CN108896021A - Method based on aerophotogrammetry data reduction plantation stand structural parameters - Google Patents

Method based on aerophotogrammetry data reduction plantation stand structural parameters Download PDF

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CN108896021A
CN108896021A CN201810879344.2A CN201810879344A CN108896021A CN 108896021 A CN108896021 A CN 108896021A CN 201810879344 A CN201810879344 A CN 201810879344A CN 108896021 A CN108896021 A CN 108896021A
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aerophotogrammetry
point cloud
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structural parameters
canopy
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CN108896021B (en
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曹林
付逍遥
刘浩
申鑫
刘坤
汪贵斌
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Nanjing Forestry University
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    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C11/00Photogrammetry or videogrammetry, e.g. stereogrammetry; Photographic surveying
    • G01C11/04Interpretation of pictures
    • GPHYSICS
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    • G01S7/4802Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

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Abstract

The present invention discloses a kind of method based on aerophotogrammetry data reduction plantation stand structural parameters, filters to airborne laser radar discrete point cloud data, and interpolation generates digital terrain model, point cloud data normalized;True color picture extracts characteristic point, matches, carries out three encryption of sky and generates aerophotogrammetry point cloud, aerophotogrammetry point cloud data is normalized using the digital terrain model of generation;Based on normalization aerophotogrammetry data reduction characteristic variable;Combined ground measured data and the characteristic variable of extraction construct multivariate regression models respectively to predict each stand structure feature.Pass through the high degree of overlapping image data of unmanned plane effective acquisition, and by stereophotogrammetric survey method from image as centering extract three-dimensional point cloud, to obtain Forest Canopy three-dimensional structural feature, the inversion accuracy of plantation stand structural parameters is helped to improve, and effectively inhibits structural parameters inverting " saturation " problem of forest cover degree height, the high standing forest of biomass.

Description

Method based on aerophotogrammetry data reduction plantation stand structural parameters
Technical field
The invention belongs to forest reserves detection technique fields, and in particular to one kind is based on aerophotogrammetry data reduction people The method of work woods stand structure parameter.
Background technique
Accurate plantation stand structural parameters extract, for forest resource monitoring, ecological factor investigation and two packing spaces Journal of Sex Research is significant.Meanwhile these information can be used for grasping forest space structure and dynamic rule, and to gloomy Management, ecological environment modeling and the carbon cycle analysis of woods provide data and support.Conventional plantation stand structural parameters mention It takes and depends on field investigation and aerophotograph or defend piece interpretation etc., precision is not often high, and is difficult to the functionization on " face " and pushes away Extensively.
In recent years, the research based on aerophotogrammetry data stand structure parameter extraction is:Zhang etc. 2016 exists 《Biological Conservation》" the Seeing the forest from drones delivered on volume 198: Testing the potential of lightweight drones as a tool for long-term forest Monitoring ", the true color image data which obtains by unmanned plane, by extraction canopy and terrain variable, and Combined ground measured data is extracted the stand structure parameter of subtropical forest on the basis of assessing these variable importances.Wang Mei Plum etc. 2017 exists《Forest resources management》" the sink-source dynamics tree based on unmanned plane visible image delivered on volume 4 Hat parameter information automatically extracts ", which obtains visual remote sensing image using unmanned plane, and is obtained based on object-oriented method Tree crown information, and estimated the stand structure parameter of sink-source dynamics accordingly.Sui Dandan etc. 2017 exists《Two packing spaces Property》" Evergreen Broadleaved Forest of The Dinghu Mountain gap distribution pattern and its origin cause of formation " delivered on volume 4, the research use nobody The image that machine obtains, has estimated stand structure parameter in conjunction with band math and supervised classification method.However, above method is all base Feature is extracted in spliced bidimensional image, there is no extract the three-dimensional structural feature of canopy to extract plantation stand structure Parameter.Meanwhile it more having no and deeply calculating artificial storey aerophotogrammetry point cloud feature and stand structure parameter extraction comprehensively Method.
Summary of the invention
Goal of the invention:It is surveyed in view of the deficienciess of the prior art, the object of the present invention is to provide one kind based on aeroplane photography The method for measuring data reduction plantation stand structural parameters.
Technical solution:In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is as follows:
A method of based on aerophotogrammetry data reduction plantation stand structural parameters, include the following steps:
(1) in ground setting sample, high degree of overlapping image data and LiDAR original point cloud data are acquired by unmanned plane; And tree species are recorded in sample ground and are counted, and measure the diameter of a cross-section of a tree trunk 1.3 meters above the ground and tree height of every wood;
(2) to the filtering of LiDAR original point cloud data and interpolation generation digital terrain model;Processing life is carried out to image data At aerophotogrammetry point cloud;Aerophotogrammetry point cloud data is normalized using the digital terrain model of generation Obtain normalization aerophotogrammetry point cloud;
(3) based on normalization aerophotogrammetry data reduction artificial forest canopy structure characteristic variable;
(4) characteristic variable is screened by correlation analysis;
(5) using ground actual measurement stand structure parameter as dependent variable, aerophotogrammetry point cloud characteristic variable is used as from change Amount establishes multivariate regression models and predicts each artificial forest stand structure parameter.
Further, in step (1), high degree of overlapping image data is acquired by fixed-wing unmanned plane, and use more rotors The LiDAR sensor of UAV flight carries out the acquisition of LiDAR original point cloud data;The actual measurement diameter of a cross-section of a tree trunk 1.3 meters above the ground is combined according to unitary volume equation It estimates accumulation, calculates ground biomass by the way that the different rate growth formula combination diameter of a cross-section of a tree trunk 1.3 meters above the ground and tree are high.
Further, in step (2), the noise point of LiDAR original point cloud data is removed first, is based on IDW filtering method Non-ground points are removed, then by calculating the average value of laser point height in each pixel, generate digital terrain model.
Further, in step (2), it includes extracting and matching feature points, aerial triangle that the image data, which carries out processing, Measurement and three-dimensional point cloud encryption.
Further, research area's digitized video is shot by remote sensing platform, is recorded in real time by Inertial Measurement Unit (IMU) The attitude parameter of every width image;Then, it obtains the characteristic point of image picture pair and carries out Feature Points Matching, shadow is carried out by flux of light method As the parsing and combination aerial triangulation of internal and external orientation generate aerophotogrammetry point cloud;In aerophotogrammetry point cloud On the basis of encryption, spatial position correction is carried out to aerophotogrammetry point cloud by the way that ground control point is added, and pass through life At digital terrain model aerophotogrammetry point cloud is normalized, the aerophotogrammetry point after being normalized Cloud data.
Further, artificial forest canopy structure characteristic variable described in step (3) includes three groups, respectively percentile height Variable, each layer coverage variable and canopy volume and profile features variable.
Further, the percentile height variable includes:Canopy height is distributed percentile, and the distribution of canopy point cloud is average Coverage more than height, the coefficient of variation of canopy point cloud distribution;
Each layer coverage variable is the percentage that point of the point cloud quantity more than each percentage height accounts for all the points cloud;
The canopy volume and profile features variable:Canopy height profile is fitted using Weibull function Obtain 2 profile features amount Weibull α and Weibull β;Each structured sort volume accounting of canopy, including open tier, photic zone, Four canopy structure classifications of low photosphere and confining bed, the volume percentage of each canopy structure classification.
Further, in step (4), first screening characteristic variable between correlation be lower than 0.6 characteristic variable, then into One step screens the characteristic variable of characteristic variable and each stand structure dependence on parameter higher than 0.6.
Further, in step (5), the variable of model is entered with method of gradual regression selection, i.e., in previously given F water Flat lower progress significance test is rejected if level of signifiance p > 0.1 is not achieved in t inspection;T inspection reaches the level of signifiance P < 0.05, then entered;Correlativity matrix is calculated by principal component analysis and obtains controlling elements k, and k is Maximum characteristic root Square root and smallest real eigenvalue ratio, less than 30 models of k are further selected.
Further, in step (5), mould is returned using the coefficient of determination, root-mean-square error and opposite root-mean-square error evaluation The effect and estimation precision of type fitting:
In formula:xiFor certain stand structure parameter measured value;Average value is surveyed for certain stand structure parameter;For certain standing forest The model estimated value of structural parameters;N for sample ground quantity;I is for some sample.
Beneficial effect:Compared with prior art, the present invention has the following advantages that:
Unmanned Aerial Vehicle Data acquisition is flexible, convenient, at low cost, by the high degree of overlapping image data of unmanned plane effective acquisition, And by stereophotogrammetric survey method from image as three-dimensional point cloud is extracted in centering, to obtain Forest Canopy three-dimensional structural feature, It will be helpful to improve the inversion accuracy of plantation stand structural parameters, and effectively inhibit forest cover degree height, the high standing forest of biomass Structural parameters inverting " saturation " problem.Previous method is all based on spliced image and directly extracts two dimensional character, and originally Application is then to be then based on a cloud as centering extraction three-dimensional point cloud from image and obtain canopy structure spy by stereophotogrammetric survey Sign.Since stand structure parameter and Forest Canopy structure feature have correlation well and mechanism to contact, therefore the application enhances The ability and precision of stand structure parametric inversion.The application is in depth extracted the artificial storey aerophotogrammetry of multiple groups comprehensively Point cloud feature, and it is preferred to have carried out characteristic variable, to be extracted plantation stand structural parameters in high quality.Meanwhile the hair Bright not only to explain conducive to the mechanism of characteristic variable, being also easy to the transplanting of carry out method (can also be into i.e. in wildwood and scondary forest Row application).Verification result show through the invention to the chief species of plain artificial forest (i.e. poplar and metasequoia) structural parameters into Row extracts, and compared with using other close remote sensing techniques to carry out stand structure parameter, the coefficient of determination improves 5% or more.
Detailed description of the invention
Fig. 1 is aerophotogrammetry point cloud band effect picture (a);
Fig. 2 is aerophotogrammetry and laser radar point cloud overlay effect diagram (b);
Fig. 3 is three typical samples ground laser radar point cloud side view (a);
Fig. 4 is three typical samples ground laser radar point cloud top view (b);
Fig. 5 is three typical samples ground laser radar and aerophotogrammetry point cloud section (c);
Fig. 6 is three typical samples ground aerophotogrammetry point cloud vertical distribution section and Weibull curve matching figure (d).
Specific embodiment
Combined with specific embodiments below, the present invention is furture elucidated, and embodiment is under the premise of the technical scheme of the present invention Implemented, it should be understood that these examples are only for illustrating the present invention and are not intended to limit the scope of the present invention.
The method based on aerophotogrammetry data reduction plantation stand structural parameters of the application mainly includes following Step:
(1) in ground setting sample, high degree of overlapping image data and LiDAR original point cloud data are acquired by unmanned plane; And tree species are recorded in sample ground and are counted, and measure the diameter of a cross-section of a tree trunk 1.3 meters above the ground and tree height of every wood;
(2) to the filtering of LiDAR original point cloud data and interpolation generation digital terrain model;Processing life is carried out to image data At aerophotogrammetry point cloud;
(3) acquisition normalizing is normalized to aerophotogrammetry point cloud data using the digital terrain model of generation Change aerophotogrammetry point cloud;
(4) based on normalization aerophotogrammetry data reduction artificial forest canopy structure characteristic variable;
(5) characteristic variable is screened by correlation analysis;
(6) using ground actual measurement stand structure parameter as dependent variable, aerophotogrammetry point cloud characteristic variable is used as from change Amount establishes multivariate regression models and predicts each artificial forest stand structure parameter.
Specifically, the application acquires high degree of overlapping image data by fixed-wing unmanned plane, and uses in step (1) The LiDAR sensor that multi-rotor unmanned aerial vehicle is carried carries out the acquisition of LiDAR original point cloud data;LiDAR sensor, that is, laser radar Distance measuring sensor (Light Detection And Ranging-LiDAR).In ground setting sample, and tree is recorded in sample ground It plants and counts, and measure the diameter of a cross-section of a tree trunk 1.3 meters above the ground and tree height of every wood;The actual measurement diameter of a cross-section of a tree trunk 1.3 meters above the ground is combined to estimate accumulation according to unitary volume equation, by different The fast growth equation combination diameter of a cross-section of a tree trunk 1.3 meters above the ground and the high calculating ground biomass of tree.
Step (2), to the filtering of LiDAR original point cloud data and interpolation generates digital terrain model;Image data is carried out Processing generates aerophotogrammetry point cloud;Normalizing is carried out to aerophotogrammetry point cloud data using the digital terrain model of generation Change processing and obtains normalization aerophotogrammetry point cloud.
When data prediction, the noise point of LiDAR original point cloud data is removed first, and go unless ground by filtering Point generates digital terrain model (DTM) (spatial resolution then by calculating the average value of laser point height in each pixel For 0.5m).
Being further processed for image data adds including extracting and matching feature points, aerial triangulation and three-dimensional point cloud It is close.First by remote sensing platform (being equipped with the unmanned plane of remote sensor in the present invention) shooting research area's digitized video, by used Property measuring unit (IMU) records the attitude parameter of every width image in real time;Then, it obtains the characteristic point of image picture pair and carries out feature Point matching carries out the parsing of image internal and external orientation by flux of light method and aerial triangulation is combined to generate aerophotogrammetry Point cloud;Aerophotogrammetry point cloud encryption on the basis of, by be added ground control point come to aerophotogrammetry point cloud into The correction of row spatial position, and aerophotogrammetry point cloud is normalized in the digital terrain model by generating, and obtains Aerophotogrammetry point cloud data after normalization.
Step (3), based on normalization aerophotogrammetry data reduction multiple groups artificial forest canopy structure characteristic variable;
Artificial forest canopy structure characteristic variable include three groups, respectively percentile height variable, each layer coverage variable and Canopy volume and profile features variable.
Percentile height variable includes:Canopy height is distributed percentile (H25, H50, H75, H95), the distribution of canopy point cloud Coverage (CCmean) more than average height, the coefficient of variation (Hcv) of canopy point cloud distribution;
Each layer coverage variable:Point cloud quantity each percentage height (30th, 50th, 70th, 90th, i.e. D3, D5, D7, D9 the point more than) accounts for the percentage of all the points cloud;
Canopy volume and profile features variable:Weibull function is fitted to obtain 2 and cut open to canopy height profile Region feature amount α, β (i.e. Weibull α and Weibull β);Each structured sort volume accounting of canopy, including open tier, photic zone are low Four canopy structure classifications of photosphere and confining bed, each canopy structure classification volume percentage (i.e. OpenGap, Oligophotic, Euphotic, ClosedGap).
Step (4), screens characteristic variable by correlation analysis;
First screen characteristic variable between correlation be lower than 0.6 characteristic variable, then further screening characteristic variable with Each stand structure dependence on parameter is higher than 0.6 characteristic variable.
Step (5), using ground actual measurement stand structure parameter as dependent variable, aerophotogrammetry point cloud characteristic variable conduct Independent variable establishes multivariate regression models.
Enter the variable of model with method of gradual regression selection, i.e., carry out significance test in the case where previously given F is horizontal, If level of signifiance p > 0.1 is not achieved in t inspection, rejected;T inspection reaches level of signifiance p < 0.05, then is entered; Correlativity matrix is calculated by principal component analysis and obtains controlling elements k, and k is the square root and smallest real eigenvalue of Maximum characteristic root Ratio, less than 30 models of k are further selected.Wherein F represents F inspection, i.e. homogeneity test of variance.It is a kind of in zero vacation If under, statistical value obeys the inspection of F- distribution.T represents t inspection, it indicates to be occurred with t distribution theory come inference difference general Rate, so that whether the difference for comparing two average is significant.
Using the coefficient of determination (R2), root-mean-square error (RMSE) and opposite root-mean-square error (rRMSE) evaluate regression model The effect and estimation precision of fitting:
In formula:xiFor certain stand structure parameter measured value;Average value is surveyed for certain stand structure parameter;For certain standing forest The model estimated value of structural parameters;N for sample ground quantity;I is for some sample.
The application is explained further as research area in the Huanghai Sea National forest park domestic using Jiangsu Province's Yancheng City:
Research area is located at the domestic Huanghai Sea National forest park of Jiangsu Province's Yancheng City, geographical location for 32 ° 33 ' of north latitude~ 32 ° 57 ', 120 ° 07 '~120 ° 53 ' of east longitude.The domestic topography of East Platform is gentle, and ground elevation 1.4m~5.1m, most area exists Between 2.6m~4.6m.The area belongs to representative north subtropical monsoon climate district, has apparent transitional, maritime and monsoon gas It waits, sunshine is enriched.Temperature on average is 14.5 DEG C throughout the year, and annual mouth is 2169.6h, percentage of possible sunshine 51%, frost-free period according to sum For 225d, rainfall 1051mm, the soil texture is sand.Forest farm afforestation rate is about 85%, and Forest Types are behaved Work woods, chief species are metasequoia (Metasequoia) and poplar (Populus).
Step (1) acquires high degree of overlapping image data by fixed-wing unmanned plane, and multi-rotor unmanned aerial vehicle is carried LiDAR sensor carries out LiDAR data acquisition.44 round samples are set within the scope of research area (26, poplar, metasequoia 18 It is a), each sample diameter be 30m.Sample center point coordinate measured using GPS (TrimbleGeoXH6000), GPS passes through reception GPS wide area differential GPS signal framing, precision are better than 0.5m.And tree species are recorded in sample ground and are counted, while measuring the diameter of a cross-section of a tree trunk 1.3 meters above the ground and the tree of every wood It is high.Accumulation combines the actual measurement diameter of a cross-section of a tree trunk 1.3 meters above the ground to be estimated that ground biomass is combined by different rate growth formula according to unitary volume equation The diameter of a cross-section of a tree trunk 1.3 meters above the ground and tree height are calculated.According to the stand structure parameter of single wooden survey data with being aggregated into sample scale, including the density of crop, Mean DBH increment, basal area, mean stand height, accumulation and ground biomass, are shown in Table 1:
Survey stand characteristics information summary sheet to 1 sample of table
Each stand structure parameter in assessing model and model prediction accuracy is calculated using (2)-(5) the step of the application, Specifically it is shown in Table 2.Three typical samples ground (1,2 and the 3) Contrast on effect of laser radar point cloud and aerophotogrammetry point cloud, Yi Jihang Empty photogrammetric cloud vertical distribution section and Weibull curve matching effect are shown in Fig. 3-Fig. 6.
Each stand structure parameter in assessing model of table 2 and model prediction accuracy
Stand characteristics Intercept H25 H50 H75 H95 D5 D7 α β R2 RRMSE (%)
The density of crop 7239.59 -168.72 -1879.87 -6902.28 0.48 53.97
Mean DBH increment -7.64 1.25 2.71 19.95 0.72 22.42
Basal area 23.89 0.37 -5.18 -1.68 0.52 41.57
Mean stand height -4.41 1.18 15.71 0.26 0.83 25.28
Accumulation 81.75 -3.02 5.99 62.97 0.66 47.66
Ground biomass 70.73 0.74 13.55 -3.53 0.63 40.73
Note:H25, H50, H75, H95 are canopy 25%, and 50%, 75%, 95% height is distributed percentile;D5, D7 are Point of the point cloud quantity on percentage height 50th and 70th accounts for the percentage of all the points cloud;α, β are Weibull function to canopy 2 profile features amounts that height profile is fitted;R2For the coefficient of determination;RRMSE is opposite root-mean-square error.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered It is considered as protection scope of the present invention.

Claims (10)

1. a kind of method based on aerophotogrammetry data reduction plantation stand structural parameters, which is characterized in that including with Lower step:
(1) in ground setting sample, high degree of overlapping image data and LiDAR original point cloud data are acquired by unmanned plane;And Tree species are recorded in sample ground and are counted, and measure the diameter of a cross-section of a tree trunk 1.3 meters above the ground and tree height of every wood;
(2) to the filtering of LiDAR original point cloud data and interpolation generation digital terrain model;Processing is carried out to image data and generates boat Empty photogrammetric cloud;Acquisition is normalized to aerophotogrammetry point cloud data using the digital terrain model of generation Normalize aerophotogrammetry point cloud;
(3) based on normalization aerophotogrammetry data reduction artificial forest canopy structure characteristic variable;
(4) characteristic variable is screened by correlation analysis;
(5) using ground actual measurement stand structure parameter as dependent variable, aerophotogrammetry point cloud characteristic variable is built as independent variable Vertical multivariate regression models predicts each artificial forest stand structure parameter.
2. the method according to claim 1 based on aerophotogrammetry data reduction plantation stand structural parameters, It is characterized in that:In step (1), high degree of overlapping image data is acquired by fixed-wing unmanned plane, and take using multi-rotor unmanned aerial vehicle The LiDAR sensor of load carries out the acquisition of LiDAR original point cloud data;Actual measurement diameter of a cross-section of a tree trunk 1.3 meters above the ground estimation accumulation is combined according to unitary volume equation Amount calculates ground biomass by the way that the different rate growth formula combination diameter of a cross-section of a tree trunk 1.3 meters above the ground and tree are high.
3. the method according to claim 1 based on aerophotogrammetry data reduction plantation stand structural parameters, It is characterized in that:In step (2), the noise point of LiDAR original point cloud data is removed first, is gone based on filtering method unless ground Point generates digital terrain model then by calculating the average value of laser point height in each pixel.
4. the method according to claim 1 based on aerophotogrammetry data reduction plantation stand structural parameters, It is characterized in that:In step (2), it includes extracting and matching feature points, aerial triangulation and three that the image data, which carries out processing, Dimension point cloud encryption.
5. the method according to claim 4 based on aerophotogrammetry data reduction plantation stand structural parameters, It is characterized in that:Firstly, shooting research area's digitized video by remote sensing platform, every width image is recorded in real time by Inertial Measurement Unit Attitude parameter;Then, it obtains the characteristic point of image picture pair and carries out Feature Points Matching, foreign side in image is carried out by flux of light method The parsing of bit element simultaneously combines aerial triangulation to generate aerophotogrammetry point cloud;In the base of aerophotogrammetry point cloud encryption On plinth, spatial position correction, and the number by generating are carried out to aerophotogrammetry point cloud by the way that ground control point is added Aerophotogrammetry point cloud is normalized in relief model, the aerophotogrammetry point cloud data after being normalized.
6. the method according to claim 1 based on aerophotogrammetry data reduction plantation stand structural parameters, It is characterized in that:Artificial forest canopy structure characteristic variable described in step (3) includes three groups, respectively percentile height variable, each Layer coverage variable and canopy volume and profile features variable.
7. the method according to claim 6 based on aerophotogrammetry data reduction plantation stand structural parameters, It is characterized in that:The percentile height variable includes canopy height distribution percentile, and canopy point cloud is distributed average height or more Coverage, canopy point cloud distribution the coefficient of variation;
Each layer coverage variable is the percentage that point of the point cloud quantity more than each percentage height accounts for all the points cloud;
The canopy volume and profile features variable:Canopy height profile is fitted to obtain 2 using Weibull function A profile features amount α and β;Each structured sort volume accounting of canopy, including open tier, photic zone, low photosphere and confining bed four Canopy structure classification, the volume percentage of each canopy structure classification.
8. the method according to claim 1 based on aerophotogrammetry data reduction plantation stand structural parameters, It is characterized in that:In step (4), correlation is lower than 0.6 characteristic variable, then further screening first between screening characteristic variable Characteristic variable and each stand structure dependence on parameter are higher than 0.6 characteristic variable.
9. the method according to claim 1 based on aerophotogrammetry data reduction plantation stand structural parameters, It is characterized in that:In step (5), the variable of model is entered with method of gradual regression selection, i.e., is carried out in the case where previously given F is horizontal Significance test is rejected if level of signifiance p > 0.1 is not achieved in t inspection;T inspection reaches level of signifiance p < 0.05, Then entered;Correlativity matrix is calculated by principal component analysis and obtains controlling elements k, and k is the square root of Maximum characteristic root With the ratio of smallest real eigenvalue, less than 30 models of k are further selected.
10. the method according to claim 1 based on aerophotogrammetry data reduction plantation stand structural parameters, It is characterized in that:In step (5), using coefficient of determination R2, root-mean-square error RMSE and opposite root-mean-square error rRMSE evaluation return The effect and estimation precision of models fitting:
In formula:xiFor certain stand structure parameter measured value;Average value is surveyed for certain stand structure parameter;For certain stand structure The model estimated value of parameter;N for sample ground quantity;I is for some sample.
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