CN104700115B - The detection method of crater during Mars probes soft landing based on sparse lifting integrated classifier - Google Patents
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Abstract
The detection method of crater during a kind of Mars probes soft landing based on sparse lifting integrated classifier of the present invention, it has four big steps：Step 1. determines candidate's crater；Step 2. candidate's crater Texture Feature Extraction；Step 3. carries out feature selecting to the textural characteristics of extraction；Step 4. is combined Boost algorithms with sparse Density Estimator algorithm RSDE WL1, devises sparse lifting integrated classifier, to realize the quick detection to the crater based on image.The advantages of present invention mainly utilizes designed sparse lifting integrated classifier to have sparse solution and reduce computation complexity, after crater textural characteristics based on image are carried out with feature extraction and selection, the classification to crater and non-crater is realized, to reach the quick detection of crater.Its degree of accuracy of classifying can reach approximately 85% and more than, during the Mars probes soft landing to reality the detection of crater there is certain reference value.
Description
Technical field
The present invention relates to a kind of Mars probes soft landing based on integrated (SparseBoost) grader of sparse lifting
The detection method of crater in journey, and in particular to the pretreatment of crater, Texture Feature Extraction and selection in martian surface image
And the design of SparseBoost graders, belong to image procossing and area of pattern recognition.
Background technology
Detection of obstacles research main purpose is to detect barrier and true accordingly during Mars probes soft landing
Determine safe landing locations.Wherein crater is the most common geological form in the celestial body such as Mars surface, have distribution is wide, area is big,
The features such as characteristics of image is obvious, it is that one of main barrier for detecting is needed during detector soft landing.
Crater is considered as a pair of crescent moons with bright and dark area in the image of Mars probes collection.True
In fixed candidate's crater, after generally being extracted to the textural characteristics of candidate's crater, the characteristic of extraction has higher
Dimension, it is necessary to by suitable image feature selection algorithm, supervised learning sorting algorithm to the crater in candidate's crater
Classified with non-crater, to determine the particular location of crater in image.
SparseBoost sorting algorithms are a kind of sparse supervised learning sorting algorithms, with existing AdaBoost,
The advantage that Boost algorithms are compared is, in each iterative process, AdaBoost algorithms utilize whole feature sets, and
SparseBoost algorithms only select that an optimal feature；Simultaneously during Weak Classifier build, AdaBoost with
The equal trade-off decision tree of Boost algorithms builds grader, and whole sample sets are utilized in calculating process, and SparseBoost algorithms are adopted
Weak Classifier is built with sparse Density Estimator RSDE-WL1, is realized merely with a small amount of sample.Therefore SparseBoost algorithms tool
Have openness and the advantages of reduce computation complexity, SparseBoost sorting algorithms are applied to mars exploration in real process
The detection of crater during device soft landing, can effectively reduce computation complexity, realize the quick detection of crater.
The content of the invention
1st, goal of the invention
During a kind of Mars probes soft landing based on sparse lifting integrated classifier
The detection method of crater, this method are pre-processed to determine candidate's crater to the image of collection first, secondly from candidate
Abstract image textural characteristics in crater, and carry out feature selecting；Then by improved sparse Density Estimator algorithm (RSDE-
WL1) it is combined with lifting Ensemble Learning Algorithms (Boost), building sparse lifting integrated classifier, (SparseBoost classifies
Device), SparseBoost graders are finally applied to the detection of crater, realize quick detection, while obtain higher classification
The degree of accuracy.
2nd, technical scheme
To reach above-mentioned purpose, the present invention is specific to be situated between according to the step in the main frame figure (Fig. 1) of crater automatic detection
The technical scheme of this method that continues.
The present invention devises crater during a kind of Mars probes soft landing based on sparse lifting integrated classifier
Detection method, this method comprises the following steps：
Step 1. determines candidate's crater
Determine that the crucial of candidate's crater is considered as having bright and dark area one in the crater in image
To crescent moon, as shown in Figure 2.The shape of each pair crescent moon can by based on the shape detecting method of mathematical morphology from image really
It is fixed, crater of the crescent moon that can be matched as candidate.The building process of candidate's crater is as shown in figure 3, input is one complete
Color image, it comprises many bright and dark features regions.Bright and dark shape parallel processing, by using original image
The bright shape of processing, and dark shape is handled using inverted image.The target of this method, which is that elimination is all, to be designated as
The noise characteristic of crater, and only retain bright and dark features.Remaining bright and dark features region matches each other, by this
A little area markings are good, the candidate region as crater.
Step 2. candidate's crater Texture Feature Extraction
In order to represent single candidate's crater in terms of rectangular characteristic, we extract the side around candidate's crater first
Shape image block.In an experiment, in order to include the edge of crater around, we use twice of candidate's aerolite pit-size as screening
Cover area.The unknown textural characteristics of each candidate's crater are encoded using 9 kinds of different size of square coverings, as shown in Figure 4.
Therefore, the attribute for candidate's crater that an image is included can be described by thousands of textural characteristics.These are special
Sign is not separate, and these complete features compensate for by the single square limitation for covering the texture information obtained.
Step 3. carries out feature selecting to the textural characteristics of extraction
According to the candidate's crater textural characteristics tentatively extracted, due to the higher-dimension of characteristic, therefore by training sample
Before grader being inputted with test sample, it is necessary to carry out feature selecting.In the present invention, we are designed using step 4
SparseBoost algorithms carry out feature selecting, and the maximum difference of itself and AdaBoost algorithms is that the former is in iteration each time
During only choose an optimal feature, and the latter generally utilizes whole feature set.So greatly reduce training sample
Intrinsic dimensionality, effectively reduce the computation complexity of classifier training.
Step 4. is combined Boost algorithms with sparse Density Estimator algorithm RSDE-WL1, and it is integrated to devise sparse lifting
Grader, to realize the quick detection to the crater based on image.
According to selected candidate's crater textural characteristics, in order to distinguish wherein crater and non-crater, the present invention is set
Count a kind of supervised learning sorting algorithm --- SparseBoost algorithms.This method combination Boost algorithms and one kind are improved dilute
Density Estimator algorithm (RSDE-WL1) is dredged, while character subset is selected, some sparse Density Estimator devices is constructed and is used for
The design of corresponding base grader, by the weighted array of base grader, finally realizes integrated classifier.
Give n candidate's crater (x1,y1),(x2,y2),...,(xn,yn), wherein yi=0,1, i=1,2 ..., n points
Non- crater (c is not correspond to0) and crater (c1) example, n0And n1The number of non-crater and crater example is correspond to respectively
Mesh, n0+n1=n.Each candidate's crater can be expressed as a characteristic vector x=(f1,f2,...,fm)T, each of which
Feature fi, i=1 ..., m are produced by the square covering of a certain ad-hoc location on candidate's crater, and m is that the feature extracted is total
Number.A series of Weak Classifier h are built using SparseBoost algorithms (detailed process such as algorithm 1)t(x) it is, and integrated by weighting
Weak Classifier is combined by method establishes final strong classifier H (x):
Wherein T is iterations (T ＜ n), αtIt is the Weak Classifier h of studyt(x) weight.
, it is necessary to the step of realizing following three cores in each iterative process：Weak Classifier study, optimal characteristics choosing
Select and updated with next iteration process sample weights.Wherein, in Weak Classifier learning process, density estimation algorithm is collected to compression
(RSDE) penalty term is added, obtains improved sparse Density Estimator algorithm RSDE-WL1.Using RSDE-WL1 algorithms to each
Its probability density function of kind classification attributes estimation, classifies to the sample of input according to Bayes decision rule, obtains weak point
Class device.
(1) Weak Classifier learns
In the t times iterative process, for the single optimal characteristics f ∈ { f of selection1,f2,...,fmStructure weak typing
Device ht(x), can be realized by building Bayes classifier.Two classification on crater and the classification of non-crater is being discussed
Before problem, Bayes classifier is introduced first.Generally for Bayes's classification problem, expectation estimation gives input sample x lower classes
Other posterior probability density.In order to obtain a probability classification on density estimation, instructed first for each category attribute c
Practice a Multilayer networks deviceWherein x is the characteristic vector for representing single candidate's crater, β
For core weight vector, c is the category attribute of candidate's crater, c ∈ { c0,c1, c0Represent non-crater classification, c1Represent aerolite
Cheat classification.Then posterior probability is calculated with Bayes rule (2), final test sample is assigned to maximum a posteriori probability
Category attribute.
For two classification problem in the present invention, two conditional probability densities under given classification are estimated firstWithThe two density can be obtained by follow-up sparse Density Estimator RSDE-WL1
(being calculated according to formula (5) and (6)).Then according to formula (2), corresponding posterior probability is calculated respectively
With(being directly calculated according to formula (2)).According to the sample size of each category attribute, two kinds are calculated
Prior probability p (the c of classification0) and p (c1)：p(c0)=n0/ n, p (c1)=n1/ n, p (c0)+p(c1)=1.Finally utilize Bayes
Decision rule (3) is classified to the sample of input
Therefore, Weak Classifier ht(x) expression formula is
Two of which category attribute lower probability densityWithSparse estimation expression difference
For:
m0And m1Non-zero core weights in sparse Density Estimator RSDE-WL1 expression formulas are correspond under two kinds of category attributes respectively
Number, n0And n1The number of non-crater and crater example, usual m are correspond to respectively0＜ n0And m1＜ n1。WithFor
Core weight vector, βkFor core weight coefficient (0≤βk≤ 1), h0And h1For the wide (h of nucleus band0＞ 0, h1＞ 0),WithFor kernel function.
Wherein, improved sparse Density Estimator RSDE-WL1 simple realization process is as follows：
Compression collection density estimation (RSDE) algorithm is introduced first.RSDE is based on experience points square error (ISE) criterion, with
Total regression matrixBased on, core weights as much as possible is tended to 0, so as to obtain the dilute of density p (x)
Dredge expression formula, wherein Ki,k=Kh(xi,xk) it is ΦNThe i-th row k column elements.Specifically, the RSDE estimations with Gaussian kernel,
Its core weight vector β can be obtained by minimizing integrated square error, as follows：Wherein,Represent N × N-dimensional matrix
Space；
Parameter beta is consistent with the meaning of parameters in formula (2) in formula (7), and dx represents differential term, Ep(x)Represent desired value；
WhereinItem can not consider, E because it is unrelated with parameter betap(x){ } is represented on density p (x)
Desired value.By Density Estimator expression formulaSubstitution formula (7), by series of transformations, obtains band
The non-negative double optimization problem of constraint
Constraints βk>=0,1≤k≤N andWherein, matrixMember
Element is defined asGh() is gaussian kernel function, h
It is wide for nucleus band,It is that the Parzen windows of each sample point are estimated
Evaluation vector, βN=[β1,β2,...,βN]T。
In order to reduce aggregation extent and the degree of rarefication that improves density estimation of the weight coefficient in some regions, we introduce power
The weighting l of value coefficient1NormAs penalty term, improved sparse Density Estimator algorithm RSDE-WL1 is obtained.
Also referred to as regularization term, whereinFor diagonal matrix.DefinitionW=
[w1,w2,...,wN]T, βN=[β1,β2,...,βN]T, add penalty term after new double optimization problem be
It is non-convex to notice problem (9), and weight coefficient can be obtained by solving above mentioned problem using corresponding iterative algorithm
Sparse solution.
(2) optimal feature selection
Calculate Weak Classifier ht(x) weighted error summation, selection meet the single optimal characteristics f of minimal errortFor structure
Build the optimal Weak Classifier of current iteration
ht(x)=h (x, ft) (11)
(3) next iteration process sample weights update
SparseBoost algorithms combine the classification knot of current sample weights and feature selected by the past in AdaBoost algorithms
Fruit is about this information, and this information helps to select current optimal characteristics.In implementation process, increase by the sample of mistake classification
This weight, and reduce the sample weights correctly classified.When calculating weighted error summation, by the sample of mistake classification more likely
It is selected in next iteration process.Weight more new-standard cement is as follows
3rd, advantage and effect
The detection of crater during a kind of Mars probes soft landing based on sparse lifting integrated classifier of the present invention
Method, it compared with the conventional method, its major advantage is：(1) time complexity of classifier algorithm is O (Tm (m0+m1)), with
Boost algorithms are compared, and the time complexity of Boost algorithms is O (Tmn), due to m0+m1＜ n0+n1=n, thus it is complicated in the time
There is significant advantage on degree.(2) every time structure Weak Classifier when, only select that an optimal feature as sample to
Amount, without utilizing whole features, computation complexity is reduced, accelerates classification speed.(3) to the crater based on image and non-
Crater is classified, classification accuracy can reach approximately 85% and more than, to reality Mars probes soft landing during
The detection of crater has certain reference value.
Brief description of the drawings
Fig. 1 crater automatic detection main frame figures.
Explain that a crater is made up of the bright and dark area as crescent moon in Fig. 2 (A) crater crescent moon region
Physical principle.
The bright and dark area of the real 1km size craters of Fig. 2 (B) one.
Fig. 3 builds candidate's crater flow chart.
2 kinds of 2- rectangles of Fig. 4 (A) cover.
2 kinds of 3- rectangles of Fig. 4 (B) cover.
5 kinds of 4- rectangles of Fig. 4 (C) cover.
Example covered to crater 2- rectangles of Fig. 4 (D).
Fig. 5 (A) West domain crater real image.
Fig. 5 (B) intermediate region crater real image.
Fig. 5 (C) East domain crater real image.
Embodiment
The detection of crater during a kind of Mars probes soft landing based on sparse lifting integrated classifier of the present invention
Method, the step of this method includes, see Fig. 1.Its main thought is to make full use of designed sparse lifting integrated classifier to have
The advantages of sparse solution and reduction computation complexity, after the crater textural characteristics based on image are carried out with feature extraction and selection,
The classification to crater and non-crater is realized, to reach the quick detection of crater.Fig. 2 (A)-(B) is crater crescent moon area
Become clear in domain and the physical principle of dark area and real example.Fig. 3 is structure candidate's crater flow chart.
Present invention selection High Resolution Stereo Camera (HRSC) full-colour image minimum point h0905_0000 part work
For test set, the image is shot by the quick airship of Mars, and as shown in Fig. 5 (A)-(C), selected image resolution ratio is
12.5 meters/pixel, size is 3000 × 4500 pixel (37500 × 56250m2).Domain expert marks by hand on this pictures
About 3500 craters as earth's surface truth compared with automatic detection result.This pictures is for automatic inspection
It is a great challenge to survey crater algorithm, because it contains the form with spatial variations, and the contrast of image
Mutually it is on duty.This pictures is divided into three parts, is designated as West domain, intermediate region and East domain, West domain has similar with East domain
Landforms, but there are more craters in West domain than East domain, and intermediate region has visibly different compared with other two regions
Surface geographical feature.
Steps 1 and 2：Determine candidate's crater and candidate's crater Texture Feature Extraction
According to the determination method of candidate's crater, we have primarily determined that 13075 candidate's aerolites from full-colour image 5
Hole.The method covered by the square rows of Fig. 4 (A) -9 kinds of (D), has extracted 1089 image texture spies from candidate's crater image
Sign.Training set randomly chooses 204 true craters from the half of candidate's crater in East domain north in experiment and 292 non-are fallen from the sky or outer space
Stone pit example forms, and the corresponding candidate's crater number of test set from West domain, middle region and East domain in experiment is respectively
2935th, 1181 and 1223.
Step 3：Feature selecting is carried out to the textural characteristics of extraction
In order to realize that selected characteristic number is as few as possible, and the degree of accuracy of classifying is as big as possible, and the present invention is calculated SpraseBoost
The iterations T of method is respectively set to 2,5,10,15,20,25,30,50,100,150,200, then in West domain, middle region
And East domain tests the classification results for choosing individual features subset respectively.Simultaneously because in candidate's crater data crater and
The disequilibrium of non-crater distribution, successfully detects that true crater is more important than non-crater.Therefore, the present invention uses
Accuracy rate (Accuracy=(TP+TN)/(TP+TN+FP+FN)), recall ratio (Recall=TP/ (TP+FN)), precision ratio
(Precision=TP/ (TP+FP)) and F measured values (F-measure=2/ (1/ (Recall)+1/ (Precision))) conduct
Evaluation index.Wherein TP represents the true crater number correctly classified, and TN represents the non-crater number correctly classified,
FP represents that by the wrong non-crater number for being categorized as crater FN represents to be categorized as the true crater of non-crater by mistake
Number.
In iterations T setting, it is by becoming clear and dark area to select 2 features to be primarily due to candidate's crater
Composition, thus represent bright and the two dark be characterized in it is most important, maximum choose 200 features be in order to other
The experimental result of document compares, and middle characteristic randomly selects.In feature selection process, Boost algorithms are utilized
Thinking, in T iterative process, choose meet the single optimal characteristics f of minimal error each timet, obtain T feature and be used for
The structure of sample set, wherein T ＜ n.
Step 4：Boost algorithms are combined with sparse Density Estimator algorithm RSDE-WL1, it is integrated to devise sparse lifting
Grader, to realize the quick detection to the crater based on image.
In the design of grader, main the step of including three cores：Weak Classifier study, optimal feature selection and under
An iteration process sample weights update.Initialized first, for the initial weight w of input sampleiIf yi=0, then
wi=1/2n0；If yi=1, then wi=1/2n1, wherein n0And n1The number of non-crater and crater example is correspond to respectively,
n0+n1=n.In Weak Classifier study, arrange parameter λ=0.001, lmax=8, ε=1/ (0.3*N), obtain improved sparse
Density Estimator device RSDE-WL1 density estimation expression formula, further according to Bayesian decision criterion, obtain in each iterative process
One Weak Classifier ht(x).In optimal feature selection, the error in classification of Weak Classifier is calculated
Choose and meet that the minimum feature of error in classification as most there is feature, sets γt=εt/1-εt.Finally process for next iteration more
The weight of new samplesSo as to obtain T Weak Classifier.This T Weak Classifier is weighted combination
Into final strong classifier, the weight of corresponding Weak Classifier is arranged to αt=ln (1/ γt)。
Table 1-3 show respectively on West domain, intermediate region and East domain, characteristic selected by different iterationses and
Classification accuracy, recall ratio, precision ratio and F measured values.It is can be seen that from table 1-3 in West domain, intermediate region and East domain
On three regions, when selected characteristic is respectively 10,20,20, corresponding classification accuracy reaches highest, is respectively
0.790,0.854 and 0.874, while F measured values also reach maximum, respectively 0.790,0.796 and 0.818.Therefore, training
In the case that collection determines, the optimal characteristics number chosen when classifying to trizonal test data is respectively 10,20 and 20.
The West domain of table 1
| Iterations T | Selected characteristic | Accuracy | Recall | Precision | F-measure |
| 2 | 2 | 0.783 | 0.840 | 0.737 | 0.785 |
| 5 | 5 | 0.788 | 0.814 | 0.765 | 0.789 |
| 10 | 10 | 0.790 | 0.796 | 0.767 | 0.790 |
| 15 | 15 | 0.788 | 0.779 | 0.774 | 0.776 |
| 20 | 20 | 0.775 | 0.724 | 0.783 | 0.752 |
| 25 | 25 | 0.771 | 0.714 | 0.781 | 0.746 |
| 30 | 30 | 0.763 | 0.691 | 0.782 | 0.734 |
| 50 | 50 | 0.740 | 0.625 | 0.781 | 0.694 |
| 100 | 100 | 0.688 | 0.502 | 0.755 | 0.603 |
| 150 | 150 | 0.658 | 0.423 | 0.737 | 0.541 |
| 200 | 200 | 0.638 | 0.378 | 0.721 | 0.496 |
The intermediate region of table 2
| Iterations T | Selected characteristic | Accuracy | Recall | Precision | F-measure |
| 2 | 2 | 0.850 | 0.761 | 0.827 | 0.751 |
| 5 | 5 | 0.848 | 0.743 | 0.836 | 0.760 |
| 10 | 10 | 0.843 | 0.700 | 0.854 | 0.769 |
| 15 | 15 | 0.844 | 0.689 | 0.869 | 0.768 |
| 20 | 20 | 0.854 | 0.761 | 0.834 | 0.796 |
| 25 | 25 | 0.841 | 0.709 | 0.842 | 0.770 |
| 30 | 30 | 0.837 | 0.707 | 0.832 | 0.764 |
| 50 | 50 | 0.831 | 0.661 | 0.854 | 0.746 |
| 100 | 100 | 0.813 | 0.587 | 0.873 | 0.702 |
| 150 | 150 | 0.782 | 0.497 | 0.866 | 0.631 |
| 200 | 200 | 0.789 | 0.512 | 0.873 | 0.646 |
The East domain of table 3
| Iterations T | Selected characteristic | Accuracy | Recall | Precision | F-measure |
| 2 | 2 | 0.861 | 0.755 | 0.838 | 0.801 |
| 5 | 5 | 0.867 | 0.746 | 0.858 | 0.811 |
| 10 | 10 | 0.865 | 0.738 | 0.883 | 0.804 |
| 15 | 15 | 0.868 | 0.725 | 0.905 | 0.805 |
| 20 | 20 | 0.874 | 0.753 | 0.894 | 0.818 |
| 25 | 25 | 0.868 | 0.716 | 0.911 | 0.802 |
| 30 | 30 | 0.867 | 0.716 | 0.909 | 0.801 |
| 50 | 50 | 0.863 | 0.699 | 0.914 | 0.792 |
| 100 | 100 | 0.860 | 0.666 | 0.941 | 0.780 |
| 150 | 150 | 0.841 | 0.611 | 0.946 | 0.743 |
| 200 | 200 | 0.842 | 0.611 | 0.950 | 0.744 |
Four kinds of supervised classification algorithms for being used for crater detection are chosen to carry out with SparseBoost algorithms proposed by the present invention
Compare, such as Boost, AdaBoost, SVM and J48 algorithm.Boost algorithms, as base grader, lifting are integrated using decision tree
Algorithm is merged with feature selecting algorithm is classified.And other three kinds of algorithms can not be to initial data in experimentation
Collection carries out feature selecting.Table 4 lists this classification accuracy of five kinds of algorithms on West domain, intermediate region and East domain
(Accuracy), recall ratio (Recall), precision ratio (Precision) and F measured values (F-measure).
The crater detection algorithm of the present invention of table 4 and other four kinds of crater detection algorithm performance comparisions
From table 4, it can be seen that on West domain and East domain, have feature selecting sorting algorithm (SparseBoost and
Boost classification accuracy and F measured values) all apparently higher than the sorting algorithm (AdaBoost, SVM and J48) without feature selecting,
Wherein SparseBoost algorithms are better than Boost algorithms.And in intermediate region, have the algorithm of feature selecting with without feature selecting
Algorithm is compared, and difference is little (such as SparseBoost, AdaBoost and J48) on classification accuracy and F measured values, even more
Poor (such as Boost), this be probably because the training sample taken come from East domain, and middle region different from East domain distinguishingly
Looks cause to lose some important characteristic informations during feature selecting, it can be seen that the geographical form in middle region is obvious from Fig. 5 (B)
There is larger difference with west, East domain.Therefore, totally apparently, SparseBoost sorting algorithms proposed by the invention are in crater
Context of detection has preferable classifying quality, and computation complexity is minimum.
It should be noted last that：Above example is only to illustrative and not limiting technical scheme, although ginseng
The present invention is described in detail according to above-described embodiment, it will be understood by those within the art that：Still can be to this
Invention is modified or equivalent substitution, and any modification or partial replacement without departing from the spirit and scope of the present invention, its is equal
It should cover among scope of the presently claimed invention.
Claims (1)
1. the detection method of crater, its feature exist during the Mars probes soft landing based on sparse lifting integrated classifier
In：This method comprises the following steps：
Step 1. determines candidate's crater
Determine that the key of candidate's crater is to regard the crater on image as a pair of crescent moons with bright and dark area,
The shape of each pair crescent moon based on the shape detecting method of mathematical morphology from image by being determined, the crescent moon that can be matched is as time
The crater of choosing；First have to input a full-colour image in the building process of candidate's crater, it comprises bright and dark
Characteristic area, become clear and dark area parallel processing, bright areas is handled by using original image, and use inverted image
To handle dark area, the target of this method be in order to eliminate it is all can not be designated as the noise characteristic of crater, and only protect
Bright and dark features are stayed, remaining bright and dark features region matches each other, and these area markings are good, as crater
Candidate region；
Step 2. candidate's crater Texture Feature Extraction
In order to express candidate's crater in terms of rectangular characteristic, the square chart around each candidate's crater is extracted first
As block, in an experiment, in order to include the edge of crater around, twice of covering of candidate's aerolite pit-size, Mei Gehou are used
The unknown textural characteristics of crater are selected using 9 kinds of different size of square coverings to encode, therefore, the time that an image is included
The attribute of crater is selected to be described by textural characteristics；These features are not separate；
Step 3. carries out feature selecting to the textural characteristics of extraction
According to the candidate's crater textural characteristics tentatively extracted, due to the higher-dimension of characteristic, therefore by training sample and survey
Before sample this input grader, it is necessary to carry out feature selecting；The SparseBoost algorithms designed using step 4 carry out feature choosing
Select, the maximum difference of itself and AdaBoost algorithms is that the former is that an optimal spy is only chosen in iterative process each time
Sign, and the latter utilizes whole feature set；
Step 4. is combined Boost algorithms with sparse Density Estimator algorithm RSDE-WL1, devises sparse lifting Ensemble classifier
Device, to realize the quick detection to the crater based on image；
According to selected candidate's crater textural characteristics, in order to distinguish wherein crater and non-crater, a kind of prison is devised
Educational inspector practises sorting algorithm --- SparseBoost algorithms；This method combination Boost algorithms and a kind of improved sparse cuclear density are estimated
Calculating method is RSDE-WL1, while character subset is selected, constructs a plurality of sparse Density Estimator devices for corresponding base point
The design of class device, by the weighted array of base grader, finally realize integrated classifier；
Give n candidate's crater (x1,y1),(x2,y2),...,(xi,yi),...,(xn,yn), wherein yi=0,1, i=1,
2 ..., n correspond to non-crater and crater example, n respectively0And n1The number of non-crater and crater example is correspond to respectively
Mesh, n0+n1=n；Each candidate's crater is expressed as a characteristic vector x=(f1,f2,...,fi,...,fm)T, wherein often
One feature fi, i=1 ..., m are produced by the square covering of a certain ad-hoc location on candidate's crater, are utilized
SparseBoost algorithms produce a series of Weak Classifier ht(x) Weak Classifier, is combined foundation by weighting method for improving
One strong integrated classifier；Before iteration starts, the weight of n candidate's crater is first initialized, for i-th of candidate's aerolite
Hole, if yi=0, then wi=1/2n0；If yi=1, then wi=1/2n1；
, it is necessary to the step of realizing following three cores in each iterative process：Weak Classifier study, optimal feature selection and under
An iteration process sample weights update；Wherein, it is RSDE to compression collection density estimation algorithm in Weak Classifier learning process
Penalty term is added, improved sparse Density Estimator algorithm RSDE-WL1 is obtained, using RSDE-WL1 algorithms to each classification
Its density function of attributes estimation, the sample of input is classified according to Bayes decision rule, so as to obtain Weak Classifier；
(1) Weak Classifier learns
In the t times iterative process, for the single optimal characteristics f ∈ { f of selection1,f2,...,fmStructure Weak Classifier ht
(x), realized by building Bayes classifier；Generally for Bayes's classification problem, expectation estimation is given under input sample x
The posterior probability density of classification；It is first each category attribute c to obtain a probability classification on density estimation
Train a density estimatorThen posterior probability, final test sample are calculated with Bayes rule (2)
Originally it is assigned to the category attribute with maximum a posteriori probability；
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</mrow>
</mrow>
<mrow>
<msub>
<mi>&Sigma;</mi>
<msup>
<mi>c</mi>
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</msup>
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<mover>
<mi>p</mi>
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<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
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<mo>)</mo>
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</mrow>
For two classification problem, two conditional probability densities under given classification are estimated firstWithThe two density are obtained by sparse Density Estimator RSDE-WL1；According to formula (1), calculate it is corresponding after
Test probabilityWithAccording to the sample size of each category attribute, prior probability p (c are calculated0)
With p (c1), wherein p (c0)+p(c1)=1；Finally the sample of input is classified using Bayes decision rule (2)
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<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
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Therefore, Weak Classifier ht(x) expression formula is
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WhereinWithSparse expression be respectively
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<mi>k</mi>
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m0And m1The number of non-zero core weights under respectively two kinds of classifications obtained by sparse Density Estimator RSDE-WL1, usual m0
＜ ＜ n0And m1＜ ＜ n1；
Wherein, sparse Density Estimator RSDE-WL1 simple realization process is as follows：
It is RSDE algorithms to introduce compression collection density estimation first, and RSDE is based on empirical mean integrated square error ISE criterions, with complete
Regression matrixBased on, core weights as much as possible is tended to 0, so as to obtain the sparse of density p (x)
Expression formula, it is manifestly that, the RSDE estimations with Gaussian kernel, its core weight vector can be obtained by minimizing integrated square error
Arrive, it is as follows
WhereinItem is not considered, E because it is unrelated with parameter betap(x){ } represents the expectation on density p (x)；
By Density Estimator expression formulaSubstitution formula (6), by series of transformations, obtain equivalent belt restraining
Non-negative double optimization problem
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Constraints βk>=0,1≤k≤N andWherein matrix WithIt is in each sample point
Parzen windows estimate vector；
In order to reduce aggregation extent and the degree of rarefication that improves density estimation of the weight coefficient in some regions, weight coefficient is introduced
Weight l1NormAs penalty term, improved sparse Density Estimator algorithm RSDE-WL1 is obtained；Also referred to as just
Then change item, whereinFor diagonal matrix, definitionW=[w1,w2,...,
wN]T, βN=[β1,β2,...,βN]T, add penalty term after new double optimization problem be
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<mo>-</mo>
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<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
It is non-convex to notice problem (8), and solving above mentioned problem using a kind of iterative algorithm obtains the sparse solution of weight coefficient；
(2) optimal feature selection
Calculate Weak Classifier ht(x) weighted error summation, selection meet the single optimal characteristics f of minimal errortWork as building
The optimal Weak Classifier of preceding iteration
<mrow>
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</mrow>
ht(x)=h (x, ft) (10)
(3) next iteration process sample weights update
The classification results that SparseBoost algorithms combine current sample weights and feature selected by the past in AdaBoost algorithms have
Close this information；In implementation process, increase by the sample weights of mistake classification, and reduce the sample weights correctly classified；
When calculating weighted error summation, more likely it is selected by the sample of mistake classification in next iteration process, weight renewal expression
Formula is as follows
<mrow>
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<msubsup>
<mi>&gamma;</mi>
<mi>t</mi>
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<mi>t</mi>
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<msub>
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</mrow>
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<msub>
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</msubsup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
Set
γt=εt/1-εt (12)
Wherein εtIt is Weak Classifier ht(x) error in classification：
<mrow>
<msub>
<mi>&epsiv;</mi>
<mi>t</mi>
</msub>
<mo>=</mo>
<msubsup>
<mi>&Sigma;</mi>
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<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</msubsup>
<msubsup>
<mi>w</mi>
<mi>i</mi>
<mi>t</mi>
</msubsup>
<mo>|</mo>
<msub>
<mi>h</mi>
<mi>t</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
Meanwhile to make weight wt+1Meet probability distribution, it is necessary to be standardized to the weight after renewal, standardization formula is as follows:
After T iteration, the final output of SparseBoost algorithms is being obtained：The strong classification being made up of Weak Classifier weighting
Device h (x)：
<mrow>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mrow>
<msubsup>
<mi>if&Sigma;</mi>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</msubsup>
<msub>
<mi>&alpha;</mi>
<mi>t</mi>
</msub>
<msub>
<mi>h</mi>
<mi>t</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>&GreaterEqual;</mo>
<msubsup>
<mi>&mu;&Sigma;</mi>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</msubsup>
<msub>
<mi>&alpha;</mi>
<mi>t</mi>
</msub>
<mo>,</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<mi>o</mi>
<mi>t</mi>
<mi>h</mi>
<mi>e</mi>
<mi>r</mi>
<mi>w</mi>
<mi>i</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein αt=ln (1/ γt), μ is given threshold value, and μ takes 0.5.
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