there is following relation with l:

$N_b\left(l\right)~l^{{-d}_b}---\left(1\right)$

D _bfor the box dimension of complex network, its value is:

$d_b=-\underset{l\→0}{\lim }\frac{1n{N}_b\left(l\right)}{1\mathrm{nl}}---\left(2\right)$

In sum, internodal distance is only determined by the limit number of connected node.This algorithm has been widely used in the fractal dimension of calculation of complex network.In actual conditions, d _bvalue equal to meet lnN _band the straight slope of the log-log plot of lnl relation (l).

Referring to Fig. 3, in the present embodiment, now l=3, network G 1 is for having 6 nodes, the primitive network on 6 limits.Network G 2 couples together and is produced new network by only G1 middle distance being not less than to 3 node.Thereby G3 is the new network that greedy algorithm is carried out to painted generation for G2.

Fig. 1 is the schematic flow sheet of the method for the invention, and Fig. 2 is concrete steps decomposing schematic representation.

As shown in Figure 1, the method for detecting image edge of node fractal dimension Network Based of the present invention comprises the following steps: step 1: RGB image is converted to undirected weighting network; Step 2: the fractal dimension of each node in computational grid; Step 3: according to local dimension's recognition image edge of each node in network.

Specifically, comprise in the present embodiment:

1, complex network node fractal dimension

In the method, using node dimension characteristic attribute based on spherical dimension node in network, node fractal dimension is defined as follows:

Given network G=(V, E, W), V represents a series of node (V ₁v _n), E represents limit, W represents weight w _k.Each node V in network _ithe asking for referring to formula (3) of node fractal dimension:

$d_i\left(l\right)~l^{{-d}_i}(0\≤l\≤L)---\left(3\right)$

D _irepresent node V _inode fractal dimension.L increases progressively until equal network diameter or d to add one form _i(l) no longer reduce along with the increase of l.D _icalculating see formula (4):

$d_i=-\underset{l\→0}{\lim }\frac{1n{d}_i\left(l\right)}{1\mathrm{nl}}---\left(4\right)$

In sum, node V _ifractal dimension be computable, then utilize formula (4) to be applied to all node V in network G, recycling formula (5) is tried to achieve the value of the node fractal dimension in network D.

D＝{d ₁,d ₂,d ₃,...,d _n}(5)

2, image is to the conversion of network

The structure example of picture network refers to Fig. 4.The rgb value of pixel is commonly used to form network.Suppose that original image comprises M*M pixel, pixel P _ijthe rgb value of (0 < i, j≤M) is R _ij, a given image network G=(V, E, W), V represents node (pixel P), and E represents limit (being connected into pairs neighbor), and W represents weight w _k, weight be connected a pair of pixel (v _ij, v _mn) edge relevant, relation is as follows:

$w_k=\frac{\left|\right|R_{\mathrm{ij}}-R_{\mathrm{mn}}\left|\right|}{\mathrm{MAX}\left(R\right)}---\left(6\right)$

W _krepresent the weight on k article of limit, R _ijrepresent to be positioned at the rgb value of the capable j row of image i place pixel.

Fig. 4 is the structure example of picture network, picture model is carried out abstract, replaces image pixel with node.Stain in (b) in Fig. 4 represents network node, straight line representative edge.Image network G meets G=(V, E, W), V represents node (pixel P), and E represents limit (being connected into pairs neighbor), and W represents weight w _k, w _kcalculating meet formula (6).

3, recognition image edge in network

After converting picture to network G, its fractal dimension D passes through proposed node fractal dimension algorithm can calculate value, after fractal dimension is carried out to illustration, can very clearly know that the node fractal dimension at edge is significantly less than other node dimension.And the node dimension at edge is in all environment, even color difference, brightness difference, all can be identified.This explanation node dimension only concentrates in pixel group, thereby has given the powerful immunity of the method to the ripple of making an uproar.

Finally explanation is, above preferred embodiment is only unrestricted in order to technical scheme of the present invention to be described, although the present invention is described in detail by above preferred embodiment, but those skilled in the art are to be understood that, can make various changes to it in the form and details, and not depart from the claims in the present invention book limited range.

Claims (6)

1. a method for detecting image edge for node fractal dimension Network Based, is characterized in that: comprise the following steps:

Step 1: RGB image is converted to undirected weighting network;

Step 2: the fractal dimension of each node in computational grid;

Step 3: according to local dimension's recognition image edge of each node in network.

2. the method for detecting image edge of a kind of node fractal dimension Network Based according to claim 1, it is characterized in that: in step 1, image pixel is considered as to network node, and limit connection layout is as neighbor, and the weight on limit obtains by the calculating of the rgb value to paired node.

3. the method for detecting image edge of a kind of node fractal dimension Network Based according to claim 2, is characterized in that: in step 1, specifically comprise: replace image pixel, tectonic network G=(V with node, E, W), V represents node, E represents limit, and W represents the weight w on limit _k, utilize following formula to calculate w _k:

$w_k=\frac{\left|\right|R_{\mathrm{ij}}-R_{\mathrm{mn}}\left|\right|}{\mathrm{MAX}\left(R\right)}$

Wherein: w _krepresent the weight on k article of limit, R _ijrepresent to be positioned at the rgb value of the capable j row of image i place pixel.

4. the method for detecting image edge of a kind of node fractal dimension Network Based according to claim 3, it is characterized in that: in step 2, box based on hausdorff covers local dimension's theory and box covering algorithm, utilizes following formula to calculate respectively the fractal dimension of each node V:

$d_i=-\underset{l\&RightArrow;0}{\lim }\frac{1n{d}_i\left(l\right)}{1\mathrm{nl}}$

Wherein, d _irepresent node V _inode fractal dimension, l increases progressively until equal network diameter or d to add one form _i(l) no longer reduce along with the increase of l.

5. the method for detecting image edge of a kind of node fractal dimension Network Based according to claim 4, is characterized in that: in step 3, according to the each node fractal dimension obtaining, utilize the fractal dimension of following formula computational grid G:

D＝{d ₁,d ₂,d ₃,...,d _n}。

6. the method for detecting image edge of a kind of node fractal dimension Network Based according to claim 4, it is characterized in that: in step 3, according to the fractal dimension of network G, by judging that the node fractal dimension at edge is significantly less than other node dimension, and the node dimension at edge is in all environment, though color difference, brightness difference, all can be identified, thereby realize, the edge of image be detected.

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