CN116309786A - Crop leaf area index image analysis algorithm based on three-dimensional aggregation index model - Google Patents
Crop leaf area index image analysis algorithm based on three-dimensional aggregation index model Download PDFInfo
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Abstract
The invention provides a crop leaf area index image analysis algorithm based on a three-dimensional aggregation index model, which introduces a leaf sequence principle in botanic classification, namely a para-generation mode, a reciprocal mode, a rotation generation mode and a clustering mode, and pushes out the porosity P of randomly distributed leaves r (theta) equation indirectly solving the problem of the distribution anisotropy of the horizontal blades, converting the color image into a binary image by using a space conversion technology of Lab after acquiring the color image of the measurement object by using a coverage photographing technology of a camera, wherein the pixel value of 0 represents soil, 255 represents vegetation, and obtaining the porosity P of the non-random distribution blades based on the binary image m (θ) according to P r (θ) and P m And (E) obtaining the aggregation index of crop canopy in the three-dimensional space by the infiltration function relation between (theta), and further accurately calculating the real leaf area index of the crop. The three-dimensional aggregation index model provided by the invention is successfulThe method solves the problem of underestimating LAI of the traditional model, develops a measuring method suitable for a crop sample, facilitates optical measurement and improves the calculation precision of the sample.
Description
Technical Field
The invention relates to the field of crop leaf area index image analysis, in particular to a crop leaf area index image analysis algorithm based on a three-dimensional aggregation index model.
Background
The aggregation index is defined as the ratio of the effective leaf area index (effective LAI, le) to the leaf area index (LAI, L), which describes the extent of aggregation or dispersion of the leaves. It is generally assumed that the leaves are randomly distributed, and we call the effective LAI. However, under field conditions, the leaves are not randomly distributed, so that the use of an aggregation index model helps to improve measurement accuracy and provides theoretical support for the upgrade of the measurement device, assuming that the randomly distributed leaves would lead to underestimation of the LAI of the field measurement.
2. Description of the prior art
The calculation of the aggregation index typically involves two steps. In a first step, a mathematical relationship between the input parameters and the aggregation index is established to describe the spatial distribution of the leaves, i.e. the aggregation index modeling. When the model is built, how to obtain the input parameters in the model is a key problem, which needs to be solved in the second step. To reduce damage to vegetation, optical device indirect measurements are typically employed to obtain input parameters in the aggregate index model. For ease of acquisition, these input parameters are variables that are easy to measure. In optical measurements, the aperture is more easily identified by the optical device. Thus, a mathematical relationship between the pore and the aggregate index can be established to further invert the aggregate index.
In the aggregation index modeling process, there are two methods to deal with the pore problem. One approach is to apply a cumulative function of pore size to describe the fraction in the cutoff (i.e., one-dimensional measurement path) that is greater than a certain pore size (length of the pore in a certain direction). Based on the cumulative function of the pore size, a mathematical equation of the pore size and the aggregation index is established, and the pore size measured by the optical equipment is used as an input parameter for inverting the aggregation index. In another approach, a penetration function is used to describe the porosity of the observation region. Similarly, the method exploits the mathematical relationship between porosity and aggregate index to invert the aggregate index. However, based on models developed by these methods, the variation of the blade distribution is generally assumed to be isotropic in the horizontal direction, for example: CC. CCL, LX, CLX aggregate index model. These models are all one-dimensional aggregate index models. In order to make the one-dimensional aggregation index model calculate the aggregation index more accurately, long-distance truncation is generally adopted when the pore size is measured, so that the measured sample size is as close to the statistical total volume as possible, and some requirements of statistics are met. Statistically, to achieve 95% accuracy according to Poisson's theory, the length of the cut-off should be at least 10 times the average distance between the main plant structures (e.g. crown and crop rows), which means that several tens of meters of measured length are required. For a forest canopy with large span and high branch height, the under-forest measurement can meet the cutting requirement. However, this method is not suitable for the measurement of crops, because the crop canopy is thick, no branch is high, and the measurement is dependent on sampling. Therefore, it is necessary to develop a three-dimensional aggregation index model to calculate the aggregation index of crops and improve the accuracy of the real leaf area index, however, the horizontal spatial distribution of the leaves of crops is complex, the anisotropy is strong, and how to consider the anisotropy of the horizontal distribution of the leaves. This is a key issue in building a three-dimensional aggregate index model.
In the second step, there are two types of optical devices for measuring the input parameters of the built model, namely the non-imaging sensor and the imaging sensor. Non-imaging sensors include line sub-sensors, radiometers, capacitive sensors, and the like, which use optical signals to measure input parameters based on truncated samples, where the acquired data is line data or stripe data. Typically, the three-dimensional aggregation index model takes into account the anisotropy of the horizontal distribution of the blade. Therefore, non-imaging sensors are not suitable for measuring input parameters involved in a three-dimensional aggregation-index model. However, imaging sensors can effectively measure area data, with the most commonly used imaging optical sensor being a camera. Two measurement methods, namely, fisheye lens-based Hemispherical Photography (HP) and standard lens-based digital overlay photography DCP, were developed depending on the lens. Hemispherical photography yields a circular image with a polar coordinate system. In a circular image, the pixels are distorted (see fig. 4.(a)), which results in inaccurate calculation of the length values. However, in the agricultural field, measurements are often made based on sampling of the sample party, i.e.: based on the area data. Compared with hemisphere photography, the digital coverage photography obtains a square (or rectangular) image in a rectangular coordinate system, and the pixel size is accurately deduced under the condition of known shooting height. The length parameters in the sample can thus be easily obtained, for example: leaf width, pore size cumulative function. In addition, digital blanket photography can obtain field measurement data that matches the remote sensing image pixels, and therefore has potential for application in interdisciplinary research.
Although digital blanket photography is used for farmland measurements, previous research has focused mainly on one-dimensional aggregation index models, such as: the most popular aggregation index model at present, the LX aggregation index model. The model is based on a penetration function, and the expression is as follows:
wherein: p (θ) is the porosity measured once,
Is the logarithmic value after calculating the average value of P (theta),
The LX aggregation index model, which is an average of the logarithm of P (θ), is a typical one-dimensional aggregation index model that calculates the aggregation index by measuring a number of P (θ) over a cutoff (the cutoff length is 10 times the leaf feature width). Although the LX aggregate index model was proposed earlier, this model has been used until now. On the basis of this model, subsequent studies have also developed some other models, for example CLX models. The model in these studies was a one-dimensional aggregation index model, ignoring the anisotropy of the horizontal distribution of the blade. Therefore, how to modify the LX model to take into account the anisotropy of the blade level distribution is an unsolved problem in agriculture.
Disclosure of Invention
The invention provides a crop leaf area index image analysis algorithm based on a three-dimensional aggregation index model based on at least one of the technical problems.
A crop leaf area index image analysis algorithm based on a three-dimensional aggregation index model comprises the following steps:
s1, constructing a 3D aggregation index model, and in order to describe the anisotropy of the horizontal distribution of the blade, analogy the method of the LX aggregation index model, namely a penetration function, and deducing a formula of the mathematical relationship between the porosity and the aggregation index, namely a 3D aggregation index model formula:
wherein: p (P) m (θ) porosity of non-randomly distributed blades, an input parameter to the model, representing porosity under field conditions measured in situ using DCP, P r (θ) is the porosity of the randomly distributed blades;
s2, calculating the porosity P of the randomly distributed blades r (θ) introduction of phyllotaxis in phytoclassification, i.e. the distribution of leaves on the stem in the horizontal direction comprises a para-genic mode, a reciprocal mode, a rotagenic mode, a clustering mode, based on which the porosity P of the leaves is randomly distributed r The calculation steps of (θ) are as follows:
s21, analyzing individual potential pore areas in the single layer, analytically calculating the individual potential pore areas of the randomly distributed blades by using grid analysis in vegetation coverage (FVC) measurement, wherein in the grid analysis, the pore areas in the blades with local random distribution are decomposed into four individual potential pore areas A according to the modes of paragenetic, intergrowth and rotagenetic i (lambda), i.e. void area 1, void area 2, void area 1X +4, void area 3, there are two cases in the X-direction and Y-direction depending on the direction of the blade tip, so four individual potential void areas A i (lambda) is further divided into 7: a is that 1_x ,A 1_y ,A 2_x ,A 2_y ,A 14_x ,A 14_y ,A 3 The formula table is as follows:
s22, calculating the average pore area A (lambda) of the single-layer randomly distributed blade:
A(λ)＝A i (λ)×n(λ) (3)
wherein: the number of individual potential pore regions in the n (λ) monolayer;
dividing the average pore area A (lambda) of randomly distributed blades in a monolayer by the viewing area A of the optical device t The porosity P (a B) of the randomly distributed blades in a single layer is obtained:
P(A∨B)＝A(λ)/A t (4)
wherein: v is the mathematical symbol "OR";
s23, deriving the porosity P in the vertical direction by considering the overlapping of the upper gap and the lower gap of the blade r The formula of (θ) is:
wherein: delta is a random number between 0 and 1;
s3, determining the actual size of the pixel representation, and calculating the actual length or the actual width in the image by adopting a geometrical optics principle, wherein a specific formula is as follows:
wherein: h the vertical height from the camera to the crown top and recorded in the measurement; the FOV is the field of view of the camera; actual length D in D image 1 Or the actual width D 2 Is a common symbol of (2);
equation (6) combines the number of pixels of the camera n pixel The actual pixel size d is obtained:
d＝D/n pixel (7)
s4, calculating the porosity P of the non-random distribution blade m (θ) converting a color image captured by a camera into a binary image using a spatial conversion technique of Lab, wherein a pixel value of 0 represents soil, 255 represents vegetation, and P is obtained based on the binary image m Formula of (θ):
wherein: n (N) s Is the number of soil pixels, N v Is the number of vegetation pixels;
s5, the porosity P of the obtained randomly distributed blade r Porosity P of (θ) and non-randomly distributed blades m And substituting the parameters obtained by (theta) and computer graphics coupling into the formula (2) to calculate the aggregation index.
Further, in step S1, a specific derivation method of the 3D aggregation index model is as follows:
s11, the penetration function is proposed in the Markov model:
wherein G (θ, θ) l ) The G function represents the projection function of the leaf area in the θ direction, namely:
wherein A (θ, θ) l ) Is a kernel function in equation (10) representing the fraction of the ratio between leaf density and leaf density in the θ direction, ψ=cos -1 (cotθcotθ l )，g(θ l ) Is the leaf inclination distribution function LADF, the Beta function was chosen to describe LADF, and in the study of the oblique spotting method, the G function was approximately equal to 0.5 when θ=57.5°, so equations (10) and (11) can be simplified as:
when the vanes are not randomly distributed, the porosity of the non-randomly distributed vanes is:
wherein Ω E Is the aggregation index, the two sides of the formula (13) and the formula (9) are divided by logarithms to obtain the formula (2):
advancing oneIn step S2, the average pore area of the randomly distributed blades in the monolayer is divided into average pore areas of randomly distributed blades in the monolayer having a autogenous or reciprocal pattern
And average pore area of single-layer wheel-shaped randomly distributed blades +.>
The expression is as follows:
wherein: lambda (lambda) 1 Is a variable representing randomly distributed blade pore size, blade tip parallel to X direction, lambda 2 Also a variable, representing randomly distributed pore size or randomly distributed blades, the tip of which is parallel to the Y direction, f being the ratio of the projected ellipse to the ellipse, f being a factor controlling the zenith angle porosity variation, expressed as:
in the formula (14), A a 、A b 、A c The pore area of the randomly distributed blades is expressed as follows:
wherein: w (w) * Is the average width of the blade, l * Is the average length of the blade, σ is the area of the blade, σ=0.25pi w * l * The actual area corresponding to the photo taken by the DCP is taken as the observation layer area, so D 1 Cut-off in the X direction, namely the photo length; d (D) 2 Is the truncation in the Y direction, i.e., the photo width;
n(λ 1 ) A random distribution She Kongxi representing blade tips parallel to the X direction is greater than lambda in size 1 Number, n (lambda) 2 ) The pore size of the randomly distributed blade representing parallel blade tips is greater than lambda 2 In the Y direction, the expression is:
wherein: l (L) p Is the projected effective leaf area index, L p ＝G(θ,θ l )L e /cosθ，G(θ,θ l ) Is the projection function of the leaf area in the theta direction, sigma p Is the projected area of the blade, w is the average width of the blade perpendicular to the cutting direction in the non-horizontal condition;
p (A, B) is divided into individual layers with average porosity of the randomly distributed leaf having a para-or trans-pattern
And average porosity of a single layer randomly distributed blade with a rotagenic pattern +.>
The expression of which expands to:
wherein: a is that t The actual area corresponding to the photographed region of the DCP is: a is that t ＝D 1 D 2 (21)
As can be seen from the above equation, equation (20) is obtained by dividing equation (5) by equation (21), and equation (20) is also a specific form of expansion of equation (4).
Further, in step S5, the parameters obtained by the computer graphics coupling are: length variable: cut-off D in X-direction 1 Cut-off D in Y direction 2 She Pingjun width w * Average length of leaf l * Average width w of leaf perpendicular to the direction of interception in non-horizontal condition, maximum pore size lambda in X-direction 1_max Maximum pore size lambda in Y direction 2_max The method comprises the steps of carrying out a first treatment on the surface of the Score variable: porosity P of non-randomly distributed blades m (θ)；
According to the formulas (6), (7) and (8), the maximum pore size lambda in the X direction can be obtained 1_max ：
for X＝i；n
for Y＝j；m
soil_value[i；j]＝max(value＝0) (22)
number_soil_pixel＝mumber(soil_value[*；j])
0 is soil pixel value, and lambda can be calculated by the same way 2_max And w;
extracting the edge of the blade by using a Canny operator, determining the image coordinates of the tip and the bottom of the blade, and calculating w based on the image coordinates of the tip and the bottom * And l * 。
Further, the derivation process of equation (19) is:
when the blades are randomly distributed, norman gives a mathematical form:
wherein: n (λ) represents the number of pore sizes greater than λ in the total ribbon length, ρ is the number of blades per unit area, σ is the blade area, w' is the average width of the blades perpendicular to the ribbon direction, D is the cutoff length, and ρσ=l e ，L e Is the effective leaf area index, and equation (23) becomes:
the effective leaf area index L in the formula (24) e Replaced by projected effective leaf area index L p Expression thereofThe formula is:
setting elliptical blade to obtain projection area sigma of blade p ：
Consider the case of non-horizontal, L p Sum sigma p If the condition is introduced into the equation (24), the equation (24) becomes:
the expressions in the X-direction and the Y-direction are obtained from the formula (27):
wherein: lambda (lambda) 1 Is a variable, representing a random distribution of She Kongxi dimensions, with the blade tip parallel to the X direction, lambda 2 Also a variable, representing a random distribution of She Kongxi sizes, with the tips parallel to the Y direction.
Further, the specific derivation of equation (20) is as follows:
according to the potential pore region (A) 1_x ,A 1_y ,A 2_x ,A 2_y ,A 14_x ,A 14_y ,A 3 ) By analyzing the geometric relationship, it is possible to obtain:
area of the pores that are paragenic and intergrowth in the X direction:
the pore region of the contra-generation and the inter-generation in the Y direction:
void area that is rotable in the X direction:
void area that is rotated in the Y direction:
the observation area of the optical device is: .
A t ＝D 1 D 2 (34)
Assuming that the probability of the void areas in the X-direction and the Y-direction are equal, the average value in the X-and Y-directions is used as 0.5[ eq. (formula (30))+ Eq. (formula (31)) ]/Eq. (formula (34)); the porosity of the randomly distributed blades with a rotagenic pattern in a single layer in the horizontal case is 0.5[ eq. (equation (32)) +
Eq. (equation (33)) ]/Eq. (equation (34)), thereby yielding:
wherein:
A c ＝A 3 (λ 1 ,λ 2 )n(λ 1 )n(λ 2 ) (39)
wherein lambda is 1 Is from 0 to lambda 1_max Variable lambda of 2 Is from 0 to lambda 2_max Thus, P oa (λ 1 ,λ 2 ) And P w (λ 1 ,λ 2 ) Is a collection, namely:
P oa (0,0),P oa (1,0),P oa (1,1),L,P oa (λ 1_max ,λ 2_max -1),P oa (λ 1_max ,λ 2_max ) (40)
P w (0,0),P w (1,0),P w (1,1),L,P w (λ 1_max ,λ 2_max -1),P w (λ 1_max ,λ 2_max ) (41)
equation (40) and equation (41) reflect P oa (λ 1 ,λ 2 ) And P w (λ 1 ,λ 2 ) The average value is selected as the final result to reflect the overall situation, i.e
And->
Calculating P in non-horizontal cases oa (λ 1 ,λ 2 ) And P w (λ 1 ,λ 2 ) The area change factor of the single layer from the horizontal condition to the non-horizontal condition, namely the ratio of the projected ellipse to the ellipse, needs to be calculated, and the formula is as follows:
in the non-horizontal case, there are only two variables of blade and void region, so the porosity of a randomly distributed blade with a para-or reciprocal mode in a single layer is:
in the non-horizontal case, the porosity of the randomly distributed blades with a rotation pattern in a single layer is:
selecting an average value as a final result to reflect the overall situation
I.e. < ->
And->
Obtaining
Wherein:
is P (A) or P (B), -, or a combination thereof>
Is P (A) or P (B).
Further, the derivation process of formula (5) is:
because of the overlapping inertia system of the upper and lower voids, based on Bayesian analysis, the overlapping relationship in the vertical direction is obtained:
wherein: p (A) is one of the randomly distributed leaf porosities in the monolayer, and P (B) is one of the randomly distributed leaf porosities in the other monolayer;
since the void fraction (P) is smaller than 1 in the formula (48), the product thereof is a small value, so that it is ignored to obtain four cases:
the conditional probability is used in equation (49) to derive the mathematical relationship between P (a|b) and P (b|a):
using Monte Carlo method, assuming P (A|B) is a random number in the range of 0 to 1, then assuming randomly distributed leaf porosity as P r_1 ,P r_2 ,P r_3 And P r_4 Is obtained by the cumulative average of (a):
in the formula (51), P r Four cases P of (θ) r_1 ,P r_2 ,P r_3 And P r_4 With the same probability, δ is a random number between 0 and 1, i.e., P (a|b).
The beneficial effects are that:
1. the three-dimensional aggregation index model provided by the invention successfully solves the problem that the previous model underestimates the LAI;
2. in the modeling, an equation describing the mathematical relationship between the aggregation index and the porosity is deduced, a theoretical basis is provided for the anisotropic problem, and the problem of how to build a 3D aggregation index model to describe the anisotropic of the spatial distribution of the blade in the horizontal direction is solved;
3. the method for measuring the input parameters of the 3D aggregation index model solves the problem of how to measure the input parameters of the established 3D model and complete indirect measurement;
4. the measuring method suitable for the crop sample is developed, the optical measurement is convenient, and the calculation accuracy of the sample is improved.
Drawings
FIG. 1 shows a schematic representation of the pore measurement of the present invention;
FIG. 2 shows a schematic representation of randomly distributed vane types and individual potential pore areas in a single layer of the present invention;
FIG. 3 shows a schematic diagram of the framework computation of the 3D aggregate index model of the present invention;
FIG. 4 shows a schematic representation of the calculation of the pore measurement of the present invention;
in fig. 1, (a) the porosity required for LX aggregation index model, (b) the porosity required for three-dimensional (3D) aggregation index model;
in fig. 2, (a) opposite growth, (b) opposite growth, (c) opposite growth or opposite growth of blade tips parallel to X direction in bottom view, (d) opposite growth or opposite growth of blade tips parallel to Y direction in bottom view, (e) rotation generation, (f) cluster generation, (g) rotation generation of blade tips parallel to X direction in bottom view, (h) rotation generation of blade tips parallel to Y direction in bottom view;
in fig. 4, (a) hemispherical photography based on polar coordinate system, (b) digital cover photography based on cartesian coordinate system, (c) geometric relation of field of view, (d) pore size in X direction and w, (e) pore size in Y direction and w, (f) pixel of leaf, (g) depth of field of leaf, w is average width of leaf perpendicular to cut-off direction in non-horizontal case.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description. It should be noted that, in the case of no conflict, the embodiments of the present application and the features in the embodiments may be combined with each other.
A crop leaf area index image analysis algorithm based on a three-dimensional aggregation index model comprises the following steps:
s1, constructing a 3D aggregation index model, and in order to describe the anisotropy of the horizontal distribution of the blade, analogy the method of the LX aggregation index model, namely a penetration function, and deducing a formula of the mathematical relationship between the porosity and the aggregation index, namely a 3D aggregation index model formula:
wherein: p (P) m (θ) porosity of non-randomly distributed blades, an input parameter to the model, representing porosity under field conditions measured in situ using DCP, P r (θ) is the porosity of the randomly distributed blades;
s2, calculating the porosity P of the randomly distributed blades r (θ) introduction of phyllotaxis in phytoclassification, i.e. the distribution of leaves on the stem in the horizontal direction comprises a para-genic mode, a reciprocal mode, a rotagenic mode, a clustering mode, based on which the porosity P of the leaves is randomly distributed r The calculation steps of (θ) are as follows:
s21, analyzing individual potential pore areas in the single layer, analytically calculating the individual potential pore areas of the randomly distributed blades by using grid analysis in vegetation coverage (FVC) measurement, wherein in the grid analysis, the pore areas in the blades with local random distribution are decomposed into four individual potential pore areas A according to the modes of paragenetic, intergrowth and rotagenetic i (lambda), i.e. void area 1, void area 2, void area 1X +4, void area 3, there are two cases in the X-direction and Y-direction depending on the direction of the blade tip, so four individual potential void areas A i (lambda) is further divided into 7: a is that 1_x ,A 1_y ,A 2_x ,A 2_y ,A 14_x ,A 14_y ,A 3 The formula table is as follows:
s22, calculating the average pore area A (lambda) of the single-layer randomly distributed blade:
A(λ)＝A i (λ)×n(λ) (3)
wherein: the number of individual potential pore regions in the n (λ) monolayer;
dividing the average pore area A (lambda) of randomly distributed blades in a monolayer by the viewing area A of the optical device t The porosity P (a B) of the randomly distributed blades in a single layer is obtained:
wherein: v is the mathematical symbol "OR";
s23, deriving the porosity P in the vertical direction by considering the overlapping of the upper gap and the lower gap of the blade r The formula of (θ) is:
wherein: delta is a random number between 0 and 1;
s3, determining the actual size of the pixel representation, and performing image analysis on undistorted images (pixels in fig. 4 (a and b)); as shown in fig. 4 (c), the actual length or the actual width in the image is calculated by using the principle of geometrical optics, and a specific formula is as follows:
wherein: h the vertical height from the camera to the crown top and recorded in the measurement; the FOV is the field of view of the camera; actual length D in D image 1 Or the actual width D 2 Is a common symbol of (2);
equation (6) combines the number of pixels of the camera n pixel The actual pixel size d is obtained:
d＝D/n pixel (7)
s4, calculating the porosity P of the non-random distribution blade m (θ) converting a color image captured by a camera into a binary image using a spatial conversion technique of Lab, wherein a pixel value of 0 represents soil and 255 represents vegetationBased on the binary image, P is obtained m Formula of (θ):
wherein: n (N) s Is the number of soil pixels, N v Is the number of vegetation pixels;
s5, the porosity P of the obtained randomly distributed blade r Porosity P of (θ) and non-randomly distributed blades m And substituting the parameters obtained by (theta) and computer graphics coupling into the formula (2) to calculate the aggregation index.
In step S1, a specific derivation method of the 3D aggregation index model is as follows:
s11, the penetration function is proposed in the Markov model:
wherein G (θ, θ) l ) The G function represents the projection function of the leaf area in the θ direction, namely:
wherein A (θ, θ) l ) Is a kernel function in equation (10) representing the fraction of the ratio between leaf density and leaf density in the θ direction, ψ=cos -1 (cotθcotθ l )，g(θ l ) Is the leaf inclination distribution function LADF, the Beta function was chosen to describe LADF, and in the study of the oblique spotting method, the G function was approximately equal to 0.5 when θ=57.5°, so equations (10) and (11) can be simplified as:
when the vanes are not randomly distributed, the porosity of the non-randomly distributed vanes is:
wherein Ω E Is the aggregation index, the two sides of the formula (13) and the formula (9) are divided by logarithms to obtain the formula (2):
in step S2, the average pore area of the randomly distributed blades in the monolayer is divided into the average pore area of the randomly distributed blades in the monolayer having a autogenous or reciprocal pattern
And average pore area of single-layer wheel-shaped randomly distributed blades +.>
The expression is as follows:
wherein: lambda (lambda) 1 Is a variable representing randomly distributed blade pore size, blade tip parallel to X direction, lambda 2 Also a variable, representing randomly distributed pore size or randomly distributed blades, the tip of which is parallel to the Y direction, f being the ratio of the projected ellipse to the ellipse, f being a factor controlling the zenith angle porosity variation, expressed as:
in the formula (14), A a 、A b 、A c The pore area of the randomly distributed blades is expressed as follows:
wherein: w (w) * Is the average width of the blade, l * Is the average length of the blade, σ is the area of the blade, σ=0.25pi w * l * The actual area corresponding to the photo taken by the DCP is taken as the observation layer area, so D 1 Cut-off in the X direction, namely the photo length; d (D) 2 Is the truncation in the Y direction, i.e., the photo width;
n(λ 1 ) A random distribution She Kongxi representing blade tips parallel to the X direction is greater than lambda in size 1 Number, n (lambda) 2 ) The pore size of the randomly distributed blade representing parallel blade tips is greater than lambda 2 In the Y direction, the expression is:
wherein: l (L) p Is the projected effective leaf area index, L p ＝G(θ,θ l )L e /cosθ，G(θ,θ l ) Is the projection function of the leaf area in the theta direction, sigma p Is the projected area of the blade, w is the average width of the blade perpendicular to the cutting direction in the non-horizontal condition;
p (A, B) is divided into individual layers with average porosity of the randomly distributed leaf having a para-or trans-pattern
And average porosity of a single layer randomly distributed blade with a rotagenic pattern +.>
The expression of which expands to:
in the middle of：A t The actual area corresponding to the photographed region of the DCP is: a is that t ＝D 1 D 2 (21)
As can be seen from the above equation, equation (20) is obtained by dividing equation (5) by equation (21), and equation (20) is also a specific form of expansion of equation (4).
In step S5, the parameters obtained by the computer graphics coupling are: length variable: cut-off D in X-direction 1 Cut-off D in Y direction 2 She Pingjun width w * Average length of leaf l * Average width w of leaf perpendicular to the direction of interception in non-horizontal condition, maximum pore size lambda in X-direction 1_max Maximum pore size lambda in Y direction 2_max The method comprises the steps of carrying out a first treatment on the surface of the Score variable: porosity P of non-randomly distributed blades m (θ)；
According to the formulas (6), (7) and (8), the maximum pore size lambda in the X direction can be obtained 1_max ：
for X＝i；n
for Y＝j；m
soil_value[i；j]＝max(value＝0) (22)
number_soil_pixel＝mumber(soil_value[*；j])
0 is soil pixel value, and lambda can be calculated by the same way 2_max And w; for w, lambda 1_max And lambda (lambda) 2_max The number of each individual soil pixel in the X direction (black line in FIG. 4 (d)) can be calculated by traversing the entire X direction of the binary image
As shown in fig. 4 (f, g), w can be calculated based on the tip and bottom image coordinates by extracting the edge of the blade using the Canny operator and determining the tip and bottom image coordinates of the blade * And l * 。
l * Depth of field (Vh) is involved and can be obtained using the method reported by Wu (as in fig. 4 (G)), specifically, many crop leaves are selected as samples, images (RGB photographs) of leaf inclination angles from 0 ° to 85 ° are taken, and then a regression relationship of the same position point between the value of G channel and Vh is established to calculate Vh. Finally reach calculation l * Is a target of (a). Thus, these input parameters of the 3D aggregation model areCalculated based on computer graphics.
The derivation of equation (19) is:
when the blades are randomly distributed, norman gives a mathematical form:
wherein: n (λ) represents the number of pore sizes greater than λ in the total ribbon length, ρ is the number of blades per unit area, σ is the blade area, w' is the average width of the blades perpendicular to the ribbon direction, D is the cutoff length, and ρσ=l e ，L e Is the effective leaf area index, and equation (23) becomes:
the effective leaf area index L in the formula (24) e Replaced by projected effective leaf area index L p The expression is:
setting elliptical blade to obtain projection area sigma of blade p ：
Consider the case of non-horizontal, L p Sum sigma p If the condition is introduced into the equation (24), the equation (24) becomes:
the expressions in the X-direction and the Y-direction are obtained from the formula (27):
wherein: lambda (lambda) 1 Is a variable, representing a random distribution of She Kongxi dimensions, with the blade tip parallel to the X direction, lambda 2 Also a variable, representing a random distribution of She Kongxi sizes, with the tips parallel to the Y direction.
The specific derivation of equation (20) is as follows:
according to the potential pore region (A) 1_x ,A 1_y ,A 2_x ,A 2_y ,A 14_x ,A 14_y ,A 3 ) By analyzing the geometric relationship, it is possible to obtain:
area of the pores that are paragenic and intergrowth in the X direction:
the pore region of the contra-generation and the inter-generation in the Y direction:
void area that is rotable in the X direction:
void area that is rotated in the Y direction:
the observation area of the optical device is: .
A t ＝D 1 D 2 (34)
Assuming that the probability of the void areas in the X-direction and the Y-direction are equal, the average value in the X-and Y-directions is used as 0.5[ eq. (formula (30))+ Eq. (formula (31)) ]/Eq. (formula (34)); the porosity of the randomly distributed blades with a rotavapor pattern in the monolayer in the horizontal case was 0.5[ eq. (equation (32)) + Eq. (equation (33)) ]/Eq. (equation (34)), resulting from that:
wherein:
A c ＝A 3 (λ 1 ,λ 2 )n(λ 1 )n(λ 2 ) (39)
wherein lambda is 1 Is from 0 to lambda 1_max Variable lambda of 2 Is from 0 to lambda 2_max Is a function of the variables of (1), and therefore,
P oa (λ 1 ,λ 2 ) And P w (λ 1 ,λ 2 ) Is a collection, namely:
P oa (0,0),P oa (1,0),P oa (1,1),L,P oa (λ 1_max ,λ 2_max -1),P oa (λ 1_max ,λ 2_max )(40)
P w (0,0),P w (1,0),P w (1,1),L,P w (λ 1_max ,λ 2_max -1),P w (λ 1_max ,λ 2_max )(41)
equation (40) and equation (41) reflect P oa (λ 1 ,λ 2 ) And P w (λ 1 ,λ 2 ) The average value is selected as the final result to reflect the overall situation, i.e
And->
/>
Calculating P in non-horizontal cases oa (λ 1 ,λ 2 ) And P w (λ 1 ,λ 2 ) The area change factor of the single layer from the horizontal condition to the non-horizontal condition, namely the ratio of the projected ellipse to the ellipse, needs to be calculated, and the formula is as follows:
in the non-horizontal case, there are only two variables of blade and void region, so the porosity of a randomly distributed blade with a para-or reciprocal mode in a single layer is:
in the non-horizontal case, the porosity of the randomly distributed blades with a rotation pattern in a single layer is:
the average value is chosen as the final result to reflect the composite situation P (a B), i.e.
And->
Obtaining
Wherein:
is P (A) or P (B), -, or a combination thereof>
Is P (A) or P (B).
The derivation process of the formula (5) is as follows:
because of the overlapping inertia system of the upper and lower voids, based on Bayesian analysis, the overlapping relationship in the vertical direction is obtained:
wherein: p (A) is one of the randomly distributed leaf porosities in the monolayer, and P (B) is one of the randomly distributed leaf porosities in the other monolayer;
since the void fraction (P) is smaller than 1 in the formula (48), the product thereof is a small value, so that it is ignored to obtain four cases:
the conditional probability is used in equation (49) to derive the mathematical relationship between P (a|b) and P (b|a):
using Monte Carlo method, assuming P (A|B) is a random number in the range of 0 to 1, then assuming randomly distributed leaf porosity as P r_1 ,P r_2 ,P r_3 And P r_4 Is obtained by the cumulative average of (a):
in the formula (51), P r Four cases P of (θ) r_1 ,P r_2 ,P r_3 And P r_4 With the same probability, δ is a random number between 0 and 1, i.e., P (a|b).
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. The crop leaf area index image analysis algorithm based on the three-dimensional aggregation index model is characterized by comprising the following steps of:
s1, constructing a 3D aggregation index model, and in order to describe the anisotropy of the horizontal distribution of the blade, analogy the method of the LX aggregation index model, namely a penetration function, and deducing a formula of the mathematical relationship between the porosity and the aggregation index, namely a 3D aggregation index model formula:
wherein: p (P) m (θ) porosity of non-randomly distributed blades, an input parameter to the model, representing porosity under field conditions measured in situ using DCP, P r (θ) is the porosity of the randomly distributed blades;
s2, calculating the porosity P of the randomly distributed blades r (θ) introduction of phyllotaxis in phytoclassification, i.e. the distribution of leaves on the stem in the horizontal direction comprises a para-genic mode, a reciprocal mode, a rotagenic mode, a clustering mode, based on which the porosity P of the leaves is randomly distributed r The calculation steps of (θ) are as follows:
s21, analyzing individual potential pore areas in the single layer, analytically calculating the individual potential pore areas of the randomly distributed blades by using grid analysis in vegetation coverage (FVC) measurement, wherein in the grid analysis, the pore areas in the blades with local random distribution are decomposed into four individual potential pore areas A according to the modes of paragenetic, intergrowth and rotagenetic i (lambda), i.e. void area 1, void area 2, void area 1X +4, void area 3, in X-direction and Y-direction, depending on the direction of the blade tipThere are two cases, so four individual potential pore areas A i (lambda) is further divided into 7: a is that 1_x ,A 1_y ,A 2_x ,A 2_y ,A 14_x ,A 14_y ,A 3 The formula table is as follows:
s22, calculating the average pore area A (lambda) of the single-layer randomly distributed blade:
A(λ)＝A i (λ)×n(λ) (3)
wherein: the number of individual potential pore regions in the n (λ) monolayer;
dividing the average pore area A (lambda) of randomly distributed blades in a monolayer by the viewing area A of the optical device t The porosity P (a B) of the randomly distributed blades in a single layer is obtained:
P(A∨B)＝A(λ)/A t (4)
wherein: v is the mathematical symbol "OR";
s23, deriving the porosity P in the vertical direction by considering the overlapping of the upper gap and the lower gap of the blade r The formula of (θ) is:
wherein: delta is a random number between 0 and 1;
s3, determining the actual size of the pixel representation, and calculating the actual length or the actual width in the image by adopting a geometrical optics principle, wherein a specific formula is as follows:
wherein: h the vertical height from the camera to the crown top and recorded in the measurement; the FOV is the field of view of the camera; actual length D in D image 1 Or the actual width D 2 Is a common symbol of (2)；
Equation (6) combines the number of pixels of the camera n pixel The actual pixel size d is obtained:
d＝D/n pixel (7)
s4, calculating the porosity P of the non-random distribution blade m (θ) converting a color image captured by a camera into a binary image using a spatial conversion technique of Lab, wherein a pixel value of 0 represents soil, 255 represents vegetation, and P is obtained based on the binary image m Formula of (θ):
wherein: n (N) s Is the number of soil pixels, N v Is the number of vegetation pixels;
s5, the porosity P of the obtained randomly distributed blade r Porosity P of (θ) and non-randomly distributed blades m And substituting the parameters obtained by (theta) and computer graphics coupling into the formula (2) to calculate the aggregation index.
2. The crop leaf area index image analysis algorithm based on the three-dimensional aggregation index model according to claim 1, wherein in step S1, the specific derivation method of the 3D aggregation index model is as follows:
s11, the penetration function is proposed in the Markov model:
wherein G (θ, θ) l ) The G function represents the projection function of the leaf area in the θ direction, namely:
wherein A (θ, θ) l ) Is a kernel function in equation (10) representing the fraction of the ratio between leaf density and leaf density in the θ direction, ψ=cos -1 (cotθcotθ l )，g(θ l ) Is the leaf inclination distribution function LADF, the Beta function was chosen to describe LADF, and in the study of the oblique spotting method, the G function was approximately equal to 0.5 when θ=57.5°, so equations (10) and (11) can be simplified as:
when the vanes are not randomly distributed, the porosity of the non-randomly distributed vanes is:
wherein Ω E The aggregation index is obtained by dividing the logarithm of the two sides of the formula (13) and the formula (9):
3. crop leaf based on a three-dimensional aggregation index model according to claim 1. An area index image analysis algorithm is characterized in that in step S2, the average pore area of randomly distributed blades in a monolayer is divided into average pore areas of randomly distributed blades in a monolayer having a para-or trans-biotic mode
And average pore area of single-layer wheel-shaped randomly distributed blades +.>
The expression is as follows:
wherein: lambda (lambda) 1 Is a variable representing randomly distributed blade pore size, blade tip parallel to X direction, lambda 2 Also a variable, representing randomly distributed pore size or randomly distributed blades, the tip of which is parallel to the Y direction, f being the ratio of the projected ellipse to the ellipse, f being a factor controlling the zenith angle porosity variation, expressed as:
in the formula (14), A a 、A b 、A c The pore area of the randomly distributed blades is expressed as follows:
wherein: w (w) * Is the average width of the blade, l * Is the average length of the blade, σ is the area of the blade, σ=0.25pi w * l * The actual area corresponding to the photo taken by the DCP is taken as the observation layer area, so D 1 Cut-off in the X direction, namely the photo length; d (D) 2 Is the truncation in the Y direction, i.e., the photo width;
n(λ 1 ) A random distribution She Kongxi representing blade tips parallel to the X direction is greater than lambda in size 1 Number, n (lambda) 2 ) The pore size of the randomly distributed blade representing parallel blade tips is greater than lambda 2 In the Y direction, the expression is:
wherein: l (L) p Is the projected effective leaf area index, L p ＝G(θ,θ l )L e /cosθ，G(θ,θ l ) Is the projection function of the leaf area in the theta direction, sigma p Is the projected area of the blade, w is the average width of the blade perpendicular to the cutting direction in the non-horizontal condition;
p (A, B) is divided into individual layers with average porosity of the randomly distributed leaf having a para-or trans-pattern
And average porosity of a single layer randomly distributed blade with a rotagenic pattern +.>
The expression of which expands to:
wherein: a is that t The actual area corresponding to the photographed region of the DCP is: a is that t ＝D 1 D 2 (21)
As can be seen from the above equation, equation (20) is obtained by dividing equation (5) by equation (21), and equation (20) is also a specific form of expansion of equation (4).
4. The crop leaf area index image analysis algorithm based on the three-dimensional aggregation index model according to claim 1, wherein in step S5, parameters obtained by computer graphics coupling are: length variable: cut-off D in X-direction 1 Cut-off D in Y direction 2 She Pingjun width w * Average length of leaf l * Average width w of leaf perpendicular to the direction of interception in non-horizontal condition, maximum pore size lambda in X-direction 1_max Maximum pore size lambda in Y direction 2_max The method comprises the steps of carrying out a first treatment on the surface of the Score variable: porosity P of non-randomly distributed blades m (θ)；
According to the formulas (6), (7) and (8), the maximum pore size lambda in the X direction can be obtained 1_max ：
for X＝i；n
for Y＝j；m
soil_value[i；j]＝max((value＝0) (22)
number_soil_pixel＝mumber(soil_value[*；j])
0 is soil pixel value, and lambda can be calculated by the same way 2_max And w;
extracting the edge of the blade by using a Canny operator, determining the image coordinates of the tip and the bottom of the blade, and calculating w based on the image coordinates of the tip and the bottom * And l * 。
5. A crop leaf area index image analysis algorithm based on a three-dimensional aggregation index model according to claim 3, wherein the derivation of equation (19) is:
when the blades are randomly distributed, norman gives a mathematical form:
wherein: n (λ) represents the number of pore sizes greater than λ in the total ribbon length, ρ is the number of blades per unit area, σ is the blade area, w' is the average width of the blades perpendicular to the ribbon direction, D is the cutoff length, and ρσ=l e ，L e Is the effective leaf area index, and equation (23) becomes:
the effective leaf area index L in the formula (24) e Replaced by projected effective leaf area index L p The expression is:
setting elliptical blade to obtain projection area sigma of blade p ：
Consider the case of non-horizontal, L p Sum sigma p If the condition is introduced into the equation (24), the equation (24) becomes:
the expressions in the X-direction and the Y-direction are obtained from the formula (27):
wherein: lambda (lambda) 1 Is a variable, representing a random distribution of She Kongxi dimensions, with the blade tip parallel to the X direction, lambda 2 Also a variable, representing a random distribution of She Kongxi sizes, with the tips parallel to the Y direction.
6. A crop leaf area index image analysis algorithm based on a three-dimensional aggregation index model according to claim 3, wherein the specific derivation of formula (20) is as follows:
according to the potential pore region (A) 1_x ,A 1_y ,A 2_x ,A 2_y ,A 14_x ,A 14_y ,A 3 ) By analyzing the geometric relationship, it is possible to obtain:
area of the pores that are paragenic and intergrowth in the X direction:
the pore region of the contra-generation and the inter-generation in the Y direction:
void area that is rotable in the X direction:
void area that is rotated in the Y direction:
the observation area of the optical device is:
A t ＝D 1 D 2 (34)
assuming that the probability of the void areas in the X-direction and the Y-direction are equal, the average value in the X-and Y-directions is used as 0.5[ eq. (formula (30))+ Eq. (formula (31)) ]/Eq. (formula (34)); the porosity of the randomly distributed blades with a rotagenic pattern in a single layer in the horizontal case is 0.5[ eq. (equation (32)) +
Eq. (equation (33)) ]/Eq. (equation (34)), thereby yielding:
wherein:
A c ＝A 3 (λ 1 ,λ 2 )n(λ 1 )n(λ 2 ) (39)
wherein lambda is 1 Is from 0 to lambda 1_max Variable lambda of 2 Is from 0 to lambda 2_max Thus, P oa (λ 1 ,λ 2 ) And P w (λ 1 ,λ 2 ) Is a collection, namely:
P oa (0,0),P oa (1,0),P oa (1,1),L,P oa (λ 1_max ,λ 2_max -1),P oa (λ 1_max ,λ 2_max )(40)
P w (0,0),P w (1,0),P w (1,1),L,P w (λ 1_max ,λ 2_max -1),P w (λ 1_max ,λ 2_max )(41)
equation (40) and equation (41) reflect P oa (λ 1 ,λ 2 ) And P w (λ 1 ,λ 2 ) The average value is selected as the final result to reflect the overall situation, i.e
And->
Calculating non-level conditionsP in case of oa (λ 1 ,λ 2 ) And P w (λ 1 ,λ 2 ) The area change factor of the single layer from the horizontal condition to the non-horizontal condition, namely the ratio of the projected ellipse to the ellipse, needs to be calculated, and the formula is as follows:
in the non-horizontal case, there are only two variables of blade and void region, so the porosity of a randomly distributed blade with a para-or reciprocal mode in a single layer is:
in the non-horizontal case, the porosity of the randomly distributed blades with a rotation pattern in a single layer is:
the average value is chosen as the final result to reflect the composite situation P (a B), i.e.
And->
Obtaining
Wherein:
is P (A) or P (B), -, or a combination thereof>
Is P (A) or P (B).
7. The three-dimensional aggregation index model-based crop leaf area index image analysis algorithm according to claim 1, wherein the derivation process of formula (5) is:
because of the overlapping inertia system of the upper and lower voids, based on Bayesian analysis, the overlapping relationship in the vertical direction is obtained:
wherein: p (A) is one of the randomly distributed leaf porosities in the monolayer, and P (B) is one of the randomly distributed leaf porosities in the other monolayer;
since the void fraction (P) is smaller than 1 in the formula (48), the product thereof is a small value, so that it is ignored to obtain four cases:
the conditional probability is used in equation (49) to derive the mathematical relationship between P (a|b) and P (b|a):
using Monte Carlo method, assuming P (A|B) is a random number in the range of 0 to 1, then assuming randomly distributed leaf porosity as P r_1 ，P r_2 ，P r_3 And P r_4 Is obtained by the cumulative average of (a):
in the formula (51), P r Four cases P of (θ) r_1 ，P r_2 ，P r_3 And P r_4 With the same probability, δ is a random number between 0 and 1, i.e., P (a|b).
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