CN109033562B - Method for calculating two-way reflection value of blade in curled state - Google Patents
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Abstract
The invention discloses a method for calculating a bidirectional reflectance value of a blade in a curled state, which comprises the following steps: establishing a curling blade form model and a global coordinate system; setting parameter information of a light source and a probe; dividing the curled leaves into micro-planes, and extracting the coordinates of the central point of each micro-plane; tracking from the sight direction of the probe by using a ray tracking algorithm, calculating the contribution of each micro-plane to the energy of the probe, and then integrating the energy reflected and transmitted by all the micro-planes in the field of view of the probe to obtain the energy reflected and transmitted by the blade received by the whole probe; calculating the energy of a lambertian body in the whole probe field of view under the condition of the lambertian body; the BRDF of the vane is calculated by the energy reflected and transmitted by the vane and the energy reflected by the Lambertian body received by the probe. The invention introduces a micro-plane and ray tracing algorithm, solves the BRDF calculation method of the leaf under the curling condition, and expands the plane BRDF model to a three-dimensional space.
Description
Technical Field
The invention relates to the technical field of blade optical measurement, in particular to a method for calculating a blade two-way reflection value in a curled state.
Background
The leaves are the main organs that receive photosynthetically active radiation in the 400nm-800nm range, whose photosynthetic properties differ with respect to wavelength and measurement configuration. The biochemical and anatomical information of the leaf can be obtained through the spectral and directional distribution of the incident light and the primary light. Most of the papers focus on correlating reflectance and transmission of the leaf spectrum with the content of chlorophyll, moisture, cellulose, nitrogen, etc. By such observation, Allen et al (1969) estimated the effective index of reflection for corn by a geometric optics based plate model. Jacquesoud and Baret (1990) have further developed a PROSPECT model that enables a more accurate estimation of the moisture, chlorophyll and dry matter content of different types of leaves. Woolley (1971), one of the first researchers interested in the spatial distribution of light reflected by cranberry, corn and soybean leaves, distinguished diffuse and specular reflectance, indicating that specular reflectance is quite different from what is normally assumed in most canopy reflectance models. Breece and Holmes (1971) scanned 19 narrow bands, and it was observed that the specular component was relatively more important in the strongly absorbing range. Finally, Brakke et al (1989) relate the characteristics of the diffuse and specular components to the anatomy of the blade, but their measurements are limited to a single band.
Previous scholars have emphasized in the study of optical properties of blades that if specular and diffuse components are to be distinguished, the correlation between biophysical parameters and remote sensing data needs to be improved. This is therefore closely related to distinguishing these two components in the reflection of the blade, as they carry different information. On the one hand, the diffuse reflection component is caused by multiple scattering of light rays inside the blade, the angular distribution of which is isotropic, and therefore the spectral change of which is determined by the biochemical information of the blade, and can be used to estimate the component content of the blade. On the other hand, the specular component is due to a single regular scattering at the blade surface, and is therefore determined by the biophysical properties of the surface. Its size and angular distribution make it possible to estimate the refractive index and the roughness of the epidermal layer. In contrast, in the visible range, leaf components like chlorophyll do not affect the spectral change of the specular reflection, or do so only minimally.
Since the two-way reflectance (BRDF) has been measured, a number of models have been proposed to fit them. Ward (1992) and Brakke et al (1989) propose simple equations for empirical parameter estimation. To explain the signal further, a physics-based model is necessary. Nicodermus et al (1977) describe in detail the concepts of dichroic reflection (BRDF) and dichroic transmission (BRTF) by collecting spectra and inverse variations of optical properties. It is now widely used in the field of remote sensing and computer generated graphics. Most BRDF models of surfaces with physical input parameters can be viewed as an ensemble of a specular and a diffuse component. The simplest way to describe the diffuse components is to assume the rays as a lambertian model of isotropy, which is, of course, an idealized behavior. Torrance and Sparrow (1967) lay the foundation for a more realistic surface BRDF model. They see the surface as a composition of many tiny surfaces that are much wider than the wavelength, and they use the laws of geometrical optics to derive the corresponding BRDF. Cook and Torrance (1981) continued the work with Oren and Nayar (1995) to obtain accurate representations of the specular and diffuse components. Covaerts et al (1966) used ray tracing techniques with Baranoski and Rokne (2004) to create a model to be able to be put into use. However, the high computation requirements prevent inversion of this model and are only applicable to BRDF calculations for flat blades.
Therefore, the invention introduces the micro-plane method, expands the plane BRDF model to the three-dimensional space model, thereby calculating the BRDF of the leaf in the curling state, introduces the ray tracing algorithm, starts the simulation ray transmission process from the reverse direction of the probe, greatly reduces the calculated amount, solves the BRDF calculation method of the leaf under the curling condition, provides a set of efficient calculation method for the curling leaf to reflect the spatial distribution characteristics of the incident light in the hemispherical direction, and can reversely show the surface attribute parameters of the leaf by the method.
Disclosure of Invention
At present, the BRDF simulation of the leaf is mostly limited to a plane model, and the BRDF simulation of the leaf in a curling state is rarely discussed. The invention aims to overcome the limitation of the conventional BRDF model and provides a method for calculating a Bidirectional Reflectance (BRDF) value of a blade in a curled state.
The invention introduces a micro-plane algorithm, expands a planar BRDF model to a three-dimensional space model, thereby calculating the BRDF of the leaf in a curling state, introduces a ray tracing algorithm starting from the reverse direction of a probe, simulates the reflection and transmission processes of rays between leaf micro-planes, greatly reduces the calculation amount of the BRDF simulation of the leaf starting from the incident light direction, solves the BRDF calculation method of the leaf under the curling condition, and has higher consistency with the actually measured BRDF of the curled leaf. Therefore, the attribute parameters of the surface of the curled leaf related to the BRDF can also be inverted by this method.
A method of calculating a leaf Bidirectional Reflectance (BRDF) value in a curled state, comprising the steps of:
step 1, establishing a curling blade shape model and a global coordinate system;
step 2, setting parameter information of a light source and a probe;
step 3, dividing the curled blades into a plurality of micro planes, and extracting the coordinates of the center point of each micro plane;
step 4, tracking the probe from the sight direction by using a ray tracking algorithm, calculating the contribution of each micro-plane to the energy of the probe, wherein the energy received by the probe comprises the energy reflected and transmitted by the blade, and then integrating the energy reflected and transmitted by all the micro-planes in the field of view of the probe so as to obtain the energy reflected and transmitted by the blade received by the whole probe;
step 5, calculating the energy reflected by the Lambert body in the whole probe field of view under the Lambert body condition;
and 6, calculating the Bidirectional Reflectance (BRDF) value of the curled blade.
In the step 1, establishing a curling blade shape model and a global coordinate system, which specifically comprises the following steps:
the center of the blade is used as an original point O, the long axis is used as a Y axis, the short axis is used as an X axis, a normal line passing through the origin of the XY plane is used as a Z axis, a global Cartesian coordinate system of the whole simulation process is established, and the blade is abstracted into an ellipse which is curled in a three-dimensional space. The blade is abstracted into an ellipse, the curled blade is abstracted into a three-dimensional space curled ellipse, and the curling degree, the length of a long shaft and the length of a short shaft of the blade are set.
In step 2, setting parameter information of the light source and the probe, specifically comprising:
the position information, the light source intensity and the incident direction of the light rays of the light source are set, the angle of view of the probe, the central direction of the view field of the probe and the position parameters are set, and the emergent direction of the light rays is also the central direction of the view field of the probe. In a cartesian coordinate system, the incident direction of the light and the center direction of the field of view of the probe can be expressed by unit vectors.
In step 3, the curled leaves are divided into a plurality of micro-planes (preferably 1/16 mm)2) Extracting the coordinates of the central point of each micro-plane, which specifically comprises the following steps:
dividing the curled blades into 1/16mm2The distance between the center points of the adjacent micro-planes is 1/4mm, the blade is curled,the symmetrical plane is a YOZ plane, and the X-axis coordinate intervals of the central points of the adjacent micro-planes are equal and are 1/4 mm; the Y-axis coordinate intervals of the central points of the adjacent micro-planes are not equal and are obtained by an iterative method; and after obtaining the Y-axis coordinate of the central point of the micro plane, obtaining the Z-axis coordinate through a blade curling equation, thereby obtaining the central point coordinate of each blade micro plane.
In step 4, calculating the contribution of each micro-plane to the energy of the probe, specifically comprising:
first, it is determined whether a two-way reflection distribution function or a transmission distribution function should be used, and whether a ray iteration algorithm should be used is determined as follows:
1. if the sight is on the front side of the blade and the light is on the back side of the blade, a transmission distribution function is required to be used, and iteration is not considered;
2. if the sight is on the back of the blade and the light is on the front of the blade, a transmission distribution function is needed, and iteration is not considered;
3. if the sight line is on the back of the blade and the light is on the back of the blade, a two-way reflection distribution function is needed, and iteration is not considered;
4. if the line of sight is on the front of the blade and the light is on the front of the blade, which is the reflection case, it is necessary to use an iterative algorithm and a two-way reflection distribution function of the light, when the light of the iteration is attenuated to be less than the original light source intensity of 1 × 10 through transmission or reflection-3And stopping iteration, and taking the energy obtained by iteration of the optical path as the contribution of the micro-plane to the energy of the probe.
In order to avoid huge operation amount of ray tracking from the incident direction of a light source, a reverse ray tracking algorithm is adopted, tracking is carried out from the direction of a sight line, a light path is regarded as being emitted from the direction of the sight line, finally, the energy reflected and transmitted by each micro plane in the view field of the probe is obtained through iterative calculation, and then the energy obtained in the whole probe is obtained by integrating the energy reflected and transmitted by all the micro planes in the view field of the whole probe.
Step 5, calculating the energy reflected by the Lambert body in the whole probe field of view under the Lambert body condition, wherein the method specifically comprises the following steps;
white board with lambertian bodyIs divided into 1/16mm2And extracting the coordinates of the central point of each micro-plane, and calculating through a two-way reflection distribution function and an integral to obtain the energy reflected by the lambertian body in the whole probe field of view.
Step 6, calculating a Bidirectional Reflectance (BRDF) value of the curled blade, which specifically comprises the following steps:
the reflectivity of the blade is obtained by the ratio of the energy reflected and transmitted by the blade received by the probe in step 4 to the energy reflected by the lambertian body within the field of view of the probe in step 5, and the reflectivity ratio pi obtains the Bidirectional Reflectance (BRDF) value of the blade in the fixed incident and reflection directions.
Compared with the prior art, the invention has the advantages that:
1. the BRDF of the curled leaf can be accurately simulated, so that the BRDF distribution characteristics of the leaf in the hemispherical direction can be directly calculated by the method, the workload of observing the BRDF distribution characteristics of the curled leaf through experiments is reduced, and the observation cost can be effectively reduced;
2. introducing a micro-plane algorithm, and expanding a planar BRDF model to a three-dimensional space model, so that the calculation is closer to the natural form of the blade;
3. a ray tracing algorithm starting from the reverse direction of the probe is introduced to simulate the reflection and transmission processes of rays between the leaf micro-planes, so that the calculation amount of the BRDF simulation of the leaves starting from the incident light direction is greatly reduced.
Drawings
FIG. 1 is a flow chart of a method of calculating a Bidirectional Reflectance (BRDF) value of a blade in a curled state according to the present invention;
FIG. 2 is a graph of BRDF distribution in the hemispherical direction for measured curled blades;
FIG. 3 is a BRDF profile in the hemispherical direction for a crimped leaf simulated using the method of the present invention.
Detailed Description
The invention is further illustrated by the following specific figures and examples.
As shown in fig. 1: the invention relates to a method for calculating BRDF (bidirectional reflectance distribution function) of leaves in a curled state, which comprises the following steps:
step 1, establishing a blade form model and a global coordinate system;
specifically, the curling degree, the length of a long shaft and the length of a short shaft of the blade are set, the center of the blade is taken as an origin O, the long shaft is taken as a Y shaft, the short shaft is taken as an X shaft, a normal line passing through the origin of an XY plane is taken as a Z shaft, a global Cartesian coordinate system of the whole simulation process is established, and the blade is abstracted into an ellipse curling in a three-dimensional space.
And 2, setting parameter information of the light source and the probe.
In particular, the two-way reflection is mainly about reflection of light rays in different directions upon incidence and emergence. The radiation brightness in the exit direction is different due to the different angle between the light incidence and exit. Here, position information of the light source, intensity of the light source, and an incident direction of the light ray are set, and a probe view field angle, a probe view field center direction, that is, an exit direction of the light ray, and position parameters are set. In a cartesian coordinate system, the incident direction of light and the center direction of the field of view can be expressed by unit vectors.
Step 3, dividing the curled blades into 1/16mm2Extracting the coordinates of the central point of each micro-plane;
in the practice of the invention, the curled blades were divided into 1/16mm2The coordinates of the center point of each micro-plane are extracted. The distance between the center points of the adjacent micro-planes is 1/4 mm. Since the leaf is curled and the plane of symmetry is the YOZ plane, the X-axis coordinates of the center points of adjacent micro-planes are equally spaced, 1/4 mm. But the Y-axis coordinate intervals of the central points of the adjacent micro-planes are not equal and need to be obtained through an iterative method. After the Y-axis coordinate of the central point of the micro-plane is obtained, the Z-axis coordinate can be obtained through a leaf curling equation. Thereby obtaining the center point coordinates of each blade micro-plane.
Step 4, tracking the probe from the sight direction by using a ray tracking algorithm, calculating the contribution of each micro-plane to the energy of the probe, and then integrating the energy reflected and transmitted by the micro-planes in the field of view of the probe so as to obtain the energy reflected and transmitted by the blade received by the whole probe;
in the implementation of the invention, in order to avoid huge operation amount of ray tracking from the incident direction of a light source, a reverse ray tracking algorithm is adopted, wherein tracking is carried out from the direction of the sight line, a light path is regarded as being emitted from the direction of the sight line, finally, the energy reflected and transmitted by each micro plane in the view field of the probe is obtained through iterative calculation, and then, the energy obtained in the whole probe is obtained by integrating the energy reflected and transmitted by all the micro planes in the view field of the whole probe. Here, if the center of the leaf micro-plane is within the field of view of the probe, the center of the leaf micro-plane is considered to have an intersection point with the line of sight, and the normal of the tangent plane where the intersection point is located is calculated. Establishing a local coordinate system by taking the normal of a tangent plane as a z-axis, storing the coordinate system into a 3 x 3 matrix, converting incident light rays and emergent light rays from a global coordinate system into a local coordinate system for representation, judging the intersection condition of the sight and the light rays on the blade, judging whether a two-way reflection distribution function or a transmission distribution function is used, and judging whether a light ray iterative algorithm is used.
The following cases are mainly divided:
1. if the line of sight is on the front of the blade and the light is on the back of the blade, which is a transmission case, since the intensity of the transmitted contribution is small, there is no need to consider the iteration of the light, only the transmission distribution function.
2. If the line of sight is at the back of the blade and the light is at the front of the blade, which is a transmission case, only the transmission distribution function needs to be considered.
3. If the line of sight is at the back of the blade and the ray is at the back of the blade, which is the reflection case, only the dichroic reflection distribution function needs to be considered, and since the back of the blade is convex, the mutual reflection between the micro-planes of the blade does not need to be considered, so the iteration of the ray does not need to be considered.
4. If the line of sight is on the front of the blade and the light is on the front of the blade, which is the case of reflection, it is necessary to use an iterative algorithm of light and a dichroic distribution function when the light of the iteration is attenuated to less than the initial source intensity of 1 × 10 by transmission or reflection-3And stopping iteration, and taking the energy obtained by iteration of the optical path as the contribution of the micro-plane to the energy of the probe.
And judging the transmission and reflection conditions in the light ray tracking process, and calculating the energy of the light rays reflected and transmitted out of the blade micro-plane by using the transmission and reflection distribution functions respectively.
Specifically, for the energy calculation of the reflection case, the radiance (R) of the reflected light of the leaf micro-plane can be obtained by multiplying irradiance (I) by a Bidirectional Reflection Distribution Function (BRDF) as shown in formula (1):
wherein, λ, θs、
θvAnd
respectively, the wavelength of the incident light, the incident zenith angle, the incident azimuth angle, the sight line zenith angle and the sight line azimuth angle. In general, the angle of incidence
The convention is set to 0. The BRDF function of a blade is also related to the refractive index and roughness coefficient of the blade. The calculation of the BRDF can be assumed to be the sum of the diffuse and specular reflection, respectively called BRDFdiffAnd BRDFspecAs shown in formula (2)
BRDF＝BRDFdiff+BRDFspec(2)
Where the diffuse component represents a small fraction of the reflected light, it is not a single specular reflection of the blade surface. We assume it as a diffuse reflecting Lambertian behavior and strongly wavelength dependent, so the BRDFdiffCan be written as:
wherein 1/pi is the BRDF, k of complete Lambertian scatteringL(λ) is the lambertian coefficient with the wavelength λ.
For specularly reflective parts, BRDFspecCan be expressed in the following form:
wherein, F (n, theta)a) Is a Fresnel factor consisting of the refractive index n of the leaf surface material and the angle of incidence θ at the normal to the micro-plane and in the direction of the incident lightaDecision α denotes the tilt angle of the facets at a lower scale, n is the refractive index of the blade and σ is the roughness coefficient.
Specifically, for the energy calculation of the transmission case, the irradiance (I) of the incident light can be converted into the radiance (R) of the transmitted light by the transmission distribution function, as shown in formula (5):
wherein the transmission distribution function is shown in the following formula (6):
wherein, tau is a transmittance parameter, kL(λ) is a Lambertian parameter.
Step 5, calculating the energy reflected by the Lambertian body in the field of view of the probe;
specifically, the lambertian white board was divided into 1/16mm2The coordinates of the center point of each micro-plane are extracted. The distance between the center points of the adjacent micro-planes is 1/4 mm. Because the white board is horizontal and the horizontal plane is an XOY plane, the Z-axis coordinates of the center points of the micro-planes are all 0, the X-axis coordinates of the center points of the adjacent micro-planes are all 1/4mm, and the Y-axis coordinates of the center points of the adjacent micro-planes are all 1/4 mm. In actual measurement, the reflectivity of the blade observed in the field angle range of the probe is the light intensity of the white board received by the probe in the same field angle range compared with the light intensity of the blade received by the probe, so a white board is simulated in the program, andand (5) carrying out corresponding treatment on the blades of the model. Since the whiteboard is lambertian, the dichroic reflection distribution function of the whiteboard is as shown in equation (3).
And 6, calculating the BRDF of the curled leaves in the whole hemispherical direction.
In the implementation of the invention, the reflectivity of the blade is obtained by the ratio of the energy of the blade received by the probe and transmitted in the step 4 to the energy of the white board received by the probe in the step 5, the BRDF value of the blade in the fixed incident and reflection directions is obtained by pi of the reflectivity ratio, and then the BRDF distribution of the blade in the whole hemispherical direction is drawn. In fig. 2, under the condition that the incident light source is at a zenith angle of 40 ° and an azimuth angle of 0 °, the actually measured BRDF of the blade in the hemispherical direction is shown, the asterisk indicates the position of the light source, and the black dot indicates the position observed by the probe. FIG. 3 is a diagram showing the BRDF of a blade in the hemispherical direction under the condition that an incident light source is at a zenith angle of 40 degrees and an azimuth angle of 0 degree, wherein asterisks indicate the positions of the light sources, and black dots indicate the positions observed by a probe. As can be seen by comparing FIGS. 2 and 3, the BRDF of the crimped leaf in the hemispherical direction simulated using the present invention is highly consistent with the BRDF of the measured crimped leaf in the hemispherical direction.
Claims (5)
1. A method for calculating a blade two-way reflection value in a curling state is characterized by comprising the following steps:
step 1, establishing a curling blade shape model and a global coordinate system;
step 2, setting parameter information of a light source and a probe;
step 3, dividing the curled leaf into a plurality of micro-planes, and extracting the coordinates of the center point of each micro-plane, wherein the method specifically comprises the following steps:
dividing the curled blades into 1/16mm2The distance between the central points of the adjacent micro-planes is 1/4mm, the blades are curled, the symmetry plane is a YOZ plane, and the X-axis coordinate intervals of the central points of the adjacent micro-planes are equal and are 1/4 mm; the Y-axis coordinate intervals of the central points of the adjacent micro-planes are not equal and are obtained by an iterative method; obtaining Y-axis coordinates of the central point of the micro-plane, obtaining Z-axis coordinates through a leaf curling equation, and obtaining each leafCoordinates of the center point of the sheet micro-plane;
step 4, tracking the probe from the sight direction by using a ray tracking algorithm, calculating the contribution of each micro-plane to the energy of the probe, wherein the energy received by the probe comprises the energy reflected and transmitted by the blade, and then integrating the energy reflected and transmitted by all the micro-planes in the field of view of the probe so as to obtain the energy reflected and transmitted by the blade received by the whole probe;
step 5, calculating the energy reflected by the Lambert body in the whole probe field of view under the Lambert body condition;
and 6, calculating the two-way reflection value of the curled blade.
2. The method for calculating the blade bidirectional reflectance value in the curled state according to claim 1, wherein in the step 1, establishing a curled blade shape model and a global coordinate system specifically comprises:
the method comprises the steps of establishing a global Cartesian coordinate system of the whole simulation process by taking the center of a blade as an origin O, a long axis as a Y axis, a short axis as an X axis and a normal passing through the origin of an XY plane as a Z axis, abstracting the blade into an ellipse curled in a three-dimensional space, abstracting the blade into the ellipse, abstracting the curled blade into the ellipse in the three-dimensional space, and setting the curling degree, the length of the long axis and the length of the short axis of the blade.
3. The method for calculating the blade dichroic reflection value in the curling state according to claim 1, wherein in the step 2, the setting of the parameter information of the light source and the probe specifically comprises:
the method comprises the steps of setting position information of a light source, light source intensity and the incident direction of light, setting a probe view field angle, a probe view field center direction and position parameters, wherein the emergent direction of the light is also the probe view field center direction, and in a Cartesian coordinate system, the incident direction of the light and the probe view field center direction are expressed by unit vectors.
4. The method for calculating the blade bidirectional reflectance value in the curled state according to claim 1, wherein in the step 4, the calculating of the contribution of each micro-plane to the probe energy specifically comprises:
first, it is determined whether a two-way reflection distribution function or a transmission distribution function should be used, and whether a ray iteration algorithm should be used is determined as follows:
4.1, if the sight is on the front side of the blade and the light is on the back side of the blade, a transmission distribution function is required to be used, and iteration is not considered;
4.2, if the sight is on the back of the blade and the light is on the front of the blade, a transmission distribution function is needed to be used, and iteration is not considered;
4.3, if the sight line is on the back of the blade and the light is on the back of the blade, a two-way reflection distribution function is needed to be used, and iteration is not considered;
4.4 if the line of sight is on the front of the blade and the light is on the front of the blade, which is the reflection case, it is necessary to use the iterative algorithm and the two-way reflection distribution function of the light, when the iterative light is attenuated to be less than the original light source intensity 1 × 10 by transmission or reflection-3And stopping iteration, and taking the energy obtained by iteration of the optical path as the contribution of the micro-plane to the energy of the probe.
5. The method for calculating the blade dichroic reflection value in the curled state according to claim 1, wherein the step 6 of calculating the dichroic reflection value of the curled blade specifically comprises:
the reflectivity of the blade is obtained through the ratio of the energy reflected and transmitted by the blade received by the probe in the step 4 to the energy reflected by the lambertian body in the whole field of view of the probe in the step 5, and the reflectivity ratio pi obtains the two-way reflection value of the blade in the fixed incidence and reflection directions.
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