CN101286233A - Fuzzy edge detection method based on object cloud - Google Patents

Abstract

The invention requests to protect a fuzzy edge detection method based on object clouds, which relates to a digital image processing technology. The method integrates the fuzzy set theory and the cloud theory to be applied in the image edge detection and designs a high efficient detection method which is applicable to the images, the object clouds are generated based on the gray features, a fuzzy object in the image is represented as the form of a could cluster, a normal cloud generator realizes the mapping of the image space and the cloud space, the cloud computing realizes the obtainment of the boundary cloud cluster and the digital features thereof, and the self-adaptive edge transition region processing is carried out according to the maximum fuzzy entropy principle; the method keeps the edge information of a great number of low gray values in the image, thus making up the shortcomings of the algorithm based on the fuzzy set theory to a great degree, taking into account of the problem of the randomness of uncertain boundary and being able to obtain good detection effect from the application in the multi-spectral image.

Description

Fuzzy edge detection method based on the object cloud

Technical field

The present invention relates to digital image processing techniques, relate in particular to the edge of image detection technique.Specifically, be based on a kind of new fuzzy theory---the technique of image edge detection of cloud theory.

Background technology

In recent years, people have carried out big quantity research for the edge detecting technology based on fuzzy theory, and many scholars are devoted to fuzzy theory is introduced Flame Image Process both at home and abroad.As fuzzy C-mean algorithm of the fuzzy enhancement algorithm of S.K.Pal, T.L.Huntsberger, fuzzy neural network algorithm, fuzzy competitive fringe detection algorithm etc.But existing various fuzzy detection operator is not perfect, and on the one hand, particularly under the more situation of picture noise, it is relatively poor to detect effect under actual conditions; On the other hand, can not be effectively applied to remote sensing images detects, particularly for the multispectral image that is widely used now, utilize common fuzzy detection operator can not obtain gratifying effect, sometimes even can't detect, be in particular in: existing fuzzy algorithm has fuzzy no thoroughness, seldom considers the influence at random that exists in the image simultaneously.As the main tool of handling fuzzy problem, fuzzy set theory is widely used in the middle of the fuzzy edge detection algorithm.Fuzzy set theory has proposed the being this or that property that the notion of degree of membership is portrayed fuzzy edge, determining that { 0,1} expands to a fuzzy membership interval [0,1], the blooming that extensively exists with the method research of mathematics for two-value membership in the set.Yet fuzzy set does not fundamentally solve the fuzzy uncertain problem.At first, the essence of fuzzy membership functions notion and the method for specifically determining still do not have final conclusion, and it determines still to be stuck in the stage that experience is judged; Secondly, represent the subjection degree of element, will make fuzzy problem precision by force fuzzy set with unique precise figures; The 3rd, when research contained the uncertain problem of ambiguity and randomness simultaneously, fuzzy set can only abandon randomness.As document (Lily RuiLiang.Carl G.Looney.Competitive Fuzzy Edge Detection.Applied softcomputing, 2003,3:123-137) a kind of fuzzy competitive fringe detection algorithm is proposed, this algorithm is according to the variation difference of gray-scale value on the different direction of pixel, introduce four-dimensional proper vector, utilize fuzzy membership function the picture element classification that is at war with.The place of this algorithm uniqueness just is that its starting point is different from traditional detection method, and the thought of the four-dimensional proper vector that induces one very dexterously and fuzzy competition has embodied the advantage of fuzzy location fully.But the extraction at image detail position still is not special ideal, and. noiseproof feature neither be very high.

Utilize an accurate subordinate function to describe a fuzzy edge set based on the common fuzzy algorithm of fuzzy set theory, with the fuzzy concept people for including accurate mathematics kingdom in, the no thoroughness of this traditional fuzzy collection theory has caused the precision by force of fuzzy edge, and the fuzzy essence of this and remotely-sensed data is runed counter to.

Summary of the invention

The present invention is directed to the above-mentioned defective of prior art, a kind of fuzzy edge detection method based on the object cloud is proposed, different objects have been carried out the cloud description, and this method has the defective that remedies based on traditional fuzzy collection theoretical algorithm, also takes into account the stochastic problems on uncertain border simultaneously.

The technical scheme that the present invention solves the problems of the technologies described above is, first cloud theory and cloud model is applied to the Image Edge-Detection field, proposes a kind of fuzzy edge detection method based on the object cloud (OCFD).This method specifically may further comprise the steps: the processing stage of (1) image denoising, the object cloud atlas is looked like to carry out the non-linear threshold noise reduction process; (2) image cloud nuclear extracts and merging phase, and based on gray feature formation object cloud, the cloud that utilizes the relaxative iteration method to generate uncertain cloud is examined the merging of racking of going forward side by side; (3) each object in the cloud image generates the cloud space stage, and the different object cloud atlas is looked like to carry out the cloud description, and the data of image space are mapped as cloud cluster by the one-to-many model in this space, realizes the mapping in image space and cloud space; (4) the adjacent object cloud is carried out logical operation and extracts the border transition district, obtain the numerical characteristic of reflection border cloud institute coverage, make up fuzzy characteristics plane, set up fuzzy matrix according to the fuzzy characteristics plane based on border cloud numerical characteristic; (5) carry out the edge transition district according to maximum fuzzy entropy principle self-adaptation and handle, calculate the degree of membership of each pixel according to border cloud numerical characteristic, the two-dimensional ensemble that all pixels that the border cloud is covered constitute is the border transition district; (6) grown in the edge and comprehensively, obtain edge line continuously and clearly.

This method provides the cloud expression of different object in the cloud space.Different object is carried out the cloud description, expressed point-like, wire and area feature with a cloud, line cloud and face cloud respectively.The data of image space are mapped as cloud cluster by the one-to-many model in this space, possess the numerical characteristic of describing its ambiguity and randomness, embody the uncertain transitional information of object cloud.Object cloud generator algorithm has been proposed on the basis of classical cloud generator algorithm.Foundation is calculated object Yun Jinhang based on the one dimension cloud spatial mappings model of pixel gray feature, based on the two-dimentional cloud spatial mappings model of image gradient feature on both direction.The extracting method of one dimension border cloud and multidimensional border cloud has been proposed.Employing is based on the transition region extraction algorithm of border cloud, structure is based on the fuzzy characteristics plane of border cloud numerical characteristic, set up fuzzy matrix according to the fuzzy characteristics plane, with each element definition of fuzzy matrix is the set of a degree of membership value that is produced by border cloud numerical characteristic, show that each pixel is under the enchancement factor influence in the image, subjection degree to a certain object is not an exact value, and showing as a kind of probability distribution, this method can embody to a certain extent in randomness influences the characteristic that hypograph has.Utilize maximum fuzzy entropy in zone of transition, to detect the edge, considered the correlativity between pixel and its neighborhood fully, estimate, detect cloud space inner boundary cloud zone of transition inward flange feature based on maximum fuzzy entropy principle definition neighborhood consistance.Utilize the fuzzy characteristics matrix to carry out the calculating of image blurring division entropy, bring the influence at random in the image into entropy find the solution, and repeatedly utilize the fuzzy entropy of dividing in the degree of membership set of obeying certain probability distribution, to seek optimum solution; In order farthest to utilize image information, proposed to estimate under the common constraint of estimating with the direction consistance extraction principle and the method for marginal point at structural integrity.

The OCFD method that the present invention proposes, fuzzy object in the object cloud atlas picture to be detected is shown as the cloud cluster form, utilize the characteristic of cloud, kept low gray-scale value marginal informations a large amount of in the image, remedied defective to a great extent, also taken into account the stochastic problems on uncertain border simultaneously based on the fuzzy set theory algorithm; In addition, opposite with the traditional detection algorithm, this algorithm is according to gradation of image data construct object cloud, replaced the pixel of microcosmic thereby computation amount with the cloud object of macroscopic view.Can obtain better detection effect, have stronger anti-noise ability simultaneously, can detect target edges preferably, in the testing result fracture place few, the omission situation is less.This method has the defective that remedies based on traditional fuzzy collection theoretical algorithm, also takes into account the stochastic problems on uncertain border simultaneously.

Description of drawings

Fig. 1 is the fuzzy edge detection method process flow diagram based on the object cloud of the present invention

Embodiment

Important means as the spatial information collection, remote sensing is in very short development time, for geoscience research provides a large amount of macroscopic views, synchronous first-hand information, and along with the fast development of spacer remote sensing technology for information acquisition, this data providing capability is more and more stronger.Full appreciation and utilize various numerals or process is learned on face of land view and ground that analog image reflected how, utilize the feature of sensor information itself to portray the attribute of aspects such as the physics of earth object, chemistry, form from number of ways, setting up image and the ground object comprehensive corresponding relation on mathematics and ground meaning, is the main research contents of filling up sensor information extraction and analysis knowledge gap.

The present invention is based on gray feature formation object cloud, extract image cloud nuclear, and to having similar intensity profile, the cloud that the distance between the sub-cloud is little merges; The forward cloud generator is realized the mapping in image space and cloud space; The cloud computing realizes that border cloud cluster and numerical characteristic thereof obtain; Carrying out the edge transition district according to maximum fuzzy entropy principle self-adaptation handles.

Below in conjunction with the drawings and specific embodiments enforcement of the present invention is described specifically.Be illustrated in figure 1 as the fuzzy edge detection method process flow diagram based on the object cloud of the present invention.This edge detection method specifically comprises following treatment step:

Image denoising is handled.Object cloud atlas to be detected is looked like to carry out the non-linear threshold noise reduction process, extract object cloud atlas picture to be detected, the image that adopts multiple dimensioned non-linear threshold method to treat the process object cloud carries out denoising.Below be that example specifically is described with a kind of wavelet decomposition and non-linear threshold denoise processing method, promptly at first the object cloud atlas is looked like to carry out wavelet decomposition, if x is true cloud atlas image signal, n is 0 noise for, average separate with x, y is an observation signal, and then cloud atlas image signal speckle noise model can be expressed as Wherein x=m-constant, the then variance of y ${\mathrm{\σ}}^2={\mathrm{m\σ}}_n^2,$ σ _n ²-be noise variance.Make ψ _{J, n}(x) be the 2-d wavelet function, A ₀Be 2 * 2 nonsingular matrix, WT _fBe the two-dimensional wavelet transformation of f (x), f (x) ∈ L ²(R ²), then have

${\mathrm{\ψ}}_{j,n}\left(\stackrel{\‾}{x}\right)={\left|A_0\right|}^{-j}\mathrm{\ψ}[A_0^{-j}\stackrel{\‾}{x}-\stackrel{\‾}{n}]$

${\mathrm{WT}}_f(j,\stackrel{\‾}{n})\⟨f\left(\stackrel{\‾}{x}\right),{\mathrm{\ψ}}_{j,n}\left(\stackrel{\‾}{x}\right)\⟩={\left|A_0\right|}^{-j}{\∫}_{x}f\left(\stackrel{\‾}{x}\right)\mathrm{\ψ}[A_0^{-j}\stackrel{\‾}{x}-\stackrel{\‾}{n}]d\stackrel{\‾}{x}$

As using the Daubechies small echo image is decomposed, the part of establishing yardstick j is:

${\hat{s}}_j(k_1,k_2)=\mathrm{WT}\hat{s}\≥(j,k_1,k_2)=\frac{1}{{\left|A_0\right|}^j}\underset{x_1}{\mathrm{\Σ}}\underset{x_2}{\mathrm{\Σ}}\hat{s}(x_1,x_2){\mathrm{\ψ}}^{*}(A_0^{-j}\stackrel{\‾}{x}-\stackrel{\‾}{k})$

ψ in the formula ^*The complex conjugate of-ψ.

After finishing wavelet decomposition, the HFS of different scale in the signal is carried out the non-linear threshold noise reduction process.Adopt the soft-threshold noise-reduction method, the threshold value that makes yardstick j is T _j, then wavelet coefficient is:

$C{\hat{s}}_j(k_1,k_2)=\left\{\begin{array}{cc}\mathrm{sign}\left[{\hat{s}}_j(k_1,k_2)\right]\left[\right|{\hat{s}}_j(k_1,k_2)|-T_j]& \left|{\hat{s}}_j(k_1,k_2)\right|\&GreaterEqual;T_j\\ 0& \left|{\hat{s}}_j(k_1,k_2)\right|<T_j\end{array}\right.$

$T_j={\mathrm{\&sigma;}}_j\sqrt{2\log (j+1)/j},$ j＝1，2，3，…，k∈z

${\mathrm{\&sigma;}}_j=\sqrt{\frac{1}{N_j^2}\underset{k_1,k_2}{\mathrm{\&Sigma;}}{({\hat{s}}_j(k_1,k_2)-E\left({\hat{s}}_j\right))}^2}$

σ in the formula _jNoise variance on the-yardstick j,

Expectation value, N _j-image

Size.

Utilize discrete wavelet inverse transformation reconstructed image at last, obtain the image behind the noise reduction, finish the denoising process of signal.

$s(x_1,x_2)=\underset{j}{\mathrm{\&Sigma;}}\underset{k_1}{\mathrm{\&Sigma;}}\underset{k_2}{\mathrm{\&Sigma;}}C{\hat{s}}_j(j,k_1,k_2)\mathrm{\&psi;}(A_0^{-j}\stackrel{\&OverBar;}{x}-\stackrel{\&OverBar;}{k})$

Image cloud nuclear extracts and merging phase.Estimate as consistance with gray-scale statistical characteristics, utilize the relaxative iteration method to generate the cloud nuclear Area of uncertain cloud.If in the pending image N pixel arranged after image denoising is handled, the original collection of an image N pixel is s={s ₁, s ₂... s _N, according to the number of peaks of image grey level histogram it is divided into the M class, get result set C={C ₁, C ₂..., C _M.Definition p _Ij ⁽⁰⁾Be s _i∈ C _j(1≤i≤N, the initial probability of 1≤j≤M), p _Ij ^(r), (r=1,2 ...) be the successive iteration probability, q _IjBe p _IjIncrement.In iterative process each time, the gray scale of each pixel all is carried out the weighting adjustment in the image, in storer, preestablish a threshold value, determine according to threshold value whether iteration reaches re-set target, and when reaching threshold value, the gray scale of pixel thinks iteration convergence, the termination of iterations process will be weighted the zone that net result produced of the image of adjusting the back acquisition as initial cloud nuclear.Because the influence of various disturbing factors may generate a plurality of " nuclears " simultaneously in the image in a bin, promptly produces cloudy phenomenon, for fear of the appearance on unnecessary border, can adopt " cloud merging " method synthesis cloudy.The cloud of judge module a plurality of to having " nuclears " judges, satisfy following condition when cloudy: " nuclear " of all sub-clouds has similar intensity profile; Distance between the sub-cloud is less than pre-set threshold, and then the cloud with a plurality of " nuclears " carries out comprehensively.With the comprehensive of two sub-clouds is that example illustrates its method.Be provided with two cloud C ₁And C ₂, its numerical characteristic is respectively (Ex ₁, En ₁, He ₁) and (Ex ₂, En ₂, He ₂), With

Be respectively C ₁And C ₂The expectation curve equation.Make that C is C ₁And C ₂New cloud after the merging, numerical characteristic be (Ex, En, He).Then:

${{\mathrm{MEC}}^{\&prime;}}_{C_1}\left(x\right)=\left\{\begin{array}{cc}{\mathrm{MEC}}_{C_1}\left(x\right),& {\mathrm{MEC}}_{C_1}\left(x\right)\&GreaterEqual;{\mathrm{MEC}}_{C_2}\left(x\right)\\ 0,& \mathrm{others}\end{array}\right.$

${{\mathrm{MEC}}^{\&prime;}}_{C_2}\left(x\right)=\left\{\begin{array}{cc}{\mathrm{MEC}}_{C_2}\left(x\right),& {\mathrm{MEC}}_{C_2}\left(x\right)\&GreaterEqual;{\mathrm{MEC}}_{C_1}\left(x\right)\\ 0,& \mathrm{others}\end{array}\right.$

${\mathrm{En}}_1^{\&prime;}=\frac{1}{\sqrt{2\mathrm{\&pi;}}}{\&Integral;}_U{{\mathrm{MEC}}^{\&prime;}}_{C_1}\left(x\right)\mathrm{dx}$ ${\mathrm{En}}_2^{\&prime;}=\frac{1}{\sqrt{2\mathrm{\&pi;}}}{\&Integral;}_U{{\mathrm{MEC}}^{\&prime;}}_{C_2}\left(x\right)\mathrm{dx}$

In the formula

For

With

Non-overlapping portions; En ' ₁, En ' ₂For blocking entropy.As can be seen, En ₁And En ₂By

With The area that is covered multiply by coefficient

And En ' ₁And En ' ₂By

With

The area that covers multiply by coefficient Thereby the cloud entropy that merges the new cloud that the back produces be two block entropy and, expectation value and super entropy are to block the weighted mean that entropy is a power.Can get the numerical characteristic of new cloud by following formula:

$\mathrm{Ex}=\frac{{\mathrm{Ex}}_1{\mathrm{En}}_1^{\&prime;}+{\mathrm{Ex}}_2{\mathrm{En}}_2^{\&prime;}}{{\mathrm{En}}_1^{\&prime;}+{\mathrm{En}}_2^{\&prime;}}$ En＝En′ ₁+En′ ₂ $\mathrm{He}=\frac{{\mathrm{He}}_1{\mathrm{En}}_1^{\&prime;}+{\mathrm{He}}_2{\mathrm{En}}_2^{\&prime;}}{{\mathrm{En}}_1^{\&prime;}+{\mathrm{En}}_2^{\&prime;}}$

Said method can get up the informix in each sub-cloud space, constitutes the numerical characteristic of object cloud in the compound cloud space.But it should be noted that here the cloud method of merginging that proposes has the restriction of strictness to its sub-cloud, " nuclear " that need satisfy all sub-clouds has similar intensity profile, and the distance between the sub-cloud is less than pre-set threshold, otherwise will lose comprehensive meaning.

Each object in the cloud image generates the cloud space.Provide the cloud expression of different object in the cloud space, different object has been carried out the cloud description, express point-like, wire and area feature with a cloud, line cloud and face cloud respectively.

1. the cloud of spatial object is described

Owing to can regard point-like atural object as area feature and handle, add that area is less, thereby approximately regard it as little disc.In this little disc, near the brightness in center is comparatively even, and more near the roundlet border, brightness changes complicated more, and image is fuzzy more.Introduce the viewpoint of cloud theory, uncertain point-like atural object can use normal cloud model (P (and i, j), Ex, Enx, Hx, Ey, Eny, Hy) expression, wherein P (i, j), (degree of membership that pixel belongs to this atural object is 1 for Ex, Ey) position and the mean flow rate of expression point-like atural object center pixel; Along with the increase of liftoff thing centre distance, the degree of membership that pixel is under the jurisdiction of this atural object reduces gradually.If regard point-like atural object as little disc, Ex=Ey then, Enx=Eny, Hx=Hy, if Ex=Ey, Enx=Eny=0, Hx=Hy=0, then this point is an accurate some position.

Because the influence of factors such as resolution, the thread like body of single pixel, single width does not exist in remote sensing images, generally is the ribbon object that is made of a plurality of adjacent image points, has certain area, and a plurality of pixels are arranged on Width.Near the banded zone center of expression linear ground object, brightness higher (also may be lower) and comparatively even, and get over the access areas border, and it is complicated more that brightness changes, and image is fuzzy more.Introduce the viewpoint of cloud theory, uncertain linear ground object can be used cloud model L (Line, En, He) expression, the core of this cloud be one by a plurality of adjacent single pixels be formed by connecting straight line or curve, the degree of membership that picture element on straight line or the curve belongs to this linear ground object is 1, along with the increase of this distance between center line, the degree of membership that pixel is under the jurisdiction of this atural object reduces gradually.Direction along the line is one and evenly distributes that the vertical line direction of this cloud is an one dimension normal state cloud, and the projection on the x-y plane is a fuzzy straight line or curve.

Introduce the viewpoint of cloud theory, uncertain area feature can be used cloud model A (Area, En, He) expression, the core of this cloud is a polygon, in this polygon inside, the degree of membership that arbitrary pixel is under the jurisdiction of this area feature is 1, along with the increase of this polygon distance, degree of membership reduces gradually.In polygonal outside, show as " partly falling cloud " this entropy and super entropy that partly falls cloud according to picture element to polygonal distance and be respectively En and He.This cloud shows as trapezoidal cloud in the vertical line direction.When the polygon core of this cloud is reduced into when a bit, this uncertain planar cloud then deteriorates to uncertain point-like cloud.

2. cloud spatial mappings model

The data of image space are mapped as cloud cluster by the one-to-many model in this space, possess the numerical characteristic of describing its ambiguity and randomness, embody the uncertain transitional information of object cloud.Object cloud generator algorithm has been proposed on the basis of classical cloud generator algorithm.The forward cloud generator is realized the mapping in image space and cloud space, and foundation is based on the one dimension cloud spatial mappings model of pixel gray feature, based on the two-dimentional cloud spatial mappings model of image gradient feature on both direction.

Because the object in the image space has ambiguity, thereby an object can be divided into " real part " and " imaginary part " two parts." real part " corresponding the main body of object, be the inside pixel collection of a spatial object in the image, the interior pixel of this set is comparatively even from gray feature, gray scale difference value is less than certain certain threshold level, the degree of membership that is under the jurisdiction of this object is 1; " imaginary part " correspondence " real part " is in addition to the pixel collection between the border, and these pixel grey scale change are violent, and gray scale difference value is bigger, and the degree of membership that is under the jurisdiction of this object is less than 1, and presents the rule that reduces apart from increase with object centers.

Conceptual Center of ubiquity or cluster centre in the fuzzy set are referred to as cloud nuclear in the cloud space." real part " of spatial object be promptly corresponding cloud nuclear in the cloud space.For a width of cloth single band image, set up one dimension cloud space with the pixel intensity profile that constitutes each object as domain, what at first will solve is exactly the generation of " cloud nuclear ".Because in the image is that point-like object or wire object all show as the zone with certain area, thereby can handle by the planar object of regarding as that these objects are unified.Obtaining of planar object " real part ", region growing method can obtain effect preferably.

1) foundation is based on the one dimension mapping model of pixel gray feature

If total n pixel among object cloud " real part " R that obtains by region growing method, for pixel gray scale f (average of R and standard deviation can be expressed as for i, function j):

${\stackrel{\&OverBar;}{x}}_R=\frac{1}{n}\underset{(i,j)\&Element;R}{\mathrm{\&Sigma;}}f(i,j)$ ${\mathrm{\&sigma;}}_R={\left[\frac{1}{n}\underset{(i,j)\&Element;R}{\mathrm{\&Sigma;}}{(f(i,j)-{\stackrel{\&OverBar;}{x}}_R)}^2\right]}^{1/2}$

Same (the P that adopts _m(i _m, j _m), Ex, En, He) four parameters are come the description object cloud, because Ex is the expectation value of cloud, also is simultaneously cloud nuclear places, thereby can makes the expectation value of the average of object cloud " real part " as cloud that Ex=x is arranged _RIf m pixel altogether among object " imaginary part " B, pixel gray scale be f ' (i, j), μ then _iFor the gray scale of each pixel in " imaginary part " is under the jurisdiction of the degree of membership of " real part " gray average, then have:

${\mathrm{\&mu;}}_i=1-\left|\frac{f^{\&prime;}(i,j)-{\stackrel{\&OverBar;}{x}}_R}{255}\right|$ (i＝1，2，…，m)

" imaginary part " pixel gray average x _BAnd standard deviation sigma _BFor:

${\stackrel{\&OverBar;}{x}}_B=\frac{1}{m}\underset{(i,j)\&Element;B}{\mathrm{\&Sigma;}}{f}^{\&prime;}(i,j)$ ${\mathrm{\&sigma;}}_B=\sqrt{\frac{1}{m}\underset{(i,j)\&Element;B}{\mathrm{\&Sigma;}}{[f^{\&prime;}(i,j)-{\stackrel{\&OverBar;}{x}}_B]}^2}$

Calculate ${\mathrm{En}}_i^{\&prime;}=\sqrt{\frac{-{(f^{\&prime;}(i,j)-{\stackrel{\&OverBar;}{x}}_R)}^2}{2\ln \left({\mathrm{\&mu;}}_i\right)}}$

Make En=stdev (f ' (i, j))=σ _B, He=stdev (En ' _i).

Four numerical characteristic (P of existing known object cloud _m(i _m, j _m), Ex, En He), can utilize back three parameters, generates water dust by X condition cloud generator.Generation is expectation value with En, and He is the normal random number En ' of standard deviation _j

En′ _j＝G(En，He)

Formula below utilizing

${\mathrm{\&mu;}}_i=\exp [-\frac{{(f^{\&prime;}(i,j)-\mathrm{Ex})}^2}{2{\mathrm{En}}_j^{\&prime;2}}]$

Calculate μ _j, make (f ' (i, j), μ _j) be water dust.

2) foundation is based on the two-dimensional map model of gradient, and calculating pixel is in the gradient mean value and the standard deviation of x direction, y direction

For most of natural images, usually have the very little zone of large stretch of gradient, these zones are in fact corresponding " real part " of object also has the comparatively violent zone of some graded in addition, represented " imaginary part " of object, the local corresponding place, edge of gradient maximum.If R is the little and interior zone uniformly of gradient in the gradient map, wherein total n pixel.If g _Ix(x y) is the gradient of i pixel in the x direction, g _XRAnd σ _XRBe gradient mean value and the standard deviation of R, then have in the x direction:

${\stackrel{\&OverBar;}{g}}_{\mathrm{xR}}=\frac{1}{n}\underset{(x,y)\&Element;R}{\mathrm{\&Sigma;}}{g}_{\mathrm{ix}}(x,y)$ ${\mathrm{\&sigma;}}_{\mathrm{xR}}=\sqrt{\frac{1}{n}\underset{(x,y)\&Element;R}{\mathrm{\&Sigma;}}{[g_{\mathrm{ix}}(x,y)-{\stackrel{\&OverBar;}{g}}_{\mathrm{xR}}]}^2}$

In like manner, make g _Iy(x y) is the gradient of i pixel in the y direction, g _YRAnd σ _YRBe gradient mean value and the standard deviation of R, then have in the y direction:

${\stackrel{\&OverBar;}{g}}_{\mathrm{yR}}=\frac{1}{n}\underset{(x,y)\&Element;R}{\mathrm{\&Sigma;}}{g}_{\mathrm{iy}}(x,y)$ ${\mathrm{\&sigma;}}_{\mathrm{yR}}=\sqrt{\frac{1}{n}\underset{(x,y)\&Element;R}{\mathrm{\&Sigma;}}{[g_{\mathrm{iy}}(x,y)-{\stackrel{\&OverBar;}{g}}_{\mathrm{yR}}]}^2}$

If B is the violent zone of the bigger variation of gradient in the gradient map, wherein total m pixel.Make g ' _Ix(x y) is the gradient of i pixel in the x direction, g ' _XBAnd σ ' _XBBe gradient mean value and the standard deviation of B in the x direction, g ' _Iy(x y) is the gradient of i pixel in the y direction, g ' _YBAnd σ ' _YBBe gradient mean value and the standard deviation of B, then have in the y direction:

${\stackrel{\&OverBar;}{g}}_{\mathrm{xB}}^{\&prime;}=\frac{1}{m}\underset{(x,y)\&Element;B}{\mathrm{\&Sigma;}}{g}_{\mathrm{ix}}^{\&prime;}(x,y)$ ${\mathrm{\&sigma;}}_{\mathrm{xB}}^{\&prime;}=\sqrt{\frac{1}{m}\underset{(x,y)\&Element;B}{\mathrm{\&Sigma;}}{[g_{\mathrm{ix}}^{\&prime;}(x,y)-{\stackrel{\&OverBar;}{g}}_{\mathrm{xB}}^{\&prime;}]}^2}$

${\stackrel{\&OverBar;}{g}}_{\mathrm{yB}}^{\&prime;}=\frac{1}{m}\underset{(x,y)\&Element;B}{\mathrm{\&Sigma;}}{g}_{\mathrm{iy}}^{\&prime;}(x,y)$ ${\mathrm{\&sigma;}}_{\mathrm{yB}}^{\&prime;}=\sqrt{\frac{1}{m}\underset{(x,y)\&Element;B}{\mathrm{\&Sigma;}}{[g_{\mathrm{iy}}^{\&prime;}(x,y)-{\stackrel{\&OverBar;}{g}}_{\mathrm{yB}}^{\&prime;}]}^2}$

By aforementioned calculation, can obtain four basic parameters: be respectively the gradient mean value and the standard deviation in object " real part " zone in gradient map, and the gradient mean value and the standard deviation in object " imaginary part " zone in gradient map.Because gradient map relates to x direction and two gradient components of y direction, thereby set up cloud spatial mappings model on the basis of two-dimentional cloud that can be in cloud model based on image gradient.

Make Ex=g _XR, Ey=g _YR, Enx=σ ' _XB, Eny=σ ' _YB, μ _XiAnd μ _YiBe respectively in " imaginary part " i pixel and be under the jurisdiction of the degree of membership of " real part " gradient mean value, g ' in the gradient of x direction and y direction _MaxBe gradient maximal value in the imaginary part.Then have:

${\mathrm{\&mu;}}_{\mathrm{xi}}=1-\left[\frac{g_{\mathrm{ix}}^{\&prime;}(x,y)-{\stackrel{\&OverBar;}{g}}_{\mathrm{xR}}}{g_{\max }^{\&prime;}}\right]$ ${\mathrm{\&mu;}}_{\mathrm{yi}}=1-\left[\frac{g_{\mathrm{iy}}^{\&prime;}(x,y)-{\stackrel{\&OverBar;}{g}}_{\mathrm{yR}}}{g_{\max }^{\&prime;}}\right]$

${\mathrm{Enx}}_i^{\&prime;}=\sqrt{\frac{{-(g_{\mathrm{ix}}^{\&prime;}(x,y)-{\stackrel{\&OverBar;}{g}}_{\mathrm{xR}})}^2}{2\ln \left({\mathrm{\&mu;}}_{\mathrm{xi}}\right)}}$ ${\mathrm{Eny}}_i^{\&prime;}=\sqrt{\frac{{-(g_{\mathrm{iy}}^{\&prime;}(x,y)-{\stackrel{\&OverBar;}{g}}_{\mathrm{yR}})}^2}{2\ln \left({\mathrm{\&mu;}}_{\mathrm{yi}}\right)}}$

Make Enx=stdev (g ' _Ix(x, y))=σ ' _XB, Eny=stdev (g ' _Iy(x, y))=σ ' _YB, Hx=stdev (Enx ' _i), Hy=stdev (Eny ' _i)

Now according to the numerical characteristic of object cloud (Ex, Ey, Enx, Eny, Hx Hy), generates water dust by X condition cloud generator.Generation with (Enx Eny) is expectation value, (and Hx, Hy) be standard deviation two-dimentional normal random number (Enx ' _i, Eny ' _i)

(Enx′ _i，Eny′ _i)＝G(Enx，Hx，Eny，Hy)

Utilize following formula to calculate μ _j, make (g ' _Ix(x, y), g ' _Iy(x, y), μ _j) be water dust.

${\mathrm{\&mu;}}_j=\exp \{-\frac{1}{2}[\frac{{(g_{\mathrm{ix}}^{\&prime;}(x,y)-{\stackrel{\&OverBar;}{g}}_{\mathrm{xR}})}^2}{E{\mathrm{nx}}_i^{\&prime;2}}+\frac{{(g_{\mathrm{iy}}^{\&prime;}(x,y)-{\stackrel{\&OverBar;}{g}}_{\mathrm{yR}})}^2}{{\mathrm{Eny}}_i^{\&prime;2}}\left]\right\}$

Border cloud and fuzzy characteristics plane thereof

The adjacent object cloud is carried out logical operation, extract border cloud cluster and numerical characteristic thereof, make up fuzzy characteristics plane, set up fuzzy matrix according to the fuzzy characteristics plane based on border cloud numerical characteristic.

1. extract border cloud cluster and numerical characteristic thereof.Through above-mentioned cloud processing, the cloud cluster that each adjacent object generates in the image, because the being this or that property of edge pixel adds the influence of super entropy, its spatial relationship presents a kind of overlapping relation.Two pairing pixels of part that cloud cluster intersects, its variation is comparatively violent, on gradient map, is the bigger zone of gradient, and these pixels have constituted the polygonal transitional region in its left and right sides jointly.Theoretically, the border cloud be average gray with image edge pixel as expectation value, calculate respectively that each pixel in the zone of transition is under the jurisdiction of the degree of membership of this gray-scale value and a kind of special cloud cluster that generates.The form of border cloud vertical direction tangent plane is typical normal state cloud.From the position, in the middle of two crossing cloud clusters, its intensity profile was between adjacent cloud nuclear gray scale about it was positioned at; From statistical nature, the pixel that it covered is the pixel in polygon imaginary part zone, the left and right sides, thereby the numerical characteristic of this border cloud is inseparable with the numerical characteristic of its left and right sides cloud cluster.

After carrying out the cloud processing for the single band image, will generate one dimension cloud space.Intersect generating of cloud cluster about border cloud in the cloud space between two crossing cloud clusters can pass through with computing, to about intersect cloud cluster and carry out three numerical characteristics that the border cloud is obtained in logical operation.If two crossing cloud cluster A=(P are arranged on the domain _A(i, j), Ex _A, En _A, He _A) and B=(P _B(i, j), Ex _B, En _B, He _B), C (L _C(i, j), Ex _C, En _C, He _C) be the border cloud.Border cloud C vertical line direction is an one dimension normal state cloud, its mathematical expectation curve A _C(x) be:

$A_C\left(x\right)=\exp [-\frac{{(x-E{x}_C)}^2}{2{\mathrm{En}}_C^2}]$

Three numerical characteristics can carry out following computing by the numerical characteristic to left and right sides object cloud and obtain:

$\left.\begin{array}{c}{\mathrm{Ex}}_C\&cong;\frac{1}{2}|({\mathrm{Ex}}_A-3E{n}_A-H{e}_A)+({\mathrm{Ex}}_B+3{\mathrm{En}}_B+H{e}_B)|\\ {\mathrm{En}}_C\&cong;\frac{1}{6}|({\mathrm{Ex}}_B+3E{n}_B+{\mathrm{He}}_B)-(E{x}_A-3E{n}_A-H{e}_A)|\\ {\mathrm{He}}_C=\mathrm{ma}x({\mathrm{He}}_A,H{e}_B)\end{array}\right\}$

For multispectral image since corresponding be a hyperspace, thereby in multidimensional cloud space, carry out the extraction of border cloud, need on each dimension, finish respectively.If multispectral image has m wave band, generate m dimension cloud space R after the cloud processing ^mAdjacent object A and B have multidimensional cloud A[Ex respectively in the image space _A1, En _A1, He _A1, Ex _A2, En _A2, He _A2..., Ex _Am, En _Am, He _Am] and B[Ex _B1, En _B1He _B1, Ex _B2, En _B2, He _B2..., Ex _Bm, En _Bm, He _Bm] corresponding with it.Respectively to the object Yun Jinhang logical operation of corresponding dimension among A and the B:

$\left.\begin{array}{c}{\mathrm{Ex}}_{\mathrm{Ck}}\&cong;\frac{1}{2}|({\mathrm{Ex}}_{\mathrm{Ak}}-3E{n}_{\mathrm{Ak}}-H{e}_{\mathrm{Ak}})+({\mathrm{Ex}}_{\mathrm{Bk}}+3{\mathrm{En}}_{\mathrm{Bk}}+H{e}_{\mathrm{Bk}})|\\ {\mathrm{En}}_{\mathrm{Ck}}\&cong;\frac{1}{6}|({\mathrm{Ex}}_{\mathrm{Bk}}+3E{n}_{\mathrm{Bk}}+{\mathrm{He}}_{\mathrm{Bk}})-(E{x}_{\mathrm{Ak}}-3E{n}_{\mathrm{Ak}}-H{e}_{\mathrm{Ak}})|\\ {\mathrm{He}}_{\mathrm{Ck}}=\mathrm{ma}x({\mathrm{He}}_{\mathrm{Ak}},H{e}_{\mathrm{Bk}})\end{array}\right\},(k=\mathrm{1,2},...,m)$

Ex in the formula _Ck, En _Ck, He _CkThe result of-Di k dimensional object cloud computing, the i.e. numerical characteristic of the border cloud that in the k dimension, extracts.

2. the extraction in border transition district.The two-dimensional ensemble that all pixels that the border cloud is covered in the definition cloud space constitute is the border transition district, and each dimension of cloud is implemented the numerical characteristic that the tonal range that border cloud cluster and reflection border cloud thereof covered is obtained in " soft with " computing respectively.

Zone of transition is the zone that the partial-pixel between target and background constitutes in the image, the locus of this part pixel is between target and background, intensity profile is also between target gray average and background gray average, therefore, zone of transition shows as the coverage of water dust outside two crossing cloud cluster cloud nuclears in the cloud space.

If two adjacent object A and B are arranged in the image I, in the cloud space, generate two crossing cloud cluster A=(P by mapping model _A(i, j), Ex _A, En _A, He _A) and B=(P _B(i, j), Ex _B, En _B, He _B).Utilize the extracting method of border cloud, between the two, generate border cloud C (L _C(i, j), Ex _C, En _C, He _C), the border cloud numerical characteristic of the tonal range that the border of acquisition reflection simultaneously cloud is covered, wherein Ex _CBe border nuclear gray scale expectation value, En _CBe entropy, the tonal range that reflection border cloud is covered embodies the nargin that the zone of transition pixel is this or that.Make that a, b are zone of transition left and right door limit value, have:

a＝Ex _C-3σ-He _C＝Ex _C-3En _C-He _C

b＝Ex _C+3σ+He _C＝Ex _C+3En _C+He _C

Then zone of transition is defined as the two-dimensional ensemble of all pixels formations that covered for the border cloud in the cloud space, promptly

TR＝{(i，j)∈I|a≤f(i，j)≤b}＝

{(i，j)∈I|Ex _C-3en _C-He _C≤f(i，j)≤Ex _C+3En _C+He _C}

3. set up fuzzy characteristics plane based on border cloud numerical characteristic

One width of cloth has L gray level, and size is the two dimensional image of M * N, can see a fuzzy dot matrix collection as, and each element in the collection all has the membership function mui with respect to certain particular gray level _Ij, all μ _Ij(i=1,2 ..., M; J=1,2 ..., N) plane of Zu Chenging is called image blurring characteristic plane.The plain μ of entry of a matrix in the fuzzy characteristics plane _Ij/ X _Ij(i j) locates gray level X all to be defined as image pixel _IjWith respect to maximum gray scale X _MaxDegree of membership.Since be subjected to the restriction of this define method, the fuzzy enhancing part in algorithm, the gray level part that will inevitably occur should strengthening in the original image does not obtain enough enhancings, and the gray level that should not strengthen part has obtained very big enhancing.Obviously, this will have influence on next step rim detection, does not reach original desired effects thereby make to detect; In addition, element in the corresponding matrix of each pixel in the zone of transition, do not consider the randomness in the image, express the degree of closeness of a fuzzy object for another object with an accurate degree of membership value, this can not solve the uncertain problem of object in particularly as a kind of remote sensing images of stochastic variable at real image.

Foundation is based on the fuzzy characteristics plane of border cloud numerical characteristic.According to the numerical characteristic of the border cloud degree of membership by each pixel of forward cloud generator algorithm computation, the set of degree of membership value is as the element in the fuzzy characteristics plane.

Because it is a plurality of that each pixel in the zone of transition to the degree of membership of border nuclear, changes into from one under the influence of super entropy, therefore for any pixel in the zone of transition, element corresponding in fuzzy matrix is not a value, but a degree of membership set.By calculating three numerical characteristic (Ex that obtain the border cloud _C, En _C, He _C), can instead release the degree of membership of each pixel according to forward cloud generator algorithm.

If f in the zone of transition (x) is the pixel gray scale, according to model E n ' _k=G (En _C, He _C) generate with En _CBe expectation value, He _CNormal random number En ' for standard deviation _k, the degree of membership of each pixel can obtain according to calculating:

${\mathrm{\&mu;}}_k=\exp [-\frac{{(f\left(x\right)-E{x}_C)}^2}{2E{n}_k^{\&prime;2}}]$

Ex in the formula _C, En _C, He _CNumerical characteristic for the border cloud.By aforementioned calculation as can be known, μ _Ij(x)={ μ _k, so the fuzzy characteristics plane can show as following form

$X_{\mathrm{ij}}=\left[\begin{array}{cccc}{\left\{{\mathrm{\&mu;}}_k\right\}}_{11}& {\left\{{\mathrm{\&mu;}}_k\right\}}_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& {\left\{{\mathrm{\&mu;}}_k\right\}}_{1N}\\ {\left\{{\mathrm{\&mu;}}_k\right\}}_{21}& {\left\{{\mathrm{\&mu;}}_k\right\}}_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& {\left\{{\mathrm{\&mu;}}_k\right\}}_{2N}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ {\left\{{\mathrm{\&mu;}}_k\right\}}_{M1}& {\left\{{\mathrm{\&mu;}}_k\right\}}_{M2}& \&CenterDot;\&CenterDot;\&CenterDot;& {\left\{{\mathrm{\&mu;}}_k\right\}}_{\mathrm{MN}}\end{array}\right]\left(\begin{array}{c}i=\mathrm{1,2},...,N;\\ j=\mathrm{1,2},...,M;k=\mathrm{1,2},...\end{array}\right)$

Each element all is the set of a degree of membership value in this fuzzy characteristics plane, and this shows that under the influence of randomness the degree of membership that each pixel is under the jurisdiction of an object is not a definite value, and shows as a kind of probability distribution.

Edge extracting based on maximum fuzzy entropy

1. utilize maximum fuzzy entropy self-adaptation to carry out the edge transition district and handle, carry out strong and weak marginal belt and divide.The zone of transition image is carried out the gradient computing, generate the zone of transition gradient image, the fuzzy collection of dividing of structure obtains fuzzy entropy of a partition, seeks optimum degree of membership, obtains optimum fuzzy characteristics plane.

Adaptable search blurs threshold value, according to the zone that the fuzzy division of band border cloud covers that is subordinate to of edge image; Utilize the fuzzy characteristics matrix to carry out the calculating of image blurring division entropy, the fuzzy entropy of dividing of utilization is sought optimum fuzzy threshold value and is carried out the edge division.

Carry out the gradient computing to extract size by the cloud computing for the zone of transition image I of M * N, total L level gray scale, generate zone of transition gradient image G, its histogram is h _r, r=1,2 ..., L-1.Suppose that this image is divided into strong marginal belt And transitional zone Two zones make { μ _k, k=1,2 ..., n is that each pixel is divided among the gradient image G

In probability, make 1-{ μ _kBe divided into for each pixel

In probability.The fuzzy collection row Q that divides of structure _i=g (i, j)=r}, r=0,1 ..., L-1, wherein (i j) is (i, the pixel value of j) locating among the gradient image G to g.Obvious Q={Q ₀, Q ₂..., Q _L-1It is exactly a kind of fuzzy division to G.By fuzzy conditional entropy of dividing as can be known, given

The fuzzy condition of dividing Q of Shi Ziran, the fuzzy characteristics matrix is:

$H\left(Q\right|\tilde{R}e)=-\underset{r=0}{\overset{L-1}{\mathrm{\&Sigma;}}}\frac{p\left(Q_r\tilde{R}e\right)}{p\left(\tilde{R}e\right)}\log \frac{p\left(Q_r\tilde{R}e\right)}{p\left(\widetilde{\mathrm{Re}}\right)}=-\underset{r=0}{\overset{L-1}{\mathrm{\&Sigma;}}}\frac{{{\mathrm{\&mu;}}_{k}h}_r}{p\left(\tilde{R}e\right)}\log \frac{{{\mathrm{\&mu;}}_{k}h}_r}{p\left(\tilde{R}e\right)}$

$p\left(\tilde{R}e\right)=\underset{r=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_k{h}_r$

In like manner, given The fuzzy conditional entropy of dividing Q of Shi Ziran, the fuzzy characteristics matrix:

$H\left(Q\right|\tilde{R}s)=-\underset{r=0}{\overset{L-1}{\mathrm{\&Sigma;}}}\frac{p\left(Q_r\tilde{R}s\right)}{p\left(\tilde{R}s\right)}\log \frac{p\left(Q_r\tilde{R}s\right)}{p\left(\widetilde{\mathrm{Rs}}\right)}=-\underset{r=0}{\overset{L-1}{\mathrm{\&Sigma;}}}\frac{(1-{\mathrm{\&mu;}}_k)h_r}{p\left(\tilde{R}s\right)}\log \frac{(1-{\mathrm{\&mu;}}_k)h_r}{p\left(\tilde{R}s\right)}$

$p\left(\tilde{R}s\right)=\underset{r=0}{\overset{L-1}{\mathrm{\&Sigma;}}}(1-{\mathrm{\&mu;}}_k)h_r$

Can blur the entropy of dividing P thus:

$H\left(P\right)=H\left(Q\right|\tilde{R}e)+H\left(Q\right|\tilde{R}s)$

$\&ap;-\underset{r=0}{\overset{L-1}{\mathrm{\&Sigma;}}}[\frac{{\mathrm{\&mu;}}_k{h}_r}{p\left(\tilde{R}e\right)}\log \frac{{\mathrm{\&mu;}}_k{h}_r}{p\left(\tilde{R}e\right)}+\frac{(1-{\mathrm{\&mu;}}_k)h_r}{p\left(\tilde{R}s\right)}\log \frac{(1-{\mathrm{\&mu;}}_k)h_r}{p\left(\tilde{R}s\right)}]$

According to maximum fuzzy entropy principle, represent in order to obtain boundary curve best in the gradient image, need seek optimum degree of membership μ _k, provide maximum fuzzy entropy criterion here, promptly selected optimum degree of membership μ _kMust meet the following conditions:

$H\left({\mathrm{\&mu;}}_k\right)=\underset{r=\mathrm{0,1,2},...,L-1}{\max }\left[H\left({\mathrm{\&mu;}}_k\right)\right]$

Make so optimum degree of membership be

Then can obtain optimum fuzzy characteristics plane

${\tilde{X}}_{\mathrm{ij}}=\left[\begin{array}{cccc}{\widetilde{\mathrm{\&mu;}}}_{11}& {\widetilde{\mathrm{\&mu;}}}_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& {\widetilde{\mathrm{\&mu;}}}_{1N}\\ {\widetilde{\mathrm{\&mu;}}}_{21}& {\widetilde{\mathrm{\&mu;}}}_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& {\widetilde{\mathrm{\&mu;}}}_{2N}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ {\widetilde{\mathrm{\&mu;}}}_{M1}& {\widetilde{\mathrm{\&mu;}}}_{M2}& \&CenterDot;\&CenterDot;\&CenterDot;& {\widetilde{\mathrm{\&mu;}}}_{\mathrm{Mn}}\end{array}\right](i=\mathrm{1,2},...,N;j=\mathrm{1,2},...,M)$

Order

For each pixel is divided into

In probability, the order

For each pixel is divided into

In probability, utilize above-mentioned formula to calculate fuzzy entropy of a partition H, if H 〉=H _Max, H then _Max=H obtains optimum degree of membership

And the fuzzy threshold value of order $T={\widetilde{\mathrm{\&mu;}}}^{\&prime;},$ Obtain optimum fuzzy threshold value.

2. the edge extracting under the multiple-factor constraint condition.Obtain simultaneously under the situation of maximum value when certain pixel satisfies three information measures, be defined as edge pixel.

Utilize aforementioned calculation to obtain the optimal dividing threshold value and can carry out the division at strong and weak edge, establishing edge image is I _E, (i j) is pixel value to e, then has

$e(i,j)=\left\{\begin{array}{ccc}0& \mathrm{if}& {\widetilde{\mathrm{\&mu;}}}_{\mathrm{ij}}\&GreaterEqual;T\\ 255& \mathrm{if}& {\widetilde{\mathrm{\&mu;}}}_{\mathrm{ij}}<T\end{array}\right.$

Truly the extraction at edge also need be carried out under the constraint that structural integrity is estimated and the direction consistance is estimated.Structural information is estimated and has been portrayed the structural of edge pixel, can distinguish edge and noise effectively; Directivity information is estimated the correct trend that then can guarantee the edge, avoids the generation of pseudo-edge or burr.Have document on the basis of fuzzy entropy, to propose two kinds of metrics:

$M(i,j)=\underset{k}{\max }|E_{R_{k1}}-E_{R_{k2}}|,$ k＝1，2，…

Based on this, need follow following criterion: have only when certain pixel satisfies three information measures and obtain simultaneously under the situation of maximum value, promptly work as based on the extraction of the image border that retrains ${\widetilde{\mathrm{\&mu;}}}_{\mathrm{ij}}\&GreaterEqual;T,$ And C (i, j)=C _Max(i, j) and M (i, j)=M _Max(i in the time of j), just can be judged as edge pixel.

3. crack edge growth.According to edge trend, the character of the edge images such as distribution of arest neighbors marginal point on every side, by certain rule grown in the edge, obtain edge line continuously and clearly.

Nearly all edge detection method all can not detect fully continuously or the edge line of sealing, especially when detected object is the remote sensing images of complexity, more impossiblely obtains desirable effect.Though this algorithm has farthest utilized image information in testing process, but still edge that may occur rupturing or omission.Therefore, Image Edge-Detection is not an image segmentation process on the complete meaning.After detecting marginal point, need a subsequent processes, by certain rule grown in the edge, to obtain edge line continuously and clearly.

The growth at edge should fully take into account as edge trend, the character of the edge images such as distribution of arest neighbors marginal point on every side.Because the marginal point that proposes herein extraction is what to carry out under the constraint of three information measures, take into full account architectural feature, trend and the neighborhood information of marginal point are existing, thereby bigger edge fracture can not appear, also avoided the generation of " false edge " simultaneously; But the edge that produces under strict like this constraint then may produce tiny fracture just.Can adopt following growth rule to carry out marginal growth:

1) seek the initial edge growing point with the grid scan mode, and with its center as 3 * 3 windows;

2) with the pixel in the window as candidate point, arrange the positive left side and under be impossible direction of growth;

3) be that the center checks whether the pixel of its eight neighborhood satisfies following similar characteristic with the growing point: (i, a certain pixel is arranged in eight neighborhoods j), and (s t) satisfies above-mentioned condition, just they can be coupled together as if the window center pixel.

4) all edge pixels are carried out same judgement and processing, can obtain continuous boundary.

4. the edge is comprehensive.Adopt each component information of method synthesis outline map of matrix stack, obtain the marginal information of atural object in multi-spectral remote sensing image.

The edge comprehensively is primarily aimed at multispectral image.Because different atural object electromagnetic radiation performance differences, same object is also different in the electromagnetic radiation performance of different-waveband, the projecting degree difference of same atural object in different spectrum segment may occur, this has also caused, and cloud cluster quantity has certain difference in the cloud space of corresponding different-waveband.Like this, the level of detail of each outline map that extracts by the border cloud method is also inconsistent.In order to make full use of multi-spectral remote sensing image information, it is comprehensive to carry out the edge to the outline map of each component, thereby obtains being reflected in the marginal information of atural object in the multi-spectral remote sensing image.

This paper adopts each component information of method synthesis of matrix stack.If multi-spectral remote sensing image has m component after Feature Conversion, the edge extracting result of each component is respectively with matrix I _Ek, (k=1,2 ..., m) expression, matrix element value 1 expression edge, 0 expression background.With the edge matrix of a certain component wherein is the background matrix, by the add up edge extracting result of each component of pixel, if a certain pixel accumulation result is more than or equal to 1, make then that this matrix element is 1, otherwise, make then that this matrix element is 0, the traversal entire image, all processed until each pixel.By said method, guaranteed the principle of compositionality of " many choosing of choosing lacked ", keep the figure surface information to greatest extent, reduce loss.

Claims (10)

1, a kind of fuzzy edge detection method based on the object cloud is characterized in that, this method may further comprise the steps: the processing stage of (1) image denoising, the object cloud atlas is looked like to carry out the non-linear threshold noise reduction process; (2) image cloud nuclear extracts and merging phase, and based on gray feature formation object cloud, the cloud that utilizes the relaxative iteration method to generate uncertain cloud is examined the merging of racking of going forward side by side; (3) each object in the cloud image generates the cloud space stage, and the different object cloud atlas is looked like to carry out the cloud description, and the data of image space are mapped as cloud cluster by the one-to-many model in this space, realizes the mapping in image space and cloud space; (4) the adjacent object cloud is carried out logical operation and extracts the border transition district, obtain the numerical characteristic of reflection border cloud institute coverage, make up fuzzy characteristics plane, set up fuzzy matrix according to the fuzzy characteristics plane based on border cloud numerical characteristic; (5) carry out the edge transition district according to maximum fuzzy entropy principle self-adaptation and handle, calculate the degree of membership of each pixel according to border cloud numerical characteristic, the two-dimensional ensemble that all pixels that the border cloud is covered constitute is the border transition district; (6) grown in the edge and comprehensively, obtain edge line continuously and clearly.

2, fuzzy edge detection method according to claim 1, it is characterized in that described step (2) specifically comprises, estimates as consistance with gray-scale statistical characteristics, to having similar intensity profile, the distance of a plurality of " nuclears " merges less than the sub-cloud of threshold value.

3, fuzzy edge detection method according to claim 1, it is characterized in that, described step (3) further specifically comprises, provide the cloud expression of different object cloud atlas picture in the cloud space, foundation is based on the one dimension cloud spatial mappings model of pixel gray feature, the average of object cloud " real part " is as the expectation value of cloud, and the gray scale of each pixel is under the jurisdiction of the degree of membership of " real part " gray average in " imaginary part "; Foundation is based on the two-dimentional cloud spatial mappings model of image gradient feature on both direction, " real part " of the regional corresponding objects cloud that gradient is little, the zone that graded is violent, " imaginary part " of corresponding objects cloud, the local corresponding objects cloud edge of gradient maximum.

4, fuzzy edge detection method according to claim 1 is characterized in that, described step (4) comprises specifically that further the two-dimensional ensemble that all pixels that the border cloud is covered in the cloud space constitute is the border transition district; Calculate the degree of membership of each pixel according to the numerical characteristic of border cloud by the forward cloud generator, the set of degree of membership value is as the element in the fuzzy characteristics plane.

5, fuzzy edge detection method according to claim 1, it is characterized in that, described step (5) further specifically comprises, utilize the fuzzy characteristics matrix to carry out the calculating of image blurring division entropy, seek optimum degree of membership, obtain optimum fuzzy threshold value thus, according to the zone that the fuzzy division of band border cloud covers that is subordinate to of edge image.

6, fuzzy edge detection method according to claim 2 is characterized in that, in relaxative iteration process each time, the gray scale of each pixel in the image is weighted adjustment, and when the gray scale of pixel reaches threshold value termination of iterations.

7, according to claim 1 or 3 described fuzzy edge detection methods, it is characterized in that, the different object image is carried out in the cloud description, express point-like, wire and area feature with a cloud, line cloud and face cloud respectively.

8, according to claim 1 or 4 described fuzzy edge detection methods, it is characterized in that, each dimension of cloud is implemented " soft with " computing respectively obtain border cloud cluster and numerical characteristic thereof.

9, fuzzy edge detection method according to claim 5 is characterized in that, is divided into strong marginal belt with being with being subordinate to of edge image

With weak marginal belt

Two zones.

10, fuzzy edge detection method according to claim 5 is characterized in that, in the process of dividing cloud covered areas territory, border, when satisfied simultaneously three information measures of the pixel of object cloud are maximum value, is defined as edge pixel.

Images