CN108090913A - A kind of image, semantic dividing method based on object level Gauss-Markov random fields - Google Patents
A kind of image, semantic dividing method based on object level Gauss-Markov random fields Download PDFInfo
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Abstract
The present invention proposes a kind of image, semantic dividing method based on object level Gauss Markov random fields, and step is：Initialization over-segmentation is carried out to pixel-level image, obtains object level image and Region adjacency graph, and defines neighborhood system, observational characteristic field and dividing mark field respectively on Region adjacency graph；Mark Label Field and neighborhood system are split according to object level, Gauss Markov modelings are carried out to the feature in each region of observational characteristic field and its feature of neighborhood, construction is for the object level equation of linear regression in each region；Probabilistic Modeling is carried out to Characteristic Field and Label Field respectively, the Posterior distrbutionp of dividing mark field is obtained according to Bayes criterions, and final segmentation result is obtained according to maximum posteriori criterion.The present invention can be used under complicated semantic and high spatial resolution background in carrying out semantic segmentation system to image in bulk, compared to artificial detection, drastically increase work efficiency.
Description
Technical field
The present invention relates to image, semantic segmentation technical field more particularly to it is a kind of based on object level Gauss-Markov with
The image, semantic dividing method on airport.
Background technology
Image, semantic segmentation refers to the pixel in image being grouped according to semantic difference expressed in image, the mistake
Journey is independently carried out by machine.
With the continuous development of modern sensor manufacturing process and imaging technique, handled image spatial resolution is more next
It is higher, and the amount of images obtained is increased with exponential form, if using segmentation by hand, inefficiency.Pervious Pixel-level
Dividing method can not consider larger range of spatial information, cause the waste of bulk information.And the ground based on object level in recent years
Reason analytical technology becomes a kind of hot spot technology for extracting image information, it is applied in image, semantic segmentation, it can be considered that
Larger range of spatial information.But the interaction relationship between provincial characteristics is ignored, segmentation precision has much room for improvement.Cause
This had not only ensured making full use of for spatial information, it is necessary to a kind of image, semantic dividing method, but also it can be considered that between provincial characteristics
It interacts.
The content of the invention
Cannot be taken into account for conventional images semantic segmentation method make full use of ensure spatial information and consider provincial characteristics it
Between the technical issues of interacting, the present invention proposes a kind of image, semantic segmentation based on object level Gauss-Markov random fields
Method, had not only ensured making full use of for spatial information, but also it can be considered that interaction between provincial characteristics.
In order to achieve the above object, the technical proposal of the invention is realized in this way：One kind is based on object level Gauss-
The image, semantic dividing method of Markov random fields, which is characterized in that its step are as follows：
Step 1：Initialization over-segmentation is carried out to the pixel-level image of reading, obtains the object being made of overdivided region
Grade image and corresponding object level Region adjacency graph RAG define the neighborhood system N of the image according to Region adjacency graph RAGO, it is right
As grade observational characteristic field YOWith object level dividing mark field XO；
Step 2：According to object level dividing mark field XOWith neighborhood system NOTo observational characteristic field YOEach region ri's
Feature and its feature of neighborhood carry out Gauss-Markov modelings, and construction is for each region riObject level linear regression side
Journey, i=1 ..., l；
Step 3：Respectively to observational characteristic field YOWith dividing mark field XOProbabilistic Modeling is carried out, and is obtained according to Bayes criterions
To dividing mark field XOPosterior distrbutionp, update iterative segmentation with maximum posteriori criterion and thus solve final segmentation.
The specific implementation step of the step 1 is as follows：
1) definition of location index set and Pixel-level are carried out to the high spatial resolution triple channel image I (R, G, B) of input
Observational characteristic set defines, it is assumed that image I (R, G, B) resolution ratio is m × n, is obtained：Location index set S={ sxy=(x, y) |
1≤x≤m；1≤y≤n }, Pixel-level observational characteristic collectionWherein,Represent picture at the s of position
The observational characteristic value of vegetarian refreshments,The respectively value of R, G of image, B component, m are the length of image, and n is the width of image
Degree, (x, y) are the position coordinates of pixel in image；
2) over-segmentation processing is carried out to pixel-level image with mean-shift methods according to the minimum area of setting：It will figure
L minimum area is segmented into as s as I (R, G, B) is undueminRegion, each region assigns label, obtains labelling matrix Ls={ ls|
S ∈ S }, wherein, element ls∈{1,…,l},s∈S；Thus the location index set R={ r of object level image are obtained1,r2,…,
rl, wherein, region ri=s | ls=i }；
3) handled to obtain object level Region adjacency graph G=(R, E) according to over-segmentation, wherein, location index set R is object
Grade element, each element represent an overdivided region, E={ eij| 1≤i, j≤l } represent syntople, element eijRepresent area
Domain riIn with region rjAdjacent number of pixels, eij≠ 0 and if only if element RiAnd RjIt is adjacent；
4) object level observational characteristic field is defined on Region adjacency graph GAnd object
Grade segmentation Label FieldWherein,Represent region riObservational characteristic, | ri| represent region ri
Interior pixel number；XOIt is a random field,It is a stochastic variable,Wherein, K is segmentation class
Do not gather, k is previously given segmentation classification number；
5) object level neighborhood system is provided according to object level Region adjacency graph G=(R, E)：Its
In,
The step 2 is as follows：
1) it can obtain what each overdivided region was included by location index set R in Region adjacency graph G=(R, E)
Number of pixels is the area parameters of object level element, obtains area matrix RS={ RSi| 1≤i≤l }, wherein RSi=| ri|；
2) x is setOIt is object level dividing mark field XOOne realization, according to xOObtain characteristic mean of all categories and feature
Covariance matrix realizes that flow is：
(a) known object grade segmentation Label Field is embodied as xO, calculate the corresponding segmentation of each pixel in original image
Generic, i.e. Pixel-level dividing mark matrixWherein
(b) characteristic mean m={ m are calculated respectivelyi| 1≤i≤k } and Eigen Covariance matrix ∑={ ∑i|1≤i≤k}：
3) for each object level element ri, give its dividing mark and be embodied asAfterwards, equation of linear regression is constructed such as
Under：
Wherein, ei~N (0, ∑h) it is a white Gaussian noise.
The specific method of the step 3 is as follows：
2) for object level observational characteristic field YO, it is not that joint probability modeling is directly carried out to observational characteristic, but to every
One object level element riResidual error item in the object level equation of linear regression constructed carries out joint modeling, obtains Characteristic Field
Likelihood function, i.e.,：
2) object level dividing mark field XOProbabilistic Modeling is carried out, from Markov-Gibbs equivalences, object level segmentation
Label Field meets Gibbs distributions, and the prior distribution for obtaining Label Field is as follows：
Wherein, Z is normalization constant, U (xO) represent that segmentation field is embodied as xOWhen energy, K for segmentation category set, V2
() is group potential-energy function, is provided by Potts models, i.e.,：
3) Posterior distrbutionp that Label Field can be obtained by Bayes formula is：
So the optimum of dividing mark is asked, which to translate into, seeks dividing mark field XOThe maximized problem of Posterior distrbutionp,
I.e.：
By loop iteration, dividing mark is updated, finally obtains segmentation result.
The specific implementation process of the loop iteration is：
5) Pixel-level MRF methods are realized by classical ICM algorithms first, obtain the segmentation generic of each pixel,
That is Pixel-level segmentation field result：xP={ xs| s ∈ S }, and then the Object Segmentation Label Field for obtaining primary iteration is realizedWhereinMode is mode function；
6) realization walked by object level dividing mark field in tIt is corresponded to according to the following formula
The characteristic mean of each classificationAnd Eigen Covariance
7) each object level element r is calculated respectivelyiObject level equation of linear regression：
8) computing object and Characteristic Field probability and Label Field probability, and by the update dividing mark of object, be specially respectively：
Beneficial effects of the present invention：Provide the molding semantic segmentation method to high spatial resolution RGB image；It can use
In the semantic segmentation of batch processing high spatial resolution RGB image, segmentation efficiency far is horizontal higher than traditional-handwork segmentation, also compares
Existing major part object-oriented grade partitioning scheme is efficient；Fixed value is directly assigned for the parameter to be estimated in equation of linear regression
Letter is simple and efficient, and precision is high.
Description of the drawings
It in order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
There is attached drawing needed in technology description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention, for those of ordinary skill in the art, without creative efforts, can be with
Other attached drawings are obtained according to these attached drawings.
Fig. 1 is the flow chart of the present invention.
Fig. 2 is the flow chart that the present invention initializes.
Fig. 3 is the exemplary plot of initialization process of the present invention.
Fig. 4 is the flow chart of equation of linear regression of the present invention construction.
Fig. 5 is the flow chart of present invention joint modeling.
Fig. 6 is experiment simulation figure of the present invention.
Specific embodiment
Below in conjunction with the attached drawing in the embodiment of the present invention, the technical solution in the embodiment of the present invention is carried out clear, complete
Site preparation describes, it is clear that described embodiment is only part of the embodiment of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art are obtained every other under the premise of not making the creative labor
Embodiment belongs to the scope of protection of the invention.
As shown in Figure 1, a kind of image, semantic dividing method based on object level Gauss-Markov random fields, step is such as
Under：
Step 1：Initialization over-segmentation is carried out to the pixel-level image of reading, obtains the object being made of overdivided region
Grade image and corresponding object level Region adjacency graph RAG define the neighborhood system N of the image according to Region adjacency graph RAGO, it is right
As grade observational characteristic field YOWith object level dividing mark field XO。
In order to carry out object level graphical analysis, efficiency of algorithm is improved, it is necessary to initialization over-segmentation be carried out, to obtain region
Adjacent map RAG.Region adjacency graph RAG is that the spatial relationship between each overdivided region according to object level image obtains.
The method that image carries out initialization over-segmentation is the mean-shift methods of minimum area factor.According to pixel-level image feature,
Object level is obtained using the mean-shift methods for being related to minimum area parameter (contained pixel number i.e. in overdivided region)
Graphical representation finally acquires object level characteristics of image.As shown in Fig. 2, its specific implementation step is as follows：
1) definition of location index set and Pixel-level are carried out to the high spatial resolution triple channel image I (R, G, B) of input
Observational characteristic set defines, it is assumed that image I (R, G, B) resolution ratio is m × n, then can be respectively obtained：Location index set S
={ sxy=(x, y) | 1≤x≤m；1≤y≤n }, Pixel-level observational characteristic collectionWherein,
Represent the observational characteristic value of pixel at the s of position,The respectively value of R, G of image, B component, m are the length of image
Degree, n are the width of image, and (x, y) is the position coordinates of pixel in image.
2) over-segmentation processing is carried out to pixel-level image with mean-shift methods according to the minimum area of setting：It will figure
L minimum area is segmented into as s as I (R, G, B) is undueminRegion, each region assigns label, obtains labelling matrix Ls={ ls|
S ∈ S }, wherein, element ls∈{1,…,l},s∈S.Thus the location index set R={ r of object level image are obtained1,r2,…,
rl, wherein, region ri=s | ls=i }.After handling result gray processing as shown in Fig. 3 (a), the lines in figure are the knots of its segmentation
Fruit.
3) handled to obtain object level Region adjacency graph G=(R, E) according to over-segmentation.Wherein, location index set R is object
Grade element, each element represent an overdivided region.E={ eij| 1≤i, j≤l } represent syntople, element eijRepresent area
Domain riIn with region rjAdjacent number of pixels, eij≠ 0 and if only if element RiAnd RjIt is adjacent.
4) object level observational characteristic field is defined on Region adjacency graph GObject level
Dividing mark fieldWherein,Represent region riObservational characteristic, | ri| represent region riIt is interior
Pixel number.XOIt is a random field,It is a stochastic variable, represents overdivided region riSegmentation classification,Wherein K is segmentation category set, and k is previously given segmentation classification number.
5) object level neighborhood system is provided according to object level Region adjacency graph G=(R, E)：Its
In,A part in rectangle frame in Fig. 3 (a) is amplified to obtain Fig. 3 (b), in Fig. 3 (b)
Each area carries out neighbourhood signatures such as Fig. 3 (c).
Step 2：Each region rs of the mark Label Field XO and neighborhood system NO to observational characteristic field YO is split according to object leveli
Feature and its feature of neighborhood carry out Gauss-Markov modelings, construction is for each region riObject level linear regression
Equation, i=1 ..., l.
Object level equation of linear regression use object level element size and boundary length as equation of linear regression
Parameter, to each object level element build equation of linear regression, as shown in figure 4, being as follows：
1) it can obtain what each overdivided region was included by location index set R in Region adjacency graph G=(R, E)
It is considered as the area parameters of object level element by number of pixels, obtains area matrix RS={ RSi| 1≤i≤l }, wherein RSi=|
ri|。
2) x is assumedOIt is object level dividing mark field XOOne realization, according to xOObtain characteristic mean of all categories and spy
Covariance matrix is levied, realizes that flow is：
(a) known object grade segmentation Label Field is embodied as xO, calculate the corresponding segmentation of each pixel in original image
Generic, i.e. Pixel-level dividing mark matrixWherein
(b) characteristic mean m={ mi | 1≤i≤k } and Eigen Covariance matrix ∑={ ∑ are calculated respectivelyi|1≤i≤k}：
3) for each object level element ri, give its dividing mark and be embodied as xiAfter O, equation of linear regression is constructed
It is as follows：
Wherein, for the ease of calculating, it is assumed that ei~N (0, ∑h) it is a white Gaussian noise.
Step 3：Respectively to observational characteristic field YOWith dividing mark field XOProbabilistic Modeling is carried out, and is obtained according to Bayes criterions
To dividing mark field XOPosterior distrbutionp, update iterative segmentation with maximum posteriori criterion and thus solve final segmentation.
Probabilistic Modeling is included by the error term construction observational characteristic field Y in object level equation of linear regressionOMultivariate Normal
It is distributed and using Potts Construction of A Model segmentation mark Label Field XOGibbs distribution.Finally segmentation result is：It is distributed using Gibbs
Sampling update iterative segmentation, final output convergence solution.As shown in figure 5, concrete operations are as follows：
1) for object level observational characteristic field YO, it is not that joint probability modeling is directly carried out to observational characteristic, but to every
One object level element riResidual error item in the object level equation of linear regression constructed carries out joint modeling, obtains Characteristic Field
Likelihood function, i.e.,：
2) object level dividing mark field XOProbabilistic Modeling is carried out, since Label Field has geneva, by Markov-Gibbs
Equivalence understands that Label Field meets Gibbs distributions, and the prior distribution for obtaining Label Field is as follows：
Wherein, Z is normalization constant, U (xO) represent that segmentation field is embodied as xOWhen energy, V2() is group potential energy letter
Number, is provided, i.e., by Potts models：
3) Posterior distrbutionp that Label Field can be obtained by Bayes formula is：
So the optimum of dividing mark is asked, which to translate into, seeks dividing mark field XOThe maximized problem of Posterior distrbutionp,
I.e.：
By loop iteration, dividing mark is updated, finally obtains result.Specific loop iteration process is as follows：
1) Pixel-level MRF (Markov are realized by classical ICM (iteration condition model) algorithm first
Random field) method, obtain the segmentation generic of each pixel, i.e. Pixel-level segmentation field result：xP={ xs|s∈
S }, and then the Object Segmentation Label Field for obtaining primary iteration is realizedWherein
I.e. for overdivided region ri, dividing mark is the mode of its interior pixels point dividing mark.
2) realization walked by object level dividing mark field in tIt is corresponded to according to the following formula
The characteristic mean of each classificationAnd Eigen Covariance
3) each object level element r is calculated respectivelyiObject level equation of linear regression：
4) computing object and Characteristic Field probability and Label Field probability, and by the update dividing mark of object, be specially respectively：
The present invention operation platform be：Core [email protected], RAM：4G, 64 win10 systems, 2015a editions
matlab.(coloured image gray processing) shown in the coloured image of Aerial Images 1024_1 such as Fig. 6 (a1), true segmentation by hand
As shown in Fig. 6 (a2).To image 1024_1 ICM methods, make β=0.5, coloured image such as Fig. 6 of obtained segmentation result
(a3) shown in.To image 1024_1 GMRF methods, make β=0.5, coloured image such as Fig. 6 (a4) institute of obtained segmentation result
Show.It is three layers, β=0.5 with " Haar " wavelet decomposition to image 1024_1 MRMRF methods, the colour of obtained segmentation result
Shown in image such as Fig. 6 (a5).To image 1024_1 OMRF methods, and make s=256, β=0.5, obtained segmentation result
Shown in coloured image such as Fig. 6 (a6).To the image 1024_1 present invention (OGMRF-RC) methods, and make s=256, β=0.5,
Shown in the coloured image of obtained segmentation result such as Fig. 6 (a7).Shown in the coloured image of Aerial Images 1024_2 such as Fig. 6 (b1),
True segmentation by hand is as shown in Fig. 6 (b2).To image 1024_2 ICM methods, make β=0.3, the colour of obtained segmentation result
Shown in image such as Fig. 6 (b3).To image 1024_2 GMRF methods, make β=0.3, the coloured image of obtained segmentation result is such as
Shown in Fig. 6 (b4).It is three layers, β=0.3 with " Haar " wavelet decomposition to image 1024_2 MRMRF methods, obtained segmentation
As a result shown in coloured image such as Fig. 6 (b5).To image 1024_2 OMRF methods, and make s=144, β=0.3 obtains
Shown in the coloured image of segmentation result such as Fig. 6 (b6).To the image 1024_2 present invention (OGMRF-RC) methods, and make s=
144, β=0.3, shown in coloured image such as Fig. 6 (b7) of obtained segmentation result.Aerial Images 1024_1's and image 1024_2
The Kappa coefficients of segmentation result are as shown in table 1, and the overall accuracy OA of segmentation result is as shown in table 2.
The Kappa coefficients of 1 segmentation result of table
The overall accuracy (Overall Accuracy, OA) of 2 segmentation result of table
The segmentation precision of the present invention is best it can be seen from data in Fig. 6 and table 1-2.Aerial Images include more
Texture information, the spectrum value of the subobject in same class differs greatly, and different classes of subobject may have it is similar
Spectrum value.For example, in urban parts, roof and garden have a different spectral values, but the trees of urban parts and forest part
Spectral value be similar.For these reasons, three kinds of methods based on pixel have many mistake classification fine crushing.With based on picture
The method of element is compared, and overdivided region is considered as elementary cell by object-based method, therefore significantly optimizes segmentation precision.
OMRF methods are modeled property field using the probability distribution of the feature of object, and OGMRF-RC methods are then to utilize object level
The probability distribution of residual error item is modeled property field in equation of linear regression.OGMRF-RC methods the advantage of doing so is that, can
With reduce in iterative process it is generic between influence of the spectrum change for segmentation.For example, in the top half of Fig. 6 (a7),
Large-scale bare area and forest are accurately divided into idle part, rather than in Fig. 6 (a6) be divided into house part OMRF that
Sample.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
With within principle, any modifications, equivalent replacements and improvements are made should all be included in the protection scope of the present invention god.
Claims (5)
1. a kind of image, semantic dividing method based on object level Gauss-Markov random fields, which is characterized in that its step is such as
Under：
Step 1：Initialization over-segmentation is carried out to the pixel-level image of reading, obtains the object level figure being made of overdivided region
Picture and corresponding object level Region adjacency graph RAG define the neighborhood system N of the image according to Region adjacency graph RAGO, object level
Observational characteristic field YOWith object level dividing mark field XO；
Step 2：According to object level dividing mark field XOWith neighborhood system NOTo observational characteristic field YOEach region riFeature and
The feature of its neighborhood carries out Gauss-Markov modelings, and construction is for each region riObject level equation of linear regression, i=
1,…,l；
Step 3：Respectively to observational characteristic field YOWith dividing mark field XOProbabilistic Modeling is carried out, and is divided according to Bayes criterions
Cut Label Field XOPosterior distrbutionp, update iterative segmentation with maximum posteriori criterion and thus solve final segmentation.
2. the image, semantic dividing method according to claim 1 based on object level Gauss-Markov random fields, special
Sign is that the specific implementation step of the step 1 is as follows：
1) definition of location index set is carried out to the high spatial resolution triple channel image I (R, G, B) of input and Pixel-level is observed
Characteristic set defines, it is assumed that image I (R, G, B) resolution ratio is m × n, is obtained：Location index set S={ sxy=(x, y) | 1≤x
≤m；1≤y≤n }, Pixel-level observational characteristic collectionWherein,Represent pixel at the s of position
Observational characteristic value,The respectively value of R, G of image, B component, m are the length of image, and n is the width of image,
(x, y) is the position coordinates of pixel in image；
2) over-segmentation processing is carried out to pixel-level image with mean-shift methods according to the minimum area of setting：By image I
(R, G, B) is too segmented into l minimum area as sminRegion, each region assigns label, obtains labelling matrix Ls={ ls|s∈
S }, wherein, element ls∈{1,…,l},s∈S；Thus the location index set R={ r of object level image are obtained1,r2,…,
rl, wherein, region ri=s | ls=i }；
3) handled to obtain object level Region adjacency graph G=(R, E) according to over-segmentation, wherein, location index set R is object level member
Element, each element represent an overdivided region, E={ eij| 1≤i, j≤l } represent syntople, element eijRepresent region ri
In with region rjAdjacent number of pixels, eij≠ 0 and if only if element RiAnd RjIt is adjacent；
4) object level observational characteristic field is defined on Region adjacency graph GSplit with object level
Label FieldWherein,Represent region riObservational characteristic, | ri| represent region riInterior picture
Vegetarian refreshments number；XOIt is a random field,It is a stochastic variable,Wherein, K is segmentation classification collection
It closes, k is previously given segmentation classification number；
5) object level neighborhood system is provided according to object level Region adjacency graph G=(R, E)：Wherein,
3. the image, semantic dividing method according to claim 1 based on object level Gauss-Markov random fields, special
Sign is that the step 2 is as follows：
1) pixel that each overdivided region included can be obtained by location index set R in Region adjacency graph G=(R, E)
Number is the area parameters of object level element, obtains area matrix RS={ RSi| 1≤i≤l }, wherein RSi=| ri|；
2) x is setOIt is object level dividing mark field XOOne realization, according to xOObtain characteristic mean of all categories and feature association side
Poor matrix realizes that flow is：
(a) known object grade segmentation Label Field is embodied as xO, calculate class belonging to the corresponding segmentation of each pixel in original image
Not, i.e. Pixel-level dividing mark matrixWherein
(b) characteristic mean μ={ μ is calculated respectivelyi| 1≤i≤k } and Eigen Covariance matrix ∑={ ∑i|1≤i≤k}：
<mrow>
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<mi>&mu;</mi>
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</munder>
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</mfrac>
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<mn>1</mn>
<mo>&le;</mo>
<mi>h</mi>
<mo>&le;</mo>
<mi>k</mi>
<mo>,</mo>
</mrow>
<mrow>
<msub>
<mi>&Sigma;</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<munder>
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<mrow>
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<msubsup>
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<mi>i</mi>
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</msubsup>
<mo>=</mo>
<mi>h</mi>
</mrow>
</munder>
<munder>
<mi>&Sigma;</mi>
<mrow>
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<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
</mrow>
</munder>
<msup>
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<mi>&mu;</mi>
<mi>h</mi>
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</mrow>
<mi>T</mi>
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</mrow>
</mrow>
<mrow>
<munder>
<mi>&Sigma;</mi>
<mrow>
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<mi>i</mi>
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</msubsup>
<mo>=</mo>
<mi>h</mi>
</mrow>
</munder>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>s</mi>
<mo>&Element;</mo>
<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
</mrow>
</munder>
<mrow>
<mo>|</mo>
<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
</mrow>
</mrow>
</mfrac>
<mo>,</mo>
<mn>1</mn>
<mo>&le;</mo>
<mi>h</mi>
<mo>&le;</mo>
<mi>k</mi>
<mo>;</mo>
</mrow>
3) for each object level element ri, give its dividing mark and be embodied asAfterwards, it is as follows to construct equation of linear regression：
<mrow>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mi>O</mi>
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</msub>
<mo>=</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
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<mi>r</mi>
<mi>j</mi>
</msub>
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<msubsup>
<mi>N</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
</mrow>
</munder>
<msub>
<mi>&theta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mrow>
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<mi>j</mi>
<mi>O</mi>
</msubsup>
<mo>-</mo>
<msub>
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<mi>j</mi>
<mi>O</mi>
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</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>e</mi>
<mi>i</mi>
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</mrow>
<mrow>
<msub>
<mi>&theta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>e</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mrow>
<munder>
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</munder>
<msub>
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<mrow>
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</msup>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>&CenterDot;</mo>
<mfrac>
<mrow>
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<msub>
<mi>r</mi>
<mi>j</mi>
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<mrow>
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<mi>i</mi>
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</mrow>
</munder>
<mrow>
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<msub>
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<msup>
<mi>j</mi>
<mo>&prime;</mo>
</msup>
</msub>
<mo>|</mo>
</mrow>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
Wherein,It is a white Gaussian noise.
4. the image, semantic dividing method according to claim 1 based on object level Gauss-Markov random fields, special
Sign is that the specific method of the step 3 is as follows：
1) for object level observational characteristic field YO, it is not that joint probability modeling is directly carried out to observational characteristic, but it is right to each
As grade element riResidual error item in the object level equation of linear regression constructed carries out joint modeling, obtains the likelihood letter of Characteristic Field
Number, i.e.,：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>p</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>Y</mi>
<mi>O</mi>
</msup>
<mo>=</mo>
<msup>
<mi>y</mi>
<mi>O</mi>
</msup>
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<msup>
<mi>X</mi>
<mi>O</mi>
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<msup>
<mi>x</mi>
<mi>O</mi>
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</mrow>
<mo>=</mo>
<munderover>
<mi>&Pi;</mi>
<mrow>
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</mrow>
<mi>l</mi>
</munderover>
<mi>p</mi>
<mrow>
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<msubsup>
<mi>Y</mi>
<mi>i</mi>
<mi>O</mi>
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<msubsup>
<mi>X</mi>
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<mi>j</mi>
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</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<munderover>
<mi>&Pi;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>l</mi>
</munderover>
<mfrac>
<mn>1</mn>
<mrow>
<msup>
<mrow>
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<mn>2</mn>
<mi>&pi;</mi>
<mo>)</mo>
</mrow>
<mrow>
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<mo>/</mo>
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</mrow>
</msup>
<msup>
<mrow>
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<msub>
<mi>&Sigma;</mi>
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</msub>
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</mrow>
<mrow>
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<mn>2</mn>
</mrow>
</msup>
</mrow>
</mfrac>
<mi>exp</mi>
<mo>&lsqb;</mo>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
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<msub>
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<munder>
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</mrow>
</munder>
<msub>
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<mrow>
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<mi>j</mi>
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</mrow>
</munder>
<msub>
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</mrow>
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</mrow>
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</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<munderover>
<mi>&Pi;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>l</mi>
</munderover>
<mfrac>
<mn>1</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mi>&pi;</mi>
<mo>)</mo>
</mrow>
<mrow>
<mn>3</mn>
<mo>/</mo>
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</mrow>
</msup>
<msup>
<mrow>
<mo>|</mo>
<msub>
<mi>&Sigma;</mi>
<msubsup>
<mi>x</mi>
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<mi>O</mi>
</msubsup>
</msub>
<mo>|</mo>
</mrow>
<mrow>
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</mrow>
</msup>
</mrow>
</mfrac>
<mi>exp</mi>
<mo>&lsqb;</mo>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msub>
<mi>e</mi>
<mi>i</mi>
</msub>
<msup>
<mrow>
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<msub>
<mi>&Sigma;</mi>
<msubsup>
<mi>x</mi>
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</mrow>
<mrow>
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</mrow>
</msup>
<msubsup>
<mi>e</mi>
<mi>i</mi>
<mi>T</mi>
</msubsup>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
2) object level dividing mark field XOProbabilistic Modeling is carried out, from Markov-Gibbs equivalences, object level dividing mark field
Meet Gibbs distributions, the prior distribution for obtaining Label Field is as follows：
<mrow>
<mi>P</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>X</mi>
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</mrow>
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<mi>Z</mi>
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<munder>
<mo>&Sigma;</mo>
<mrow>
<msub>
<mi>r</mi>
<mi>i</mi>
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<mo>&Element;</mo>
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<mi>j</mi>
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<msubsup>
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</munder>
<msub>
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<mo>&Element;</mo>
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</mrow>
</mrow>
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</mrow>
<mo>&ap;</mo>
<munderover>
<mi>&Pi;</mi>
<mrow>
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<mn>1</mn>
</mrow>
<mi>l</mi>
</munderover>
<mi>P</mi>
<mrow>
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<msub>
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</mrow>
</mrow>
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mi>P</mi>
<mrow>
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<mrow>
<munder>
<mi>&Sigma;</mi>
<mrow>
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<mi>K</mi>
</mrow>
</munder>
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<mrow>
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</mrow>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
<mo>:</mo>
<msub>
<mi>r</mi>
<mi>j</mi>
</msub>
<mo>&Element;</mo>
<msubsup>
<mi>N</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
</mrow>
</munder>
<msub>
<mi>V</mi>
<mn>2</mn>
</msub>
<mo>(</mo>
<mrow>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>x</mi>
<mi>j</mi>
<mi>O</mi>
</msubsup>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<munder>
<mi>&Sigma;</mi>
<mrow>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>&Element;</mo>
<mi>K</mi>
</mrow>
</munder>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
<mo>:</mo>
<msub>
<mi>r</mi>
<mi>j</mi>
</msub>
<mo>&Element;</mo>
<msubsup>
<mi>N</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
</mrow>
</munder>
<msub>
<mi>V</mi>
<mn>2</mn>
</msub>
<mo>(</mo>
<mrow>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>x</mi>
<mi>j</mi>
<mi>O</mi>
</msubsup>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>;</mo>
</mrow>
Wherein, Z is normalization constant, U (xO) represent that segmentation field is embodied as xOWhen energy, K for segmentation category set, V2(·)
For group potential-energy function, provided by Potts models, i.e.,：
<mrow>
<msub>
<mi>V</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>x</mi>
<mi>j</mi>
<mi>O</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>&beta;</mi>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>&NotEqual;</mo>
<msubsup>
<mi>x</mi>
<mi>j</mi>
<mi>O</mi>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>0</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>x</mi>
<mi>j</mi>
<mi>O</mi>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<mi>i</mi>
<mo>&NotEqual;</mo>
<mi>j</mi>
<mo>;</mo>
</mrow>
3) Posterior distrbutionp that Label Field can be obtained by Bayes formula is：
<mrow>
<mi>P</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>X</mi>
<mi>O</mi>
</msup>
<mo>=</mo>
<msup>
<mi>x</mi>
<mi>O</mi>
</msup>
<mo>|</mo>
<msup>
<mi>Y</mi>
<mi>O</mi>
</msup>
<mo>=</mo>
<msup>
<mi>y</mi>
<mi>O</mi>
</msup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>P</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>Y</mi>
<mi>O</mi>
</msup>
<mo>=</mo>
<msup>
<mi>y</mi>
<mi>O</mi>
</msup>
<mo>|</mo>
<msup>
<mi>X</mi>
<mi>O</mi>
</msup>
<mo>=</mo>
<msup>
<mi>x</mi>
<mi>O</mi>
</msup>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mi>P</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>X</mi>
<mi>O</mi>
</msup>
<mo>=</mo>
<msup>
<mi>x</mi>
<mi>O</mi>
</msup>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>P</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>Y</mi>
<mi>O</mi>
</msup>
<mo>=</mo>
<msup>
<mi>y</mi>
<mi>O</mi>
</msup>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
So the optimum of dividing mark is asked, which to translate into, seeks dividing mark field XOThe maximized problem of Posterior distrbutionp, i.e.,：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mi>O</mi>
</msup>
<mo>=</mo>
<munder>
<mrow>
<mi>arg</mi>
<mi>max</mi>
</mrow>
<msup>
<mi>x</mi>
<mi>O</mi>
</msup>
</munder>
<mi>P</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>X</mi>
<mi>O</mi>
</msup>
<mo>=</mo>
<msup>
<mi>x</mi>
<mi>O</mi>
</msup>
<mo>|</mo>
<msup>
<mi>Y</mi>
<mi>O</mi>
</msup>
<mo>=</mo>
<msup>
<mi>y</mi>
<mi>O</mi>
</msup>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<munder>
<mrow>
<mi>arg</mi>
<mi>max</mi>
</mrow>
<msup>
<mi>x</mi>
<mi>O</mi>
</msup>
</munder>
<mi>P</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>Y</mi>
<mi>O</mi>
</msup>
<mo>=</mo>
<msup>
<mi>y</mi>
<mi>O</mi>
</msup>
<mo>|</mo>
<msup>
<mi>X</mi>
<mi>O</mi>
</msup>
<mo>=</mo>
<msup>
<mi>x</mi>
<mi>O</mi>
</msup>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mi>P</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>X</mi>
<mi>O</mi>
</msup>
<mo>=</mo>
<msup>
<mi>x</mi>
<mi>O</mi>
</msup>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
By loop iteration, dividing mark is updated, finally obtains segmentation result.
5. the image, semantic dividing method according to claim 4 based on object level Gauss-Markov random fields, special
Sign is that the specific implementation process of the loop iteration is：
1) Pixel-level MRF methods are realized by classical ICM algorithms first, obtains the segmentation generic of each pixel, i.e. picture
Plain grade splits field result：xP={ xs| s ∈ S }, and then the Object Segmentation Label Field for obtaining primary iteration is realizedWhereinMode is mode function；
2) realization walked by object level dividing mark field in tIt obtains according to the following formula corresponding each
The characteristic mean of classificationAnd Eigen Covariance
<mrow>
<msubsup>
<mi>&mu;</mi>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>=</mo>
<mfrac>
<mrow>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>:</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>O</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mo>=</mo>
<mi>h</mi>
</mrow>
</munder>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>s</mi>
<mo>&Element;</mo>
<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
</mrow>
</munder>
<msubsup>
<mi>y</mi>
<mi>s</mi>
<mi>P</mi>
</msubsup>
</mrow>
<mrow>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>:</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>O</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mo>=</mo>
<mi>h</mi>
</mrow>
</munder>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>s</mi>
<mo>&Element;</mo>
<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
</mrow>
</munder>
<mrow>
<mo>|</mo>
<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
</mrow>
</mrow>
</mfrac>
<mo>,</mo>
</mrow>
<mrow>
<msubsup>
<mi>&Sigma;</mi>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>=</mo>
<mfrac>
<mrow>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>:</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>O</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mo>=</mo>
<mi>h</mi>
</mrow>
</munder>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>s</mi>
<mo>&Element;</mo>
<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
</mrow>
</munder>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mi>s</mi>
<mi>P</mi>
</msubsup>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mi>h</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mi>s</mi>
<mi>P</mi>
</msubsup>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mi>h</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>:</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>O</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mo>=</mo>
<mi>h</mi>
</mrow>
</munder>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>s</mi>
<mo>&Element;</mo>
<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
</mrow>
</munder>
<mrow>
<mo>|</mo>
<msub>
<mi>r</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
</mrow>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
3) each object level element r is calculated respectivelyiObject level equation of linear regression：
<mrow>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>&mu;</mi>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>=</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mi>j</mi>
<mo>:</mo>
<msub>
<mi>r</mi>
<mi>j</mi>
</msub>
<mo>&Element;</mo>
<msubsup>
<mi>N</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
</mrow>
</munder>
<msub>
<mi>&theta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mi>j</mi>
<mi>O</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>&mu;</mi>
<msubsup>
<mi>x</mi>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msubsup>
<mi>e</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</msubsup>
</mrow>
4) computing object and Characteristic Field probability and Label Field probability, and by the update dividing mark of object, be specially respectively：
<mrow>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>O</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mo>=</mo>
<munder>
<mrow>
<mi>arg</mi>
<mi>max</mi>
</mrow>
<mrow>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>&Element;</mo>
<mi>K</mi>
</mrow>
</munder>
<mi>p</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>Y</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>|</mo>
<msubsup>
<mi>X</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>y</mi>
<mi>j</mi>
<mi>O</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>x</mi>
<mi>j</mi>
<mrow>
<mi>O</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mo>,</mo>
<msub>
<mi>r</mi>
<mi>j</mi>
</msub>
<mo>&Element;</mo>
<msubsup>
<mi>N</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mi>P</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>|</mo>
<msubsup>
<mi>x</mi>
<mi>j</mi>
<mrow>
<mi>O</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mo>,</mo>
<msub>
<mi>r</mi>
<mi>j</mi>
</msub>
<mo>&Element;</mo>
<msubsup>
<mi>N</mi>
<mi>i</mi>
<mi>O</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
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