Improving Otsu Method Parameters for Accurate and Efficient in LAI Measurement Using Fisheye Lens

Abstract

The leaf area index (LAI) is an essential indicator for assessing vegetation growth and understanding the dynamics of forest ecosystems and is defined as the ratio of the total leaf surface area in the plant canopy to the corresponding surface area below it. LAI has applications for obtaining information on plant health, carbon cycling, and forest ecosystems. Due to their price and portability, mobile devices are becoming an alternative to measuring LAI. In this research, a new method for estimating LAI using a smart device with a fisheye lens (SFL) is proposed. The traditional Otsu method was enhanced to improve the accuracy and efficiency of foreground segmentation. The experimental samples were located in Gansu Ziwuling National Forest Park in Qingyang. In the accuracy parameter improvement experiment, the variance of the average LAI value obtained by using both zenith angle segmentation and azimuth angle segmentation methods was reduced by 50%. The results show that the segmentation of the front and back scenes of the new Otsu method is more accurate, and the obtained LAI values are more reliable. In the efficiency parameter improvement experiment, the time spent is reduced by 17.85% when the enhanced Otsu method is used to ensure that the data anomaly rate does not exceed 10%, which improves the integration of the algorithm into mobile devices and the efficiency of obtaining LAI. This study provides a fast and effective method for the near-ground measurement of forest vegetation productivity and provides help for the calculation of forest carbon sequestration efficiency, oxygen release rate, and forest water and soil conservation ability.

1. Introduction

The leaf area index (LAI) is a measure of plant cover density and vegetation blocking sunlight. Its units are expressed in square meters of leaf area per square meter of ground area (m²/m²). LAI was first introduced by Watson in 1947 and is defined as the ratio of the total surface area of a leaf in the plant canopy to the corresponding surface area below it [1]. In general, the leaf area index of vegetation is usually between 0.5 and 6. Its exact value will vary depending on the situation. Areas such as short grasslands and shrublands typically have a lower leaf area index, while areas such as forests have a higher leaf area index. As an important structural parameter of the ecosystem, LAI provides information on the canopy status regarding the assemblage of above-ground plant elements on a spatio-temporal basis [2]. It can be used to evaluate vegetation growth status, productivity [3,4], photosynthesis intensity [5], water use efficiency [6], etc., and has a wide range of applications in obtaining plant health, carbon cycle, and forest ecosystem information.

According to whether or not they are exposed to the vegetation environment, LAI measurement technology can be divided into direct measurement and indirect measurement [7,8,9]. Direct measurement methods, including mass and sampling, can cause serious damage to vegetation [10]. Due to the complex manual operation required by personnel, direct measurement can be costly and difficult to apply to large-scale measurement work [11]. The mass method requires collecting fallen leaves from the forest environment for weighing, obtaining parameters such as leaf density, and then calculating the LAI. The sampling method involves taking leaves from growing plants and calculating LAI based on the number and area of the leaves.

At present, indirect measurements are widely developed, and LAIs are mainly estimated by measuring other variables such as canopy clearance ratio or transmittance radiant intensity [12,13]. Indirect measurement methods have the characteristics of convenience, automation, and non-destructiveness, and the specific classification includes radar remote sensing and optical remote sensing. Radar remote sensing is penetrating and less affected by light. Because it can penetrate the tree canopy, radar remote sensing combining radar and laser technology can quickly obtain high-precision forest canopy and internal structure parameters in a large area. The disadvantage of using lidar to calculate the leaf area index is that there is a loss of information in the scanning of the target object. And compared with smart devices, lidar equipment needs to be purchased separately, which is inconvenient to carry.

In the optical remote sensing method, Digital Hemispherical Photography (DHP) is an imaging technique used to study forest ecosystems and vegetation structure. Digital hemispheric photography has been widely used for the estimation of LAI values [14,15]. DHP usually captures ecological parameters such as the leaf area index (LAI) of vegetation by photographing the hemispheric region directly above vegetation and dividing the vegetation and background pixels in the image into the foreground and background. DHP has been widely used for LAI measurement of various vegetation types [16,17]. The use of Unmanned Aerial Vehicles (UAV) as a remote sensing platform has recently gained increasing attention, but their applications in forestry are still at an experimental stage [18]. Unmanned aerial vehicle low-altitude remote sensing monitoring has the characteristics of non-contact, large area, high efficiency, and strong adaptability [19]. High-resolution images from unmanned aerial vehicles can be used to describe the state of forests at regular time periods in a cost-effective manner [20]. In the process of implementing forestry-related projects, drone technology also faces some problems. These include insufficient UAV battery capacity, the high price of UAV sensors, difficulty in multi-source data fusion, limited UAV clustering and intelligence capabilities, and the urgent need to improve UAV-related laws and regulations [21].

The main software types include commercial software such as HemiView V2.1 and WinScanopy (2014) and free software such as CSN-EYE V6.496, CIMES (2022), GLA V2.0, etc. [22,23]. Obtaining LAI through DHP has the advantages of low cost and convenient operation. However, after acquiring canopy images, due to the complexity of the equipment used to measure canopy parameters and the high operation cost, the related equipment technology is not yet mature, and the existing technology is few. The process of obtaining LAI using computer software cannot be carried out in the field, which limits the real-time development of field measurement work. This cannot meet the current need for large-scale access to forest ecological samples [24,25,26].

As a supplement and alternative tool to commercial instruments, smart devices have the advantages of portability, multi-function, and ease of use, providing a more convenient and efficient solution for data acquisition and processing. In 2013, Confalonieri et al. proposed two methods for measuring the LAI of tree canopy, called APP-L and APP-G [27]. In 2015, Patrignani et al. produced an application to obtain LAI by inversion of the gap score on a smartphone, in which the Canopeo method was employed [28]. In 2016, De et al. estimated the LAI of the grapevine canopy via a smartphone or tablet and proposed the VitiCanopy method [29]. In 2018, Wang et al. captured tree canopy images with a smartphone with a fisheye lens and proposed a method called LAI-Mobile to obtain LAI values indoors via computers [30]. In 2020, Qu et al. proposed a method for estimating LAIs applied to oblique smartphone cameras [31]. In summary, in the research on the participation of smart devices in obtaining LAI, the shooting and calculation links are mostly split into two parts.

In this research, fisheye lenses were used to acquire images. The improvement of the Otsu method parameters provided a more efficient and accurate method for evaluating leaf area index. In order to overcome the influence of fisheye lens distortion and uneven light, the zenith angle segmentation and azimuth angle segmentation methods were proposed to obtain more accurate foreground and foreground segmentation effects. In terms of efficiency parameter improvement, a method of obtaining the threshold of traversal interval according to the histogram is proposed, which improves the efficiency of foreground and foreground segmentation.

This study provides a useful tool for the study of ecological indicators in the ecological environment and has great significance for the development and protection of forest resources.

2. Study Area and Data Source

This research was conducted in Ziwuling National Forest Park, Qingyang City, Gansu Province, China (108°34′ E, 35°26′ N). Gansu Ziwuling National Forest consists of four major areas: Huachi, Ningxian, Heshui, and Zhengning.

Gansu Ziwuling National Forest Park is composed of four major areas: Huachi, Ningxian, Heshui, and Zhengning, with an area of 37,350 hectares, located in the temperate climate zone, mostly in the hilly and gully area of the Loess Plateau, with a forest coverage rate of 84.42%. The vegetation of the park mainly includes evergreen coniferous and deciduous broad-leaved mixed forest, deciduous broad-leaved forest, temperate coniferous forest, and other types, mainly natural secondary forest on the Loess Plateau (Figure 1).

According to the vegetation type, it was divided into different experimental sampling groups, such as coniferous forest, broad-leaved forest, and mixed coniferous and broad-leaved forest. Eighty ideal sampling points were randomly selected in each group, and corresponding SFL images were taken (

Table 1. Overview of the samples in the experimental area.

SN	Name of Vegetation	Type of Vegetation	Experimental Site	Number of Plots
1	Quercus wutaishanica	broadleaf forests	Qingyang, Gansu, China	80
2	Robinia pseudoacacia	broadleaf forests	Qingyang, Gansu, China	80
3	Pinus tabuliformis and Robinia pseudoacacia	mixed coniferous and broadleaved forest	Qingyang, Gansu, China	80

).

In this research, when measuring LAI using a smartphone, the height of the device from the ground was kept at about 1 m, and the front camera was ensured to shoot vertically upwards. The equipment has a certain height from the ground, mainly to prevent photographing portraits and ground plants, and one meter is taken to facilitate operation. The fisheye lens used in this study is Yum Wind Proud, with a 180° viewing angle and a double-layer coating. In order to avoid measurement errors due to poor light and direct sunlight, the time period between 10:00 am and 2:00 pm was selected for LAI measurement images. The program that calculates the LAI will be run locally on the smartphone for subsequent calculations and processing. Smartphones can also be replaced by other mobile devices, such as tablets, laptops, and other smart devices that have both shooting and computing capabilities.

3. Enhanced Otsu Method in SFL

3.1. Traditional Otsu Method in SFL

In the measurement of LAI, obtaining forest canopy parameter information from fisheye images plays an important role, which will directly affect the measurement accuracy. Currently, forest canopy information is mainly obtained from fisheye images through the binarization process. The binarization process refers to segmenting the circular effective area in the fisheye image into the foreground vegetation and the background sky. The porosity of the tree canopy is obtained by calculating the proportion of foreground and background, which is used as a forest canopy parameter for calculating leaf area index. Binarization methods include the fixed threshold method, the Otsu method, etc. The fixed threshold method has poor segmentation results due to subjective influence. The Otsu method, also called the maximum inter-class variance method, was first proposed by the Japanese scholar Otsu in 1979 [32,33,34,35]. This method traverses the image histogram and calculates the maximum inter-class variance as the threshold for segmenting the foreground and background of the image. It has the advantages of strong versatility and adaptability. The inter-class variance is defined as follows:

$${\sigma }_{\mathrm{B}}^2={{\omega }_0{\omega }_1(u_0-u_1)}^2$$

(1)

where ${\omega }_0$ is the proportion of pixels contained in the first category under threshold T segmentation, ${\omega }_1$ is the proportion of pixels contained in the second category, $u_0$ is the average gray value of the pixels of the first category, and $u_1$ is the average gray value of the pixels of the second category. When T traverses all grayscale values from 0 to 255, the interclass variance ${\sigma }^2$ can reach the maximum value. The threshold T currently is the best threshold for segmentation.

Porosity is the proportion of the bright void in the middle of the tree to the total area, and the hemispherical image under the fisheye lens is represented as the ratio of the pixels of the background image to the pixels of the effective area of the circle [36].

$$P(\theta )=\frac{C_0\left(\theta \right)}{C_0\left(\theta \right)+C_1\left(\theta \right)}$$

(2)

where $P\left(\theta \right)$ represents the canopy porosity at the zenith angle $\theta$, while $C_0\left(\theta \right)$ and $C_1\left(\theta \right)$ represent the number of pixels in the background and foreground at the zenith angle $\theta$ [37].

3.2. Accuracy Parameter Improvement Based on Otsu Method

Otsu’s method is a powerful image processing tool, particularly useful in scenarios where automatic threshold determination is required for accurate image binarization. However, it also has limitations and may not be suitable for images with complex backgrounds or significant variations in lighting conditions, necessitating consideration of enhancement methods in specific situations. Fisheye lens distortion and uneven illumination distribution will significantly reduce the accuracy of the traditional Otsu method of LAI measurement. This study analyzes the influencing mechanisms of the two factors and provides accuracy parameters and improvement methods, respectively.

3.2.1. Fisheye Lens Distortion and Zenith Angle Segmentation Method

In order to project the infinite three-dimensional space into a limited two-dimensional image plane, the fisheye lens uses a certain projection model. The projection model causes image distortion in order to meet imaging requirements. Projection models are generally divided into four types: equidistant projection, equiangular projection, orthographic projection, and stereographic projection, as shown in

Table 2. Fisheye lens projection models.

Projection Model	Projection Function	Features
Equidistant Projection	$r_d=f\theta$	The distance from the center is proportional to the incidence angle.
Equiangular Projection	$r_d=2fsin(\theta /2)$	The solid angle occupied by the object remains constant.
Orthographic Projection	$r_d=fsin\left(\theta \right)$	The distortion is the largest, and the maximum view field cannot be greater than 180°.

.

Where $r_d$ is the distance between the point in the two-dimensional image and the distortion center point. $f$ is the focal length of the fisheye lens. $\theta$ is the incident angle between the optical axis of the fisheye lens and the incident light.

The equidistant projection fisheye lens used in this research. According to the isometric projection model, the fisheye camera lens has serious distortion, and the degree of distortion increases toward the outside of the image. This will cause the center area of the circular image near the zenith angle of 0°, which is less distorted, to contain less scenery, with a brighter field of view and stronger illumination. Correspondingly, the edge area near the zenith angle of 90$°$ is seriously distorted, with more scenery, darker fields of view, and poor lighting. The smaller image area accommodates far more scenes than the central area. In this case, directly applying the traditional Otsu method to the entire image for binarization will cause errors in foreground and background segmentation and affect the accuracy of LAI measurement.

In order to solve the LAI measurement error caused by fisheye lens distortion, this research proposes a zenith angle segmentation method based on the Otsu method. Based on the characteristic that the distortion of the fisheye image increases with the zenith angle, this method divides the circular effective area in the fisheye image into rings based on the zenith angle and uses the Otsu method to perform threshold segmentation in each ring area. And use the corresponding porosity obtained in different zenith-angle areas to perform LAI inversion to obtain a more accurate LAI.

In the zenith-angle segmentation method based on the Otsu method, the circular effective area of the fisheye image can be subdivided into various forms according to the zenith angle. In practical applications, considering computing speed and effect, this research uses equal-radius segmentation to divide the circular effective area into three parts (Figure 2).

3.2.2. Uneven Light Distribution and Azimuth Angle Segmentation Method

When measuring leaf area index with a fisheye lens, the distribution of the canopy is not uniform at different azimuth angles, and the light source is also uneven. Where there are tree trunks, the sky area is relatively small, and the brightness in this area is generally low. In addition, the sun has a certain angle relative to the shooting position, and the overall brightness in the direction close to the sun is higher, which will also aggravate the uneven light. This makes the sky representing the background at different azimuth angles unevenly distributed, even if located in the same zenith-angle ring. Brighter areas and darker areas will still interfere with each other, affecting the accuracy of the Otsu method.

In order to solve the difficulty in distinguishing the foreground and background caused by uneven light distribution, this study proposes an azimuth segmentation method based on the Otsu method. This method is based on the zenith-angle segmentation method and further segments different azimuth angles within the same segmentation ring to ensure the reliability of threshold segmentation. To balance computing speed and segmentation effect, the azimuth segmentation step size in this study was 60°, and each ring segmentation area was equally divided into six parts (Figure 3).

3.3. Efficiency Parameter Improvement Based on Otsu Method

As a leaf area index measurement method is applied to mobile devices, more efficient image processing is required. In addition, the calculation amount of the Otsu method will further increase after the zenith angle and azimuth angle segmentation strategies are used, and it is even more necessary to improve the calculation speed of the Otsu method. When Otsu’s method looks for the optimal threshold, it traverses the brightness levels from 0 to 255, which is less efficient. When collecting fisheye lens photos, it is ensured that the image will not appear in extreme situations of being too bright or too dark, so the numbers close to both ends of the traversal range cannot be the optimal segmentation threshold. Therefore, consider narrowing the traversal range to enhance the Otsu method segmentation calculation speed.

The green channel is sensitive to the canopy foreground and sky background. As shown in the figure, this is the green channel histogram of the fisheye image. The range close to 0 in the histogram represents the sky with higher brightness, and the remaining part is the tree canopy with lower brightness. The peak at 255 is caused by the black edges in the image; do not consider it the peak. At this condition, the histogram of the green channel has only one significant peak, usually around 15. Experience shows that the optimal threshold for fisheye images calculated by the Otsu method is generally between 100 and 160. Therefore, the optimal threshold can be calculated in the interval from the peak to the back to achieve the purpose of reducing the number of calculations. In order to further speed up the calculation of the optimal threshold, the two-sided interval constraint and multiple interval constraint methods can be used. A two-sided interval constraint refers to simultaneously reducing the length of the interval where the wave peak is located on both sides of the interval from 0 to 255. For example, if the brightness level of the peak is 15, then the brightness level on both sides of the range from 0 to 255 will be reduced by 15 towards the middle; that is, the optimal threshold will be found between 16 and 240. The multiple interval constraint refers to using the multiple peak value as the search range-reducing value. In the LAI calculation, both two-sided interval constraints and multiple interval constraints are used to obtain a higher calculation speed. The Otsu method efficiency parameter improvement algorithm is as follows (Figure 4):

4. Experiments and Results

4.1. Experiments

To verify the effect of Otsu method accuracy parameter improvement and speed parameter improvement in LAI measurement, a comparative experiment is designed. The fisheye lens pictures are processed according to the following steps.

4.1.1. Effective Area Capture

Obtaining the effective circular area in the fisheye lens picture by the scanning line approximation method. Scanning from the four directions of up, down, left, and right to the center determines the boundaries in the four directions through the threshold value. The center and radius of the effective circular area can be calculated using the circumscribed square.

4.1.2. Otsu Method Image Segmentation

Image segmentation refers to dividing the obtained circular-effective area into the foreground vegetation and the background sky and calculating the proportion of the foreground and background to obtain the gap fraction of the tree canopy. The gap fraction is one of the most important forest canopy parameters [38]. Reasonable and correct division of foreground and background is the key to accurately obtaining gap fraction values [39,40]. In the accuracy comparison, three methods were compared: the traditional Otsu method, the Otsu method enhanced by zenith angle segmentation, and the Otsu method enhanced by zenith angle segmentation and azimuth angle segmentation. In the speed comparison, the efficiency parameter improvement effect under different multiplication coefficients is compared.

4.1.3. LAI Inversion

The single-angle inversion method is used to obtain LAI. The Beer-Lambert law can describe the relationship between light absorption and material concentration and thickness [41]. When the inter-canopy medium is uniform and the leaves are assumed to have an elliptical random distribution, The mathematical model is as follows:

$$\frac{I_t}{I_0}={\mathrm{e}}^{-\mathrm{K}·\mathrm{L}\mathrm{A}\mathrm{I}}$$

(3)

$$\mathrm{K}\left(\theta ,\phi \right)=\mathrm{G}\left(\theta ,\phi \right)/cos\theta$$

(4)

$$\left\{\begin{array}{c}\mathrm{G}\left(\theta \right)=\frac{({x^2 + {tan}^2\theta )}^{1/2}cos\theta }{x + \left({sin}^{-1}{\mathsf{\epsilon }}_1\right){\mathsf{\epsilon }}_1},x\le 1\\ \mathrm{G}\left(\theta \right)=\frac{({x^2 + {tan}^2\theta )}^{1/2}cos\theta }{x + \frac{1}{2{\mathsf{\epsilon }}_{2}x}\mathrm{l}\mathrm{n}[(1 + {\mathsf{\epsilon }}_2)/(1 - {\mathsf{\epsilon }}_2)]},x>1\end{array}\right.$$

(5)

$$x=-3+{(\overline{\alpha }/9.65)}^{-0.6061}$$

(6)

$$LAI=2{\int }_0^{\pi /2}ln\frac{1c}{P\left(\theta \right)}cos\theta csin\theta d\theta$$

(7)

$$LAI=2\sum _{i=0}^{n}ln\frac{1}{P\left({\theta }_i\right)}cos{\theta }_{i}sin{\theta }_i∆\theta$$

(8)

where $I_0$ and $I_t$ are the light radiation intensity above and below the canopy, so $I_t/I_0$ is the canopy gap fraction P, and K is the extinction coefficient related to the zenith angle θ and leaf inclination angle. $\mathrm{G}\left(\theta ,\phi \right)$ is the blade projection function, and φ represents the azimuth angle [42]. ${\mathsf{\epsilon }}_1={(1-x^2)}^{1/2}$, ${\mathsf{\epsilon }}_2={(1-x^{-2})}^{1/2}$, and x represents the ratio of the major axis to the minor axis of the ellipse model. x reflects the change in the average blade inclination angle [43]. Combined with (3) and (4), it is assumed that the leaves are randomly distributed and the optical medium is uniformly distributed in the canopy [44], n is the number of divided concentric circles, and $\mathsf{\Delta }\theta$ is $\pi /2n$.

Based on (4) and (5), the projection relationship between $\mathrm{G}$ and $\theta$ under different α is obtained, as shown in Figure 5.

It can be found that as $\theta$ is 57.5°, the value of $\mathrm{G}$ is approximately 0.5. Therefore, the following formula can be obtained:

$$LAI=\frac{-lnP(57.5°)cos(57.5°)}{0.5}$$

(9)

Based on the single-angle inversion method, it can be found that the function curve approximates a straight line when the zenith angle is between 20° and 60°, and different blade inclination angles correspond to different straight line slopes. Therefore, the relationship between the average leaf inclination angle $\overline{\alpha }$ and slope S of the fitting straight line can be calculated as follows:

$$\overline{\alpha }=56.63+2.52\times {10}^{3}S-141.47\times {10}^{-3}{S}^2$$

(10)

The linear fitting inversion method uses the gap fraction between 20° and 60° of the zenith angle and fits a straight line using the least-squares method to obtain G($\theta$) and its slope for LAI estimation. This method utilizes more information from the image compared with the single-angle inversion method, which only uses a single angle. It also avoids over-bright and dark areas, resulting in more reliable results. Additionally, the method can also determine the average leaf inclination angle of the canopy. Considering that the estimation method of leaf area index requires linear fitting of the gap fraction at different zenith angles, the enhanced Otsu method can be well adapted to the subsequent calculations [45,46,47].

4.2. Results

4.2.1. Accuracy Parameter Improvement Results

In the first step of accuracy parameter improvement, the radius is divided into three equal parts according to the projection of the zenith angle on the bottom circle, and the LAI values in the annular area are calculated separately. In the second step of the accuracy parameter improvement, each annular region is divided into six equal parts according to the azimuth angle. The distribution of LAI values corresponding to the three tree species under different enhancement methods is compared with the normal distribution according to their fitting as follows (Figure 6):

The boxplot plot of the distribution of LAI values corresponding to the three tree species under different enhancement methods is as follows (Figure 7):

4.2.2. Efficiency Parameter Improvement Results

According to the corresponding value of the peak value of the G channel in each image, the iteration range of the Otsu method is limited according to the limit, and the time comparison under the limit of different multiples is as follows (

Table 3. Comparison of the mean of LAI with the variance value.

	Limit		2 Limit		3 Limit		5 Limit
	Time Reduction Ratio	LAI Changes Ratio	Time Reductionratio	LAI Changes Ratio	Time Reductionratio	LAI Changes Ratio	Time Reductionratio	LAI Changes Ratio
Quercus wutaishanica	0.0731	0	0.1172	0.0125	0.1603	0.1125	0.2134	0.1875
Robinia pseudoacacia	0.0372	0	0.0881	0	0.1745	0.0641	0.2098	0.2435
Pinus tabuliformis and Robinia pseudoacacia	0.0623	0	0.1202	0	0.2007	0.0135	0.2635	0.3243

):

According to the following figure, the time reduction rate and the frequency of abnormal data are displayed, and it can be seen that the greater the limit, the higher the frequency of abnormal data. In order to ensure that the data anomaly rate does not exceed 10%, the 3-limit strategy is selected, and the time spent is reduced by 17.85% (Figure 8).

5. Discuss

5.1. Accuracy Parameter Improvement Results

The figure below shows a comparison of the parameter improvement results for each tree species (Figure 9, Figure 10 and Figure 11 and

Table 4. Mean and variance of LAI data.

	LAI Value			Variance
Parameter Improvement	Original	Zenith Angle Segmentation	Zenith and Azimuth Angle Segmentation	Original	Zenith Angle Segmentation	Zenith and Azimuth Angle Segmentation
Quercus wutaishanica	2.9891	3.4034	2.9017	0.0876	0.0514	0.0415
Robinia pseudoacacia	2.4108	3.0104	2.6591	0.1234	0.0733	0.0593
Pinus tabuliformis and Robinia pseudoacacia	2.9972	3.2105	3.0100	0.1662	0.0795	0.0974

).

When the zenith angle segmentation strategy was adopted, the original LAI variance was 0.1257, and the LAI variance was 0.0680 (

Table 5. Comparison of Quercus wutaishanica boxplot statistics.

Tree Species		Quercus wutaishanica
Parameter Improvement		Original	Zenith Angle Segmentation	Zenith and Azimuth Angle Segmentation
Median		2.8816	3.405	2.8947
75th and 25th percentile	75th percentile	3.068	3.5597	3.0467
	25th percentile	2.7268	3.2848	2.7376
	difference	0.3412	0.2749	0.3091
Extremum	Maximum	3.5512	3.9045	3.409
	Minimum	2.3054	3.0162	2.536
	difference	1.2458	0.8883	0.873

,

Table 6. Comparison of boxplot Robinia pseudoacacia statistics.

Tree Species		Robinia pseudoacacia
Parameter Improvement		Original	Zenith Angle Segmentation	Zenith and Azimuth Angle Segmentation
Median		2.3427	3.0173	2.6043
75th and 25th percentile	75th percentile	2.569	3.1639	2.7556
	25th percentile	2.1319	2.7846	2.5065
	difference	0.4371	0.3793	0.2491
Extremum	Maximum	3.1752	3.6224	3.0853
	Minimum	1.8303	2.3679	2.3226
	difference	1.3449	1.2545	0.7627

and

Table 7. Comparison of Pinus tabuliformis and Robinia pseudoacacia boxplot statistics.

Tree Species		Pinus tabuliformis and Robinia pseudoacacia
Parameter Improvement		Original	Zenith Angle Segmentation	Zenith and Azimuth Angle Segmentation
Median		3.0053	3.2246	3.1062
75th and 25th percentile	75th percentile	3.315	3.4392	3.257
	25th percentile	2.6614	3.0275	2.6706
	difference	0.6536	0.4117	0.5864
Extremum	Maximum	3.8775	3.8956	3.5165
	Minimum	2.0804	2.5528	2.3244
	difference	1.7971	1.3428	1.1921

).

The LAI value can reflect the coverage density. The overall increase in the data size of the LAI value indicates that the error of judging the foreground as the background has been improved, and the effect is good when the zenith angle segmentation enhancement strategy is adopted. The variance was reduced, and the data reflecting the LAI values of the same forest were closer to each other, which was in line with expectations.

The traditional Otsu method treats the entire target circular area as a whole. In the canopy image taken with a fisheye lens, the illumination intensity is kept at a strong level at the center and weak at the edges. As a result, setting the threshold for the entire image results in an error. According to the linear fit inversion method, gap fractions at different zenith angles are required. The circular effective region can be divided into rings, and the Otsu method is used alone in each ring to find the optimal threshold for image binarization.

Compared with the original Otsu, the LAI value as the zenith angle segmentation strategy is adopted is slightly reduced. After adopting the zenith-angle segmentation strategy, the frequency of errors in judging the background sky as the foreground leaves increased. The size of the LAI value data is slightly reduced, indicating that the error of judging the foreground as the foreground has been improved. The variance was further narrowed, and the data reflecting the LAI values of the same forest were closer to each other, which was in line with expectations.

In the boxplot, the difference between the maximum and minimum values and the difference between the quartiles decreases as the number of parameter improvement strategies taken increases. This means that the data are more centralized. This is consistent with the conclusion reflected in the variance.

The canopy may not be evenly distributed in different azimuths, and the sky pixels in different azimuths under the same ring are unevenly distributed. Considering that the method should be able to perform fast calculations on mobile devices, the split zenith and azimuth steps should not be too small, which will result in a longer calculation time. In this study, the azimuth angle was divided into six parts, with 60° as the angle occupied by each part.

Zenith angle segmentation strategy and azimuth angle segmentation strategy, both strategies can solve the problem of foreground and foreground misjudgment in principle. The reason why the zenith angle segmentation strategy is first adopted is mainly to consider the characteristics of fisheye lenses, and the effect of azimuth segmentation can be similar to that that can be achieved only by using azimuth angle segmentation.

5.2. Efficiency Parameter Improvement Results

The addition of two strategies based on zenith angle and azimuth angle seriously increases the computation time. Considering the need for the algorithm to be integrated into mobile devices, the information contained in the image histogram is analyzed to enhance the algorithm and reduce the operation time.

The relationship between the peak position of the G-channel image of the tree canopy image and the optimal threshold of the Otsu method was studied, and the iteration range of the Otsu method was narrowed by the position of the crest so as to reduce the computation time.

Reducing the number of traversals improves the speed of the algorithm, ensuring that the data anomaly rate does not exceed 10% and that the time spent is reduced by 17.85%.

5.3. Choice of Comparison Equipment

Plant canopy analyzers such as the LAI-2000 can provide high-precision measurements in the LAI measurement process, but they are expensive and portable. Remote sensing technology covers a wide range and is suitable for large-scale research, but it may be limited by cloud occlusion and resolution. Photosynthesis measurement and structured light scanning techniques can provide plant physiological and three-dimensional structural information, but they are expensive and complex to operate. Drone technology is flexible and suitable for complex terrain, but it is limited by flight time and battery life. Handheld leaf area meters are portable and easy to operate, but they need to be measured leaf by leaf. The soil spectral reflectance method is suitable for large-area measurements but is affected by soil and vegetation type.

In contrast, using digital hemispherical photography (DHP) is a simpler and faster option. With DHP, only one camera is needed to take images of the tree canopy in adequate lighting conditions. The LAI is then estimated by various methods using computer software such as CAN_EYE, CIMES, or GLA. Computing functions can also be integrated in software form into portable smart devices such as mobile phones.

By using DHP, LAI measurements can be achieved in a non-destructive and time-efficient manner, making it ideal for ecological research and monitoring. The use of DHP can also provide valuable information for other canopy parameters, such as gap fraction, leaf angle distribution, and canopy closure, which are important for understanding the structure and function of the canopy.

5.4. Deficiencies and Discussions

The results of the program in the paper were obtained by running it on a PC. If the program is run on a different platform, there will be a difference in time. The time reduction scale after parameter improvement is still indicative. If conditions permit, you can consider testing the running speed of the program on more platforms to provide more comprehensive data support.

The enhancement effect of the three tree species involved in the experiment is relatively consistent, but because there are too few tree species, it is not certain that the program will show consistency or difference in the richer tree species data. Theoretically, the method of calculating the LAI value is not limited by tree species, and the influence of tree species on the calculation of the LAI value can be studied by further expanding the collected tree canopy image data.

The current experiment method fully follows the principle of equal division. Different segmentation strategies can be considered according to the image features of specific images, and the segmentation method based on zenith angle and azimuth angle can be dynamically adjusted, which can better make up for the shortcomings of the Otsu method and provide more accurate images for the calculation of the LAI value.

6. Conclusions

In this study, the improvement of Otsu method parameters provided an accurate and convenient method for estimating the canopy leaf area index when using a fisheye lens to obtain images. On the basis of the Otsu method, the threshold segmentation strategy was carried out by using the improved method of multi-region segmentation and reducing the number of traverses so as to improve the accuracy and speed of the Otsu method.

The strategy of combining zenith angle segmentation and azimuth angle segmentation is adopted in multi-region segmentation, and the negative effects of fisheye lens distortion and uneven sunlight ray distribution on the image binarization effect are excluded in the above ways. Multi-region segmentation ensures the reliability of the LAI value obtained from the image. Under the conditions of two strategies, the problem of foreground misjudgment under the application conditions of this paper is improved, and the variance of the overall LAI value data is narrowed from 0.1257 to 0.0660. The difference between the maximum and minimum values and the difference between the quartiles in the boxplot decreases with the increase in the number of strategies employed, consistent with the conclusions reflected in the variance.

The principle of reducing the number of traversals is to consider the relationship between the peak position and the optimal threshold through the peak position of the G-channel histogram in the image, determine the traversal range after constraints, and improve the efficiency of finding the optimal threshold. Reducing the number of traversals improves the speed of the algorithm and makes up for the slow computing speed caused by multi-region segmentation. The time spent is reduced by 17.85% while ensuring that the data anomaly rate does not exceed 10%, which improves the integration of the algorithm into mobile devices and the efficiency of obtaining LAI.

By improving the algorithm, it is possible to replace DHP with a smartphone with a fisheye lens, allowing for fast, real-time acquisition of LAI. The accurate and rapid measurement of LAI provides relevant technical support for the study of the interaction between plants and the growth environment and has important theoretical significance and practical value.