CN108932520A - In conjunction with the SAR image water body probability drafting method of prior probably estimation - Google Patents
In conjunction with the SAR image water body probability drafting method of prior probably estimation Download PDFInfo
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Abstract
The invention discloses a kind of SAR image water body probability drafting methods of combination prior probably estimation, include the following steps：Step 1, SAR image picture element backscattering coefficient statistical distribution model hypothesis is established；Step 2, estimation water body is distributed prior probability；Step 3, according to survey region image backscattering coefficient σ0Estimate distribution parameter；Step 4, the conditional probability that the pixel belongs to water body is calculated.The present invention does Gauss distributional assumption to survey region image picture element backscattering coefficient using Bayesian inference, water body is done to pixel later in conjunction with k-means clustering algorithm, non-water body two is classified, calculate estimated value of the survey region water body pixel scale as water body distribution prior probability, finally combine the prior probably estimation value that backscattering coefficient theoretical probability density function is superimposed upon on statistical distribution histogram, model parameter estimation is completed using nonlinear least square fitting, obtains the probability that each pixel of survey region image belongs to water body.
Description
Technical field
The present invention relates to water body Remotely sensed acquisition technology more particularly to a kind of SAR image water bodys of combination prior probably estimation
Probability drafting method.
Background technique
Remote sensing image Clean water withdraw is a typical case of the remote sensing in water conservancy industry.SAR(synthetic
Aperture radar, synthetic aperture radar) data are round-the-clock with its, round-the-clock imaging characteristics, and it is suitable for flood damage and believes
The extraction and monitoring of breath play an important role in hydrographic remote sensing field.The process of Clean water withdraw, which can be attributed to, makees atural object
The process divided is made in classification to image.Classical remote sensing image Clean water withdraw method includes Threshold segmentation, in conjunction with manifold
Classifier segmentation, the segmentation based on Level Set Theory, image segmentation based on energy function etc..When survey region environment is complicated
When, usually occur during Clean water withdraw accidentally mentioning, the false-alarms phenomenon such as missing inspection, causes Clean water withdraw result precision not high.This ring
Border complexity bring precision problem is originated from the uncertainty of pixel classification to a certain extent.According to certain attributes to pixel
When classification, it is understood that there may be certain pixel mistakes similar to water body pixel attribute but actually not water body are divided into showing for water body
As so that there is uncertainty in pixel classification results.In addition, when the resolution ratio of data is not high, certain pixel reflections in image
Actual area may contain a variety of atural objects simultaneously, uncertainty is equally existed in classification.It can be seen that two-value water body
The Clean water withdraw result of distribution schema is unable to fully reflect this uncertainty.
Different from traditional image segmentation thinking, the drawing of water body distribution probability[9]Based on Bayesian inference, according to SAR shadow
As backscattering coefficient value calculates the probability distribution graph of water body.Its maximum feature is that every bit value range is not in result figure
It is discrete { 0,1 } set again, but continuous [0,1] section, the value indicate that the point belongs to the probability of water body.With conventional water body
The result that extracting method obtains two-value water body distribution diagram form is different, what water body distribution probability drafting method obtained be information content more
Probability graph abundant can sufficiently reflect that the classification of water body pixel is existing uncertain in SAR image.
Prior probability is a parameter important in body distribution probability drafting algorithm.However, not depending on except image
In the case where other auxiliary informations, prior probability is simply set to 0.5 default value by existing probability drafting method selection, this
The atural object backscattering coefficient statistical model that estimation can be made to obtain is not accurate enough, reduces the precision of probability charting results.Therefore exist
It is a kind of feasible thinking for improving cartographic accuracy that water body distribution prior probably estimation step is introduced in water body probability drawing operation.
Summary of the invention
The technical problem to be solved in the present invention is that for the defects in the prior art, a kind of combination prior probability is provided and is estimated
The SAR image water body probability drafting method of meter.
The technical solution adopted by the present invention to solve the technical problems is：A kind of SAR image of combination prior probably estimation
Water body probability drafting method, includes the following steps：
Step 1, SAR image picture element backscattering coefficient statistical distribution model is established it is assumed that specific as follows：
1.1) by the backscattering coefficient σ of all pixels of survey region image0The sample set of composition as water body W with
Non- water bodyTwo-part non-friendship union, wherein water body W and non-water bodyTwo categories are used to describe the state of some pixel,
Backscattering coefficient σ0For describing the scattering signatures of some pixel；Remember the backscattering coefficient distribution probability density of water body pixel
Function is p (σ0| W), the backscattering coefficient distribution probability density function of non-aqueous body image member isSurvey region is backward
The probability density function of scattering coefficient limit distribution is p (σ0), then have：
In formula, p (W) withWater body and non-aqueous body image member proportion are respectively indicated,
1.2) to the σ of water body, two class pixel of non-water body0Make Gauss distributional assumption, that is, assumes Wherein (μW,sW) it is water body pixel σ0's
Mean value, standard deviation；For non-aqueous body image member σ0Mean value, standard deviation；
Step 2, estimation water body distribution prior probability p (W)：With σ0Be characterized, using k-means clustering algorithm to research area
Domain image picture element carries out clustering, calculates low σ0Pixel sum ratio shared by cluster pixel is distributed prior probability p (W) as water body
Estimated value；
Step 3, according to survey region image backscattering coefficient σ0Estimate distribution parameter
Step 4, according to pixel σ0Value and Bayesian formula p (W | σ0)=p (W) p (σ0|W)/p(σ0), calculate the pixel category
In water body conditional probability p (W | σ0)；By distribution parameterSubstitution model p (W | σ0)=p (W) p (σ0|
W)/p(σ0) one has just been obtained from pixel σ0Be worth the pixel belong to water body conditional probability p (W | σ0) value mapping.It will mapping
The probability that each pixel in the available region of entire survey region belongs to water body is acted on, that is, completes the water body in the region
Distribution probability drawing.
According to the above scheme, the step 3) is specific as follows：The σ analyzed from image0Statistical distribution histogram h (σ0),
The σ established in step 1) by model hypothesis0Marginal distribution p (σ0), the estimated value of p (W) has been obtained in step 2, because hereafter
Continue directly by p (σ0) be added to h (σ0) on do curve matching, can estimate unknown distribution parameter in model
According to the above scheme, the step 3) is specific as follows：
3.1) survey region image backscattering coefficient statistical distribution histogram h (σ is calculated0)：What histogram calculation needed
Parameter is the width of each of which band, referred to as bandwidth, its calculation formula is：Wherein n is statistics
Number of samples, IQR are the interquartile range of sample；
3.2)h(σ0) superposition theory probability density function p (σ0)：Histogram h (σ0) value be pixel number, probability is close
Spend function p (σ0) value is probability value, the two is needed before curve matching by overlap-add operation, and specific method is first to p (σ0) multiply
With coefficient A, then with Ap (σ0) to h (σ0) curve matching is done, wherein A indicates the area (bandwidth × height) of histogram；
3.3) nonlinear fitting：Using Levenberg-Marquardt algorithm to p (σ0) and h (σ0) carry out non-linear minimum
Two multiply fitting, iterate to calculate distribution parameter.
When iteration initialization, at the beginning of using water body obtained in sorting procedure, non-water body sample average and standard deviation as algorithm
Value.
According to the above scheme, in the step 1) survey region image picture element backscattering coefficient σ0By to original SAR
Image does radiation calibration and filtering obtains.
The beneficial effect comprise that：
1, the present invention first estimates distribution parameter with cluster estimation prior probability, again with nonlinear fitting, and that estimates makes p
(σ0) more it is bonded h (σ0), i.e., it can more be bonded σ0The actual count rule of distribution, obtains higher probability cartographic accuracy.
2, when estimating the setting of model parameter initialization value, the present invention uses cluster result data initialization model parameter,
It is more efficient, at the same also avoid because initial value be arranged it is improper due to the solution procedure that can not find optimal solution that is likely to occur in iteration time
Number is excessive, even can not find the case where locally optimal solution.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing：
Fig. 1 is Xianning Prefecture's image σ0Statistical distribution histogram；
Fig. 2 is embodiment σ0Image, (a), (b), (c) respectively correspond Hebei Luquan, Huanggang, three ground of Xianning；
Fig. 3 is flow diagram of the present invention；
Fig. 4 be in parametric estimation step of the embodiment of the present invention nonlinear fitting as a result, (a), (b), (c) respectively correspond river
Northern Luquan, Huanggang, three ground of Xianning；
Fig. 5 is water body of embodiment of the present invention distribution probability charting results, and (a), (b), (c) respectively correspond Hebei Luquan, lake
Northern Huang gang, three ground of Xianning；
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that described herein, specific examples are only used to explain the present invention, is not used to limit
The fixed present invention.
The present invention in SAR image water body probability drafting method by joined the distribution of k-means cluster estimation water body first
The step of testing probability improves probability drawing process, improves probability cartographic accuracy.The method of the present invention input is survey region
Image backscattering coefficient σ0, output is the region water body distribution probability figure.Therefore before starting invention process, it is first right to need
SAR image does the pretreatment operations such as radiation calibration and filtering.
It is specific as follows：A kind of SAR image water body probability drafting method of combination prior probably estimation, includes the following steps：
Step 1, SAR image picture element backscattering coefficient statistical distribution model is established it is assumed that specific as follows：
1.1) by doing radiation calibration to original SAR image and filtering the back scattering system of acquisition survey region image picture element
Number σ0, by the backscattering coefficient σ of all pixels of survey region image0The sample set of composition is as water body W and non-water body
Two-part non-friendship union, wherein water body W and non-water bodyTwo categories are used to describe the state of some pixel, back scattering system
Number σ0For describing the scattering signatures of some pixel；The backscattering coefficient distribution probability density function for remembering water body pixel is p (σ0|
W), the backscattering coefficient distribution probability density function of non-aqueous body image member isSurvey region backscattering coefficient side
The probability density function of border distribution is p (σ0), then have：
In formula, p (W) withWater body and non-aqueous body image member proportion are respectively indicated,
1.2) to the σ of water body, two class pixel of non-water body0Make Gauss distributional assumption, that is, assumes Wherein (μW,sW) it is water body pixel σ0's
Mean value, standard deviation；For non-aqueous body image member σ0Mean value, standard deviation；
Step 2, estimation water body distribution prior probability p (W)：With σ0Be characterized, using k-means clustering algorithm to research area
Domain image picture element carries out clustering, calculates low σ0Pixel sum ratio shared by cluster pixel is distributed prior probability p (W) as water body
Estimated value；
Step 3, according to survey region image backscattering coefficient σ0Estimate distribution parameter
Step 3 is specific as follows：The σ analyzed from image0Statistical distribution histogram h (σ0), pass through mould in step 1)
Type assumes the σ established0Marginal distribution p (σ0), the estimated value of p (W) has been obtained in step 2, therefore subsequent directly by p (σ0)
Be added to h (σ0) on do curve matching, can estimate unknown distribution parameter in model
3.1) survey region image backscattering coefficient statistical distribution histogram h (σ is calculated0)：What histogram calculation needed
Parameter is the width of each of which band, referred to as bandwidth, its calculation formula is：Wherein n is statistics
Number of samples, IQR are the interquartile range of sample；
3.2)h(σ0) superposition theory probability density function p (σ0)：Histogram h (σ0) value be pixel number, probability is close
Spend function p (σ0) value is probability value, the two is needed before curve matching by overlap-add operation, and specific method is first to p (σ0) multiply
With coefficient A, then with Ap (σ0) to h (σ0) curve matching is done, wherein A indicates the area (bandwidth × height) of histogram；
3.3) nonlinear fitting：Using Levenberg-Marquardt algorithm to p (σ0) and h (σ0) carry out non-linear minimum
Two multiply fitting, iterate to calculate distribution parameter.
When iteration initialization, at the beginning of using water body obtained in sorting procedure, non-water body sample average and standard deviation as algorithm
Value
Step 4, according to pixel σ0Value and Bayesian formula p (W | σ0)=p (W) p (σ0|W)/p(σ0), calculate the pixel category
In water body conditional probability p (W | σ0)；By distribution parameterSubstitution model p (W | σ0)=p (W) p (σ0|
W)/p(σ0) one has just been obtained from pixel σ0Be worth the pixel belong to water body conditional probability p (W | σ0) value mapping.It will mapping
The probability that each pixel in the available region of entire survey region belongs to water body is acted on, that is, completes the water body in the region
Distribution probability drawing.
The embodiment of the present invention has chosen No. three satellite images of high score on Hebei Luquan, Huanggang, three ground of Xianning as base
Notebook data, Fig. 2 are No. three images of case study region high score handled by radiation calibration.It is 3* that image, which have passed through window size,
3 Gamma filtering processing, resolution ratio include 3 meters, 8 meters, 10 meters, be related to the scattered small water-body such as paddy field, irrigation canals and ditches, river and
Large-scale beach, wetland etc. are difficult to the atural object distinguished with water body, can be used for examining the present invention in a variety of resolution ratio, complicated atural object
Under the conditions of effect.
Process of the embodiment of the present invention is as shown in figure 3, include the following steps：
Step 1 statisticallys analyze backscattering coefficient image.
By the backscattering coefficient σ of all pixels of survey region image0The set of value is denoted as A, and backscattering coefficient is by original
Beginning SAR image does radiation calibration and filtering gained.Calculate the statistical distribution histogram h (σ of sample set A0).Specifically, in order to
Inhibit the influence of noise, the element of preceding 1.5% and rear 1.5% is sorted by size in removal set A first.Then by set A's
Value range is equidistantly divided into a series of bands, counts the number of each value band section interior element.Wherein, band is divided
Width is referred to as bandwidth, its calculation formula is：Wherein n is number of samples, i.e. pixel number.IQR
For the interquartile range of sample.
Step 2 does k-means cluster to backscattering coefficient image.
The element in set A is pressed into σ using k-means algorithm0Value sub-clustering, that is, proceed as follows：
1, setting cluster centre number is k=2, i.e., A is divided to for two clusters；
2, each sample point in A is calculated to the distance of two cluster centres, and is divided at a distance of the nearest cluster in center；
3, the center for updating two clusters calculates the average value that its value is each cluster sample；
4,2,3 liang of steps are repeated, the threshold value for being less than setting until reaching maximum number of iterations or cluster centre more new change.
Water body due to its mirror-reflection phenomenon be rendered as in SAR image low backscattering coefficient value region, be different from it is big
The non-water body atural object in part, it can be considered that it is water body picture that set A, which is clustered the low backscattering coefficient cluster that algorithm partition obtains,
First cluster, another cluster are then non-water body pixel clusters.At this point, ratio, that is, water body of total pixel number shared by low backscattering coefficient cluster pixel
It is distributed the estimated value of prior probability p (W).In addition, calculating separately the mean value and standard deviation of two cluster samples
For subsequent operation.
Step 3, nonlinear fitting solve parameter.
With known histogram h (σ0) model of fit assume establish σ0Marginal distribution p (σ0), it proceeds as follows：
1, the midpoint x in each band section of histogram is takeniWith swath height (element number in the section) yi, obtain sample
Data (xi,yi)；
2、yiValue be pixel number, probability density function p (σ0) value is probability value, the two is before curve matching
Overlap-add operation need to be passed through.Specific method is first to p (σ0) multiplied by coefficient L, then with Lp (σ0) to (xi,yi) curve matching is done,
Middle L indicates the area (bandwidth × height) of histogram；
3, using Levenberg-Marquardt algorithm pair
Curve matching is done, estimates unknown parameterNoteFor wait estimate
Parameter is counted,σ0=xiFor a series of sample points, Y=(y1,…,yi,…,yn)
For observation vector.Concrete operations are：
3.1 take initial valueTermination control constant is ∈, other parameters λ0=10-3,v
=10, calculate ∈0=| | Y-f (c0)||；
3.2 calculate Jacobi matrix Jk, calculateConstruct increment normal equation
3.3 solution increment normal equations obtain δk：
(1) if | | x-f (pk+δk)||<∈k, then c is enabledk+1=ck+δkIf | | δk||<∈ stops iteration, exports result；It is no
Then enable λk+1=λ v, go to 3.2；
(2) if | | x-f (pk+δk)||≥∈k, then λ is enabledk+1=λ v solves normal equation again and obtains δk, return (1).
The result of embodiment nonlinear fitting is as shown in Figure 4.
Step 4 is by distribution parameterSubstitution model p (W | σ0), model is acted on into entire research area
Each pixel belongs to the probability of water body in the available region in domain.Result such as Fig. 5 institute of embodiment water body distribution probability drawing
Show.
It should be understood that for those of ordinary skills, it can be modified or changed according to the above description,
And all these modifications and variations should all belong to the protection domain of appended claims of the present invention.
Claims (4)
1. combining the SAR image water body probability drafting method of prior probably estimation, which is characterized in that include the following steps：
Step 1, SAR image picture element backscattering coefficient statistical distribution model is established it is assumed that specific as follows：
1.1) by the backscattering coefficient σ of all pixels of survey region image0The sample set of composition is as water body W and non-water bodyTwo-part non-friendship union, wherein water body W and non-water bodyTwo categories are used to describe the state of some pixel, backward to dissipate
Penetrate factor sigma0For describing the scattering signatures of some pixel；Note water body pixel backscattering coefficient distribution probability density function be
p(σ0| W), the backscattering coefficient distribution probability density function of non-aqueous body image member isSurvey region back scattering system
The probability density function of number limit distribution is p (σ0), then have：
In formula, p (W) withWater body and non-aqueous body image member proportion are respectively indicated,
1.2) to the σ of water body, two class pixel of non-water body0Make Gauss distributional assumption, that is, assumes Wherein (μW,sW) it is water body pixel σ0's
Mean value, standard deviation；For non-aqueous body image member σ0Mean value, standard deviation；
Step 2, estimation water body distribution prior probability p (W)：With σ0Be characterized, using k-means clustering algorithm to survey region shadow
As pixel progress clustering, low σ is calculated0Pixel sum ratio shared by cluster pixel is estimated as water body distribution prior probability p (W)
Evaluation；
Step 3, according to survey region image backscattering coefficient σ0Estimate distribution parameter
Step 4, according to pixel σ0Value and Bayesian formula p (W | σ0)=p (W) p (σ0|W)/p(σ0), it calculates the pixel and belongs to water body
Conditional probability p (W | σ0)；By distribution parameterSubstitution model p (W | σ0)=p (W) p (σ0|W)/p(σ0)
Just one has been obtained from pixel σ0Be worth the pixel belong to water body conditional probability p (W | σ0) value mapping.By Mappings in whole
Each pixel belongs to the probability of water body in the available region of a survey region, that is, completes the water body distribution probability in the region
Drawing.
2. the SAR image water body probability drafting method of combination prior probably estimation according to claim 1, feature exist
In the step 3) is specific as follows：The σ analyzed from image0Statistical distribution histogram h (σ0), pass through model in step 1)
Assuming that the σ established0Marginal distribution p (σ0), the estimated value of p (W) has been obtained in step 2, therefore subsequent directly by p (σ0) folded
It is added to h (σ0) on do curve matching, can estimate unknown distribution parameter in model
3. the SAR image water body probability drafting method of combination prior probably estimation according to claim 1, feature exist
In the step 3) is specific as follows：
3.1) survey region image backscattering coefficient statistical distribution histogram h (σ is calculated0)：Histogram calculation need parameter be
The width of each of which band, referred to as bandwidth, its calculation formula is：Wherein n is statistical sample
Number, IQR are the interquartile range of sample；
3.2)h(σ0) superposition theory probability density function p (σ0)：Histogram h (σ0) value be pixel number, probability density letter
Number p (σ0) value is probability value, the two is needed before curve matching by overlap-add operation, and specific method is first to p (σ0) multiplied by being
Number A, then with Ap (σ0) to h (σ0) curve matching is done, wherein A indicates the area of histogram；
3.3) nonlinear fitting：Using Levenberg-Marquardt algorithm to p (σ0) and h (σ0) carry out non-linear least square
Fitting iterates to calculate distribution parameter.
4. the SAR image water body probability drafting method of combination prior probably estimation according to claim 1, feature exist
In the backscattering coefficient σ of survey region image picture element in the step 1)0By to original SAR image do radiation calibration and
Filtering obtains.
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