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Evaluation of a Laser Scanning Sensor in Detection of Complex-Shaped Targets for Variable-Rate Sprayer Development
H. Liu, H. Zhu
Published in Transactions of the ASABE 59(5): 1181-1192 (doi: 10.13031/trans.59.11760). 2016 American Society of Agricultural and Biological Engineers.
Submitted for review in January 2016 as manuscript number MS 11760; approved for publication by the Machinery Systems Community of ASABE in July 2016.
Mention of trade names or commercial products in this publication is solely for the purpose of providing specific information and does not imply recommendation or endorsement by the USDA or Jiangsu University. The USDA is an equal opportunity provider and employer.
The authors are Hui Liu, ASABE Member, Associate Professor, School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, China; Heping Zhu, ASABE Member, Agricultural Engineer, USDA-ARS Application Technology Research Unit, Wooster, Ohio. Corresponding author: Heping Zhu, USDA-ARS Application Technology Research Unit, 1680 Madison Ave., Wooster, OH 44691; phone: 330-263-3871; e-mail: firstname.lastname@example.org.
Abstract. Sensors that can accurately measure canopy structures are prerequisites for development of advanced variable-rate sprayers. A 270° radial range laser sensor was evaluated for its accuracy in measuring the dimensions of target surfaces with complex shapes and sizes. An algorithm for data acquisition and three-dimensional (3-D) canopy image construction were designed and processed with an embedded computer. Test targets included three beach balls at three heights, a rectangular box, a cylinder, two artificial trees, and three field-grown ornamental trees. Other variables included 2, 3, 4, and 5 m detection distances and sensor travel speeds of 3.2, 4.8, 6.4, and 8.0 km h-1. The laser sensor measurements of the test targets were statistically similar with the actual measurements. The average root mean square error (RMSE) and coefficient of variation (CV) varied slightly with detection distance and travel speed. Among all the dimension measurements in the ranges of 0.58 to 2.54 m in the X direction, 0.58 to 2.54 m in the Y direction, and 0.58 to 2.94 m in the Z direction, the highest average RMSE of 68 mm occurred in the Z direction and the highest average CV of 8.6% occurred in the Y direction. Similarity of paired images from the laser sensor and a camera was greater than 0.85 for all targets. These tests confirmed the capability of the laser sensor and the algorithm to accurately measure complex-shaped targets, offering potential for integration of the sensor and algorithm into sprayers that would make real-time adjustment of spray outputs to match plant structures and travel speeds.
Keywords.Automation, Canopy measurement, Laser sensor, Nursery, Orchard, Precision sprayer.
The structure and in-row spacing of trees in nurseries and orchards vary greatly throughout a growing season. For example, in the early growing season when leaves are small, the tree in-row spacing is narrower and trees are smaller than in the summer when foliage is fully developed. In many cases, tree structures vary instantaneously even in the same row when different varieties and species are planted. Conventional constant-rate sprayers, due to lack of automatic capability to adjust spray volume to match tree structure variations, are unable to apply a consistent quantity of spray deposition per unit area throughout the canopy of these irregular-shaped trees (Chen et al., 2013a). Furthermore, they continuously discharge sprays into non-target areas, causing significant pesticide waste and unnecessary pesticide risk to the environment (Zhu et al., 2006, 2008; Salyani et al., 2007; Chen et al., 2013b). Variable-rate spray technologies potentially can resolve these problems by controlling spray outputs to match plant canopy presence and structure, discharging sprays to target areas as needed (Fox et al., 2008; Giles et al., 2011; Wei and Salyani, 2004; Jeon and Zhu, 2012; Chen et al., 2012).
Measurements of canopy height, depth, width, and foliage density are critical for determining the necessary amounts of chemicals for effective variable-rate spray applications (Walklate et al., 2002). Extensive research with different sensor technologies has been conducted to characterize tree structures. Among these technologies, radar and ultrasonic sensors are most popular (Rosell and Sanz, 2012); unfortunately, these sensors have limitations for field spray applications. Radar sensors only detect canopy structures at macroscopic levels and at very low spatial resolutions (Bongers, 2001). Similarly, although multiple ultrasonic sensors can be combined to estimate canopy volume (Jeon et al., 2011), the divergence angle of ultrasonic waves still limits the spatial resolution for accurate measurements (Palleja et al., 2010; Rosell and Sanz, 2012). Consequently, the inaccuracy of these sensors can cause them to easily miss new growth at the edges of canopies where many insects and diseases likely occur, resulting in this part of the canopy being under-sprayed or not sprayed.
LIDAR (light detection and ranging) sensors, although more expensive than ultrasonic and radar sensors, can provide more accurate detection of tree canopy structures under different environmental conditions (Wei et al., 2004, 2005; Palacin et al., 2007; Sanz-Cortiella et al., 2011; Chen et al., 2012; Rosell and Sanz, 2012). Among LIDAR-based sensor technologies, the laser scanning sensor (SICK, Dusseldorf, Germany) has been extensively investigated for sprayer development (Palacin et al., 2007; Rosell et al., 2009a, 2009b; Palleja et al., 2010; Llorens et al., 2011; Sanz-Cortiella et al., 2011; Chen et al., 2012). This sensor can detect targets in a 180° radial range at distances up to 80 m with an angular resolution up to 0.5° and a response time of 13 to 53 ms. The sensor was first successfully integrated into an air-assisted variable-rate sprayer to detect tree structures and automatically control the spray output of each nozzle in real-time (Chen et al., 2012). However, due to the maximum 180° radial scanning range limitation, two sensors are required for simultaneous detection of trees on both sides of a sprayer. The use of two sensors can cause difficulties when synchronization of automatic control functions is required and also can result in excessive costs.
A 270° radial range laser sensor (UTM-30LX, Hokuyo Automatic Co., Ltd., Osaka, Japan) capable of detecting targets at a higher speed and wider range was recently introduced for air-assisted variable-rate sprayer development (Liu et al., 2013). For tree crop spray applications, spray targets are located on both sides of the sprayer, so there is no need for sensors to detect a target under the sprayer. Therefore, the use of one 270° laser sensor might solve the problems associated with the use of two 180° laser sensors if the sensor is mounted on the sprayer with its 90° blind surface facing toward the ground. However, before it is integrated into variable-rate spraying systems, the accuracy and capability of the sensor to detect trees of different structures should be evaluated. The objective of this research was to determine the errors of the 270° radial range laser sensor to measure objects with complex shapes and different sizes at differentsensor travel speeds and detection distances between the sensor and targets, in an effort to provide baseline information on potential errors of the laser sensor before adaptation for the development of precision sprayers.
Materials and Methods
Laser Sensor and Image Construction
The 270° radial range laser scanning sensor (fig. 1a) was 60 mm × 60 mm × 87 mm in size and weighed 210 g. Its laser wavelength was 905 nm with a total power consumption of less than 8 W. The sensor was ingress protection rated as IP64 (dustproof and water immersion protection), and it was designed to measure object surface distances based on the time-of-flight principle in outdoor environmental applications with ambient air temperatures ranging from -10° to 50°C. The time between transmission and reception of the laser signals was used to measure the distance between the sensor and the object surface. A precision step motor inside the sensor rotated the laser beam evenly to detect the object surface with a radial range of 270° and an angular resolution of 0.25°. It was able to complete a 270° scan from 0.1 to 30 m distances within 25 ms. During each 25 ms scanning detection cycle, the sensor released 1080 laser beams to detect 1080 points (270°/0.25° = 1080).
The sensor was mounted 1.60 m above the ground on the centerline of an air-assisted sprayer and a tractor (fig. 1b). It was positioned so that its 1080 detection points were on the same fan-shaped plane perpendicular to both the sky and the sprayer travel direction, which provided a two-dimensional grid of line-of-sight distances between the sensor and the object when the sensor was stationary. When the sensor traveled horizontally, it provided a matrix of distances to form a 3-D surface with proper algorithms. Because of its 270° radial detection range, the 90° blind surface of the sensor faced toward the ground. In this way, the sensor was able to detect objects on both sides of the sprayer, and each side had a maximum 540 detection points. A non-contact Doppler radar sensor (Radar III, Dickey-john Co., Springfield, Ill.) was mounted at the bottom of the sprayer to measure sprayer travel speed (fig. 1b).
(a) Laser sensor dimensions (b) Laser sensor position Figure 1. The 270° radial range laser sensor used for evaluation of its accuracy to detect object surface: (a) laser sensor dimensions, (b) position of the laser sensor (inside the blue circle) on the vehicle centerline between a tractor and an air-assisted sprayer.
The laser sensor was connected to an embedded computer (model MXE-1301, ADLINK Technology, New Taipei, Taiwan) through a universal serial bus (USB) for data communications (fig. 2). A 12 VDC power supply was used for the USB connection. A touch screen was also connected to the embedded computer to perform human-machine interface functions through a serial RS-232 COM port. These electronic devices were mounted in the tractor cab. An algorithm was written in C++ based on Visual Studio (ver. 2005, Microsoft Corp., Redmond, Wash.) and Matlab (ver. 126.96.36.1991, Mathworks, Inc., Natick, Mass.) and data was saved in the embedded computer for the object structure measurements (fig. 3). The C++ program was responsible for acquiring real-time signals from the laser sensor and travel speed sensor and storing the signals in the embedded computer. The Matlab program converted the signals to distances between the sensor and points on the object surface and calculated the dimensions of objects from the measured distances. The distance data matrix was stored in a format of gray-scale values for constructing pseudo-color images that mapped the 3-D object surface. The scanned image contours were extracted based on the morphological operator and edge detection method (Chen et al., 2012). During the image construction process, the algorithm also filtered unnecessary measurement points that were beyond the detection range or reflected from the ground.
Figure 2. Schematic of the data acquisition, storage, and management system for integration of the 270° radial range laser sensor.
Figure 3. Flowchart for the MATLAB algorithm compiled with C++ program module for detecting and constructing 3-D object surfaces.
Indoor and Outdoor Tests
The accuracy of the laser sensor in detecting tree canopy structures was evaluated under both indoor and outdoor conditions at the USDA-ARS Application Technology Research Unit in Wooster, Ohio. For the indoor conditions, which were in an open area of a 25.2 long, 15.8 m wide, and 6.1 m high ventilated warehouse, the tests included five different shapes of artificial objects at four constant travel speeds (3.2, 4.8, 6.4, and 8.0 km h-1) and four horizontal distances (2, 3, 4, and 5 m) between the sensor and the object centerlines. In this study, the horizontal distance between the object centerlines and the laser sensor (or centerline of the sprayer) was defined as the detection distance. The artificial objects included three regular-shaped objects and two artificial trees. The regular-shaped objects were three plastic beach balls (fig. 4a), a rectangular box (fig. 4b), and a cylinder (fig. 4c). Their dimensions are listed in table 1. The balls were red, the rectangular box was light brown, the cylinder was black, and the artificial trees were green. The three balls were con-nected in a vertical line, and their centers were at 0.6, 1.6, and 2.5 m heights above the ground. The two artificial trees were Acer rubrum (fig. 4d) and Ficusbenjamina (fig. 4e), and their sizes are listed in table 1.
Table 1. Dimensions of regular-shaped objects and two artificial trees for the indoor tests and three field-grown trees for the outdoor tests. Objects Height (m) Width (m) Length (m) Diameter (m) Test Location Ball at 0.6 m height - - - 0.58 Indoor Ball at 1.6 m height - - - 0.58 Indoor Ball at 2.5 m height - - - 0.58 Indoor Rectangular box 2.94 0.45 0.58 - Indoor Cylinder 1.24 - - 0.35 Indoor Artificial tree 1 3.35 2.54 - - Indoor Artificial tree 2 2.54 0.96 - - Indoor Field tree 1 2.46 0.91 - - Outdoor Field tree 2 2.79 0.99 - - Outdoor Field tree 3 0.86 0.79 - - Outdoor
(a) (b) (c) (d) (e) (f) (g) (h) (i) (j) Figure 4. Paired images of five artificial objects obtained with the camera (a to e) and laser sensor (f to j): (a and f) three 0.58 m diameter beach balls, (b and g) a 0.58 × 0.45 × 2.94 m rectangular box, (c and h) a 1.24 m high and 0.34 m diameter cylinder, (d and i) artificial tree 1, and (e and j) artificial tree 2. The 3-D reconstructed images from the laser sensor were taken at 3.2 km h-1 travel speed and 2 m detection distance, and different colors represent different horizontal distances from target surfaces to the laser sensor.
These objects were positioned on the ground so that their centerlines were located in a straight line that was parallel to the laser sensor travel direction. The diagonal of the rectangular box was positioned on the straight line so that the sensor would be able to detect three edges of the box. There were 16 combinations of the four different detection distances and the four travel speeds to verify the sensor detection accuracy under indoor conditions. Each combination was repeated five times.
The outdoor tests included three field-grown trees of different sizes (fig. 5). The trees were planted in a row with a spacing range of 1.2 to 3.0 m. The three trees were Malus ‘spring snow’ (field tree 1), Carpinus betulus (field tree 2), and Prunus cistena (field tree 3). Their height and maximum width are listed in table 1. The outdoor tests were conducted with four travel speeds (3.2, 4.8, 6.4, and 8.0 km h-1) on a sunny day with average wind speeds of 7.4 km h-1. The detection distance (i.e., the horizontal distance between the sensor and the in-row centerline of the three trees) was 2.0 m. Each measurement was repeated five times.
The dimensions of each object detected with the laser sensor in three Cartesian coordinates (X, Y, and Z) at each detection distance and each travel speed were measured and compared with the actual dimensions to verify the sensor detection accuracy. The X coordinate represents the horizontal width direction, which was parallel to the sensor travel direction, Y represents the object depth direction, which was perpendicular to the sensor travel direction, and Z represents the vertical direction of object height. The measured dimensions included diameters of the three balls at three heights; height and diameter of the cylinder; height, diagonal length, and depth of the rectangular box; and heights and widths of the two artificial trees and three field-grown trees. Outline profiles of object images constructed from the laser sensor detections were compared with images taken with a digital camera (figs. 4 and 5).
The dimensions of objects in the X direction were measured by counting the number of laser beam reflections from the object surface and the number of laser scanning cycles as well as the travel speed. The dimensions of objects in the Y direction were measured by doubling the distance differences between the closest scanning point and the centerline of the object. The dimensions of objects in the Z direction were measured by calculating the height difference between the lowest and highest points of the objects detected by the laser sensor.
(a) (b) (c) (d) (e) (f) Figure 5. Paired images of the three field trees obtained with the camera (a to c) and laser sensor (d to f): (a and d) Malus ‘spring snow’, (b and e) Carpinus betulus, and(c and f) Prunus cistena. The 3-D reconstructed images from the laser sensor were taken at 3.2 km h-1 travel speed and 2 m detection distance, and different colors represent different horizontal distances from target surfaces to the laser sensor.
The root mean square error (RMSE) and percentage coefficient of variation (CV) of the mean dimensions of each object measured with the sensor for each detection distance and each travel speed from five replications were calculated to determine the accuracy and repeatability of the sensor. RMSE represents the difference between the actual and measured dimensions of detected objects, and CV is the relative error of the measurements. The RMSE values also reflect the errors that occurred when the detection of object edges was possibly missed by the laser sensor. The equation for calculating RMSE is:
and the equation for calculating CV (as a percentage) is:
where di (i = 1, 2, 3, 4, 5) is the measured dimension of the object in the X, Y, or Z coordinate, and d is the actual dimension of the object in the X, Y, or Z coordinate.
Paired Image Similarity Evaluation
Edge similarity score (ESS) was used to compare the degrees of similarity of paired images from the digital camera and the laser sensor for each object (Sud and Manocha, 2003). ESS was calculated from the absolute correlation coefficient between two edge distance fields of the paired images with the following equation:
where a is a vector transformed from the edge profile of the laser sensor image, ß is a vector transformed from the camera image, aj and ßj (j = 1, 2, …, n) are pixel points at the edge profiles, and and are the means of aj and ßj, respectively. The range of ESS values is from 0 to 1, where 0 indicates that the outline profiles of the paired images do not have any similarity, and 1 indicates that the two profiles do not have any difference. Thus, paired images with EES values closer to 1 would have a higher similarity.
Results and Discussion
Images of the five artificial objects and three field-grown trees obtained with the digital camera and the laser sensor are shown in figures 4 and 5, respectively. The images from the laser sensor were reconstructed from the test with 2.0 m detection distance and 3.2 km h-1 travel speed, and the colors in the images represent distances from the object surface to the sensor, which allowed the 3-D surface reconstruction. Visual observation demonstrates that the paired images of the objects under indoor and outdoor conditions match each other very well. Detailed measurement errors are given below.
Table 2. RMSE (mm) and CV (%) of measured diameters of 0.58 m diameter balls in the X, Y, and Z directions from the laser sensor at four detection distances (2, 3, 4, and 5 m) and four travel speeds (3.2, 4.8, 6.4, and 8.0 km h-1). Ball Height
X Direction Y Direction Z Direction RMSE CV RMSE CV RMSE CV 0.6 2 3.2 24 4.1 39 6.7 31 5.3 4.8 38 6.6 36 6.2 21 3.6 6.4 33 5.7 65 11.2 39 6.7 8.0 31 5.3 90 15.5 39 6.7 3 3.2 15 2.6 61 10.5 60 10.3 4.8 43 7.4 73 12.6 47 8.1 6.4 35 6.0 40 6.9 49 8.4 8.0 35 6.0 55 9.5 55 9.5 4 3.2 28 4.8 41 7.1 58 10.0 4.8 67 11.6 54 9.3 68 11.7 6.4 35 6.0 39 6.7 58 10.0 8.0 75 12.9 70 12.1 69 11.9 5 3.2 27 4.7 58 10.0 66 11.4 4.8 94 16.2 57 9.8 51 8.8 6.4 62 10.7 81 14.0 63 10.9 8.0 34 5.9 90 15.5 50 8.6 1.6 2 3.2 19 3.3 36 6.2 10 1.7 4.8 38 6.6 33 5.7 10 1.7 6.4 25 4.3 9 1.6 10 1.7 8.0 31 5.3 79 13.6 11 1.9 3 3.2 54 9.3 28 4.8 13 2.2 4.8 38 6.6 49 8.4 19 3.3 6.4 27 4.7 30 5.2 9 1.6 8.0 26 4.5 30 5.2 24 4.1 4 3.2 12 2.1 33 5.7 24 4.1 4.8 27 4.7 20 3.4 24 4.1 6.4 15 2.6 24 4.1 17 2.9 8.0 33 5.7 27 4.7 24 4.1 5 3.2 24 4.1 93 16.0 31 5.3 4.8 38 6.6 48 8.3 45 7.8 6.4 15 2.6 67 11.6 20 3.4 8.0 48 8.3 66 11.4 27 4.7 2.5 2 3.2 46 7.9 54 9.3 13 2.2 4.8 17 2.9 48 8.3 11 1.9 6.4 46 7.9 76 13.1 12 2.1 8.0 27 4.7 45 7.8 23 4.0 3 3.2 56 9.7 60 10.3 20 3.4 4.8 20 3.4 44 7.6 18 3.1 6.4 46 7.9 41 7.1 9 1.6 8.0 21 3.6 33 5.7 13 2.2 4 3.2 44 7.6 22 3.8 22 3.8 4.8 11 1.9 38 6.6 22 3.8 6.4 38 6.6 29 5.0 13 2.2 8.0 27 4.7 76 13.1 13 2.2 5 3.2 40 6.9 56 9.7 35 6.0 4.8 16 2.8 39 6.7 36 6.2 6.4 38 6.6 42 7.2 35 6.0 8.0 64 11.0 62 10.7 49 8.4
Measurements of Regular-Shaped Objects
The RMSE values between the measured and actual diameters and the CV values of the three 0.58 m balls in the X, Y, and Z directions at various traveling speeds (3.2 to 8.0 km h-1) and detection distances (2 to 5 m) are shown in table 2. In the X direction (sprayer travel direction), the RMSE ranged from 11 to 94 mm (35 mm average) for the three balls tested at four detection distances and four travel speeds. The average RMSE and CV across the four detection distances and four travel speeds were 42 mm and 7.3%, 29 mm and 5.1%, and 35 mm and 6.0% for the balls at heights of 0.6, 1.6, and 2.6 m, respectively.
Analysis of variance (ANOVA) of the data in table 2 showed that neither travel speed in the range of 3.2 to 8.0 km h-1 nor detection distance in the range of 2 to 5 m significantly influenced the RMSE and CV of ball diameter measurements in the X direction. The average RMSE and CV for the three balls across the four detection distances were 32 mm and 5.6%, 37 mm and 6.4%, 35 mm and 6.0%, and 38 mm and 6.5% for travel speeds of 3.2, 4.8, 6.4, and 8.0 km h-1, respectively. The average RMSE and CV for the three balls across the four travel speeds were 31 mm and 5.4%, 35 mm and 6.0%, 34 mm and 5.9%, and 42 mm and 7.2% for detection distances of 2, 3, 4, and 5 m, respectively.
The sensor detection resolution in the X direction was supposed to be directly proportional to the travel speed. With the 25 ms scanning detection cycle time, the sensor detection resolution in the X direction would be 22.2, 33.3, 44.4, and 55.6 mm for travel speeds of 3.2, 4.8, 6.4, and 8.0 km h-1, respectively. However, because the first position that the sensor detected on the ball diameter at any travel speed was random, the measurement error at each travel speed could fall in the range of doubled detection resolution associated with this travel speed. Thus, with five replications for each measurement, test results could not demonstrate significant differences in the accuracy of measuring ball diameters in the X direction among the different travel speeds.
In the Y direction (depth direction), the RMSE and CV of ball diameter measurements ranged from 9 to 93 mm (50 mm average) and from 1.6% to 16% (9% average), respectively. The mean RMSE and CV of the three balls across the four travel speeds were 51 mm and 8.8%, 45 mm and 7.8%, 39 mm and 6.8%, and 63 mm and 10.9% at detection distances of 2, 3, 4, and 5 m, respectively. The mean RMSE and CV of the three balls across the four detection distances were 48 mm and 8.3%, 45 mm and 7.7%, 45 mm and 7.8%, and 60 mm and 10.4% at travel speeds of 3.2, 4.8, 6.4, and 8.0 km h-1, respectively. Similar to the X direction, the largest mean RMSE across the four detection distances and four travel speeds among the diameter measurements of the three balls in the Y direction was 59 mm, which was observed at the 0.6 m height, and the lowest mean RMSE was 42 mm, which was observed at the 1.6 m height. Significant difference in the accuracy of measuring ball diameters in the Y direction was found among different travel speeds but not detection distances.
In the Z direction (height direction), the RMSE of ball diameter measurements ranged from 9 to 69 mm with an average of 31 mm, and CV ranged from 1.6% to 11.9% with an average of 5.0%. The mean RMSE of the three balls across the four travel speeds increased from 19 to 38 mm, and the mean CV increased from 3.3% to 6.5% as the detection distance increased from 2.0 to 5.0 m. The reason was that the sensor had a wider angular view at longer detection distances to detect entire balls in the Z direction. For travel speeds from 3.2 to 8.0 km h-1, the mean RMSE of the three balls across the four detection distance ranged from 28 to 33 mm, and the largest mean RMSE occurred at the travel speed of 8.0 km h-1. For the three heights, the largest mean RMSE was 52 mm, which was observed at the 0.6 m height, and the lowest mean RMSE was 20 mm, which was observed at the 1.6 m height. Significant difference in the accuracy of measuring ball diameters in the Z direction was found among different detection distances but not travel speeds.
(a) (b) Figure 6. Mean CV values of dimensions measured in the X, Y, and Z directions with the laser sensor across travel speeds of 3.2, 4.8, 6.4, and 8.0 km h-1 and detection distances of 2, 3, 4, and 5 m for (a) regular-shaped objects (three balls, rectangular box, and cylinder), and (b) two artificial trees and three field-grown trees. The X, Y, and Z directions represent the sensor travel direction, object depth, and object height, respectively. Error bars are standard deviations.
In general, diameter measurements of the middle ball (1.6 m height) had the lowest mean RMSE and CV in the X, Y, and Z directions because the sensor and the ball center were at the same height. The probabilities of the laser beam detecting the edges of the balls in the X and Y directions were lower when the ball heights were farther from the sensor. Detection distance in the range of 2 to 5 m affected the diameter measurement accuracy in the Z direction but not in the X and Y directions, and the travel speed in the range of 3.2 to 8.0 km h-1 slightly affected the diameter measurement accuracy in the Y direction but not in the X and Z directions. The mean CV values for the diameter measurements in the X, Y, and Z directions were 6.1% ±2.9%, 8.6% ±3.5%, and 5.3% ±3.2%, respectively (fig. 6a). Among the X, Y, and Z directions, the mean CV in the Y direction was highest (fig. 6a). This was because the diameter in the Y direction was calculated by doubling the radius measurement, which could increase accumulated errors.
For the rectangular box, because its diagonal was parallel to the X direction, the dimensions measured with the laser sensor were the height, diagonal length, and diagonal depth. The actual diagonal length and depth of the rectangular box were calculated from its actual length and depth based on its geometry. The RMSE values between the measured and actual dimensions of the rectangular box and the CV values in the X, Y, and Z directions are shown in table 3. Travel speeds in the range of 3.2 to 8.0 km h-1 slightly influenced the laser sensor detection accuracy of the rectangular box in the X and Z directions but not in the Y direction with respect to RMSE and CV, while detection distances in the range of 2 to 5 m influenced the detection accuracy in all three directions. The mean RMSE and CV for the measurements across the four detection distances increased from 23 mm and 5.0% to 40 mm and 8.8% in the X direction and from 34 mm and 1.2% to 44 mm and 1.5% in the Z direction when the travel speed increased from 3.2 to 8.0 km h-1, while the mean RMSE and CV changed from 26 mm and 4.4% to 24 mm and 4.1% in the Y direction. The probabilities of missing the detection of box edges in the X and Z directions increased as the travel speed increased. In comparison, the mean RMSE and CV across the four travel speeds increased from 18 mm and 3.9% to 36 mm and 8.0% in the X direction, from 24 mm and 4.2% to 31 mm and 5.3% in the Y direction, and from 25 mm and 0.9% to 53 mm and 1.8% in the Z direction when the detection distance increased from 2.0 to 5.0 m. Even though the measurement errors occurred in all directions, the average CV across the four travel speeds and four detection distances was only 5.9% in the X direction, 4.2% in the Y direction, and 2.1% in the Z direction (fig. 6a).
Table 3. RMSE (mm) and CV (%) of measured width, depth, and height of a 0.45 m × 0.58 m × 2.94 m rectangular box in the X, Y, and Z directions from the laser sensor at four detection distances (2, 3, 4, and 5 m) and four travel speeds (3.2, 4.8, 6.4, and 8.0 km h-1). Detection
RMSE CV RMSE CV RMSE CV 2 3.2 23 5.1 27 4.7 23 0.8 4.8 9 2.0 9 1.6 20 0.7 6.4 19 4.2 40 6.9 28 1.0 8.0 19 4.2 20 3.4 29 1.0 3 3.2 11 2.4 26 4.5 23 0.8 4.8 9 2.0 13 2.2 30 1.0 6.4 32 7.1 29 5.0 31 1.1 8.0 31 6.9 19 3.3 35 1.2 4 3.2 25 5.6 22 3.8 38 1.3 4.8 17 3.8 14 2.4 48 1.6 6.4 23 5.1 27 4.7 45 1.5 8.0 62 13.8 23 4.0 52 1.8 5 3.2 31 6.9 27 4.7 50 1.7 4.8 40 8.9 52 9.0 53 1.8 6.4 26 5.8 11 1.9 48 1.6 8.0 47 10.4 32 5.5 59 2.0
Table 5. RMSE (mm) and CV (%) of measured widths and heights of artificial trees from the laser sensor at four travel speeds (3.2, 4.8, 6.4, and 8.0 km h-1) and four detection distances (2, 3, 4, and 5 m). Detection
Artificial Tree 1 Artificial Tree 2 X Direction Z Direction X Direction Z Direction RMSE CV RMSE CV RMSE CV RMSE CV 2 3.2 24 0.9 97 2.9 34 3.5 20 0.8 4.8 32 1.3 87 2.6 17 1.8 38 1.5 6.4 34 1.3 97 2.9 45 4.7 32 1.3 8.0 36 1.4 93 2.8 39 4.1 35 1.4 3 3.2 34 1.3 59 1.8 40 4.2 31 1.2 4.8 30 1.2 63 1.9 32 3.3 23 0.9 6.4 24 0.9 60 1.8 44 4.6 37 1.5 8.0 27 1.1 51 1.5 54 5.6 28 1.1 4 3.2 21 0.8 63 1.9 33 3.4 28 1.1 4.8 33 1.3 73 2.2 43 4.5 38 1.5 6.4 28 1.1 70 2.1 41 4.3 35 1.4 8.0 29 1.1 63 1.9 46 4.8 37 1.5 5 3.2 34 1.3 65 1.9 18 1.9 72 2.8 4.8 35 1.4 59 1.8 59 6.1 72 2.8 6.4 44 1.7 43 1.3 42 4.4 52 2.0 8.0 33 1.3 56 1.7 45 4.7 57 1.5
For the 0.35 m diameter and 1.24 m high cylinder with detection distances from 2 to 5 m and travel speeds from 3.2 to 8. 0 km h-1, the RMSE and CV ranged from 11 to 33 mm and 3.1% to 9.4% in the X direction, from 12 to 46 mm and 3.4% to 13.1% in the Y direction, and from 10 to 62 mm and 0.8% to 5.0% in the Z direction, respectively (table 4). Similar to the measurements of the rectangular box, the RMSE and CV of the cylinder did not have much variation with travel speed in all three directions but varied with detection distance in all three directions. For example, the RMSE and CV in the Z direction increased from 23 mm and 0.8% to 73 mm and 2.5% when detection distance increased from 2.0 to 5.0 m. Compared to the actual dimensions, the magnitudes of these errors were small. The mean CV values for the cylinder measurements in the X, Y, and Z directions were 5.7% ±1.7%, 8.1% ±2.7%, and 3.1% ±1.4%, respectively (fig. 6a).
Table 4. RMSE (mm) and CV (%) of measured diameter and height of a 0.35 m diameter and 1.24 m high cylinder in the X, Y, and Z directions from the laser sensor at four detection distances (2, 3, 4, and 5 m) and four travel speeds (3.2, 4.8, 6.4, and 8.0 km h-1). Detection
RMSE CV RMSE CV RMSE CV 2 3.2 11 3.1 13 3.7 23 1.9 4.8 18 5.1 26 7.4 10 0.8 6.4 22 6.3 16 4.6 11 0.9 8.0 15 4.3 39 11.1 28 2.3 3 3.2 21 6.0 28 8.0 20 1.6 4.8 19 5.4 12 3.4 27 2.2 6.4 23 6.6 24 6.9 37 3.0 8.0 15 4.3 25 7.1 32 2.6 4 3.2 23 6.6 30 8.6 40 3.2 4.8 11 3.1 28 8.0 54 4.4 6.4 23 6.6 46 13.1 53 4.3 8.0 26 7.4 27 7.7 54 4.4 5 3.2 23 6.6 36 10.3 62 5.0 4.8 33 9.4 29 8.3 51 4.1 6.4 23 6.6 41 11.7 61 4.9 8.0 15 4.3 35 10.0 48 3.9
Measurements of Artificial Trees and Field-Grown Trees
For the artificial trees and field-grown trees, due to their irregular shapes, only the RMSE and CV values of their maximal widths in the X direction and heights in the Z direction detected with the laser sensor are reported (table 5). The mean RMSE of tree width measurement in the X direction for the four detection distances and four travel speeds was 31 mm for artificial tree 1 (2.54 m wide) and 39 mm for artificial tree 2 (0.96 m wide). Detection distances of 2 to 5 m and travel speeds of 3.2 to 8.0 km h-1 had a slight influence on the sensor measurements of artificial tree widths in the X direction. When the detection distance was between 2 and 5 m, the mean RMSE of width measurements varied from 28 to 37 mm for artificial tree 1 and from 34 to 43 mm for artificial tree 2. When the travel speed increased from 3.2 to 8.0 km h-1, the mean RMSE of tree width varied from 28 to 33 mm for artificial tree 1 and from 31 to 46 mm for artificial tree 2. The average CV for the width measurement in the X direction with the laser sensor was 1.2% for artificial tree 1 and 4.1% for artificial tree 2 (fig. 6b).
The mean RMSE of tree height measurements in the Z direction for the four detection distances and four travel speeds was 68 mm for artificial tree 1 (3.35 m high) and 38 mm for artificial tree 2 (2.54 m high). The sensor had a better line of sight to detect the tops of trees when the detection distance was greater. For example, when the detection distance increased from 2 to 5 m, the mean RMSE of tree height decreased from 94 to 56 mm for artificial tree 1 but increased from 31 to 58 mm for artificial tree 2. The RMSE values of artificial tree 1 in the Z detection were greater than those of artificial tree 2 because part of tree 1 could impede the sensor in detecting the top of the tree. When the travel speed was between 3.2 and 8.0 km h-1, the mean RMSE of tree height ranged from 66 to 71 mm for artificial tree 1 and from 34 to 43 mm for artificial tree 2. Thus, travel speeds from 3.2 to 8.0 km h-1 did not influence the tree height measurement very much. The average CV for height measurement was 2.1% for artificial tree 1 and 1.5% for artificial tree 2 (fig. 6b).
Similar to the measurements of artificial trees, the RMSE and CV values of the measured heights and widths of the three field-grown trees were also small (table 6). The travel speed had slight influence on the accuracy of the laser sensor to measure tree widths in the X direction and had little influence on height measurements in the Z direction (fig. 6b). Across the four travel speeds at 2 m detection distance, the mean RMSE and CV of tree width measurements were 32 mm and 3.5% for field tree 1 (0.9 m wide ), 43 mm and 4.3% for field tree 2 (0.99 m wide), and 41 mm and 5.2% for field tree 3 (0.79 m wide). In comparison, the mean RMSE and CV of tree height measurements were 54 mm and 2.2% for field tree 1 (2.46 m high), 60 mm and 2.2% for field tree 2 (2.79 m high), and 60 mm and 7.0% for field tree 3 (0.86 m high). Compared to ultrasonic sensors (Jeon et al., 2011), the laser sensor had much lower RMSE and CV values with faster responses and longer detection ranges.
Table 6. RMSE (mm) and CV (%) of measured widths and heights of three field-grown trees from the laser sensor at 2 m detection distance and four travel speeds (3.2, 4.8, 6.4, and 8.0 km h-1). Travel
Field Tree 1 Field Tree 2 Field Tree 3 X Direction Z Direction X Direction Z Direction X Direction Z Direction RMSE CV RMSE CV RMSE CV RMSE CV RMSE CV RMSE CV 3.2 17 1.9 53 2.2 43 4.3 55 2.0 45 5.7 56 6.5 4.8 38 4.2 63 2.6 40 4 48 1.7 30 3.8 66 7.7 6.4 33 3.6 56 2.3 44 4.4 65 2.3 34 4.3 61 7.1 8.0 39 4.3 43 1.7 45 4.5 72 2.6 54 6.8 56 6.5
Calculated Detection Errors
The laser sensor detection resolution in the X direction was the product of travel speed and the 25 ms scanning detection cycle and was 22.2, 33.3, 44.4, and 55.6 mm for travel speeds of 3.2, 4.8, 6.4, and 8.0 km h-1, respectively. The sensor might not be able to detect objects if their dimensions in the X direction were smaller than these resolutions. Under ideal conditions, the total maximum error for the dimension measurements of an object in the X direction was the sum of the maximum errors in detecting two edges of the object, and each edge maximum error was equal to the sensor detection resolution. Thus, the total maximum errors in the X direction were 44.4, 66.6, 88.8, and 111.2 mm for travel speeds of 3.2, 4.8, 6.4, and 8.0 km h-1, respectively.
Figure 7. Geometry analysis of maximum error (EM) and actual error (?h) for the laser sensor in detecting the top edge of an object at height H above the sensor.
The measurement errors of an object in the Y direction depended on the changes in its shape within the 25 ms travel time. For a flat surface parallel to the travel direction, the error was assumed to be close to zero because the laser beam traveled at the light speed. Due to the fixed sensor height, the length covered by each 0.25° detection point on a vertical surface would not be equal for all 540 points during a scanning cycle. Therefore, the detection resolution in the Z direction varied with the object height above or below the sensor (fig. 7). For an object with a top edge height of Ht and bottom edge height of Hb above the laser sensor, the maximum calculated error (EM) and actual calculated error (?h) for the sensor in measuring the vertical dimension (Ht - Hb) could be calculated with equations 4 and 5 based on the geometry analysis (fig. 7) when the sensor travel speed is zero:
where D is the detection distance between the sensor and object, a is the sensor angular resolution (0.25°), and nt and nb are the numbers of points that the laser sensor detects at heights Ht and Hb, respectively. The values of nt and nb are calculated with following equations:
Equations 4 through 7 could also be used to calculate the maximum and actual errors for objects that have top or bottom edges below the laser sensor.
Table 7. Maximum errors (EM) calculated with equation 4 and actual errors (?h) calculated with equation 5 for vertical dimensions (Z direction) of regular-shaped objects and artificial and field-grown trees detected by the laser sensor at detection distances of 2, 3, 4, and 5 m. Object Maximum and Actual Errors (mm) at 2 m at 3 m at 4 m at 5 m EM ?h EM ?h EM ?h EM ?h Ball at 2.5 m height 21 2 29 9 37 11 45 17 Ball at 1.6 m height 18 0 26 2 35 21 44 12 Ball at 0.6 m height 22 12 29 11 37 23 45 35 Rectangular box 27 13 33 9 40 6 47 24 Cylinder 23 11 30 13 38 12 46 35 Artificial tree 1 30 21 34 5 41 15 48 27 Artificial tree 2 25 17 31 13 39 21 47 37 Field tree 1 25 10 31 19 38 14 46 24 Field tree 2 26 9 32 13 39 9 47 36 Field tree 3 24 17 31 13 38 6 46 31
Table 7 shows the calculated EM and ?h for the laser sensor in measuring the diameters of the three balls in the Z direction and the heights of the rectangular box, cylinder, two artificial trees, and three field-grown trees. Similar to the RMSE values of the objects in the Z direction shown in tables 2 through 6, the EM values for all objects increased as the detection distance increased. Because of the 0.25° angular resolution of the sensor, the number of points that the sensor detected on the same object decreased, and therefore the vertical measurement range per 0.25° on the object increased, as the detection distance increased (fig. 7). However, ?h did not have this trend. For example, for the 2.94 m high rectangular box, EM was 27, 33, 40, and 47 mm while ?h was 13, 9, 6, and 24 mm when the detection distance was 2, 3, 4, and 5 m, respectively; ?h did not increase with detection distance because the last detection point on the object varied with the object height (fig. 7).
Table 7 also shows that some actual measurement errors were greater than the calculated errors. The reason was that the calculated errors did not consider effects of travel speed. Because the sensor resolution in the X direction increased as the travel speed increased, there was a higher probability of missing detection of the outermost edges in the X, Y, and Z directions at higher travel speeds. Therefore, the accuracy of the sensor in the Z direction was affected by travel speed. Although the RMSE values of the objects shown in tables 2 through 6 were not equal to the EM and ?h values shown in table 7, their differences were within 5% of the object heights.
(a) (b) (c) (d) Figure 8. Processing edge similarity score (ESS) for paired images of artificial tree 1 from the camera and the laser sensor: (a) image from the camera, (b) reconstructed image from the laser sensor, (c) canopy outline profile from (a), and (d) canopy outline profile from (b).
Canopy Outline Profile Similarity
The ESS values for the three regular-shaped objects, two artificial trees, and three field trees were calculated with equation 3. Figure 8 shows the process of calculating the ESS from the outline profile similarity for the paired images of artificial tree 1 from the camera and the laser sensor. For all objects under all test conditions, the ESS values were close to or greater than 0.900 (table 8). Travel speed and detection distances apparently did not affect the EES.
Under indoor conditions, the mean EES was 0.947 ±0.020 for the three balls at three different heights, 0.971 ±0.007 for the rectangular box, 0.977 ±0.008 for the cylinder, 0.947 ±0.013 for artificial tree 1, and 0.904 ±0.012 for artificial tree 2. Under outdoor conditions, the mean EES was 0.866 ±0.015 for field-grown tree 1, 0.931 ±0.007 for field-grown tree 2, and 0.859 ±0.009 for field-grown tree 3. Perfect similarities were not obtained due to variations in the positions of the camera and the laser sensor as well as other uncontrollable factors. The EES values of the field-grown trees were lower than those of the indoor artificial trees because the field trees were disturbed by wind and the ground in the field was not as flat as the indoor floor. Even though the EES values were less than 1, they all were greater than 0.85. Therefore, the values of RMSE, CV, and EES obtained from the tests verified that the laser sensor had the capability to accurately characterize objects of different shapes accurately under indoor and outdoor conditions.
Table 8. Edge similarity scores (ESS) for paired images of regular-shaped objects, artificial trees, and field-grown trees from the camera and the laser sensor at different detection distances and travel speeds. Object Detection
Travel Speed (km h-1) 3.2 4.8 6.4 8.0 Beach ball at 0.6 m height 2 0.974 0.971 0.965 0.943 3 0.951 0.957 0.953 0.955 4 0.939 0.960 0.966 0.964 5 0.906 0.900 0.923 0.939 Beach ball at 1.6 m height 2 0.958 0.973 0.973 0.964 3 0.953 0.952 0.957 0.941 4 0.924 0.911 0.956 0.961 5 0.936 0.903 0.925 0.940 Beach ball at 2.5 m height 2 0.970 0.957 0.970 0.954 3 0.964 0.962 0.961 0.960 4 0.920 0.937 0.943 0.946 5 0.933 0.919 0.939 0.945 Rectangular box 2 0.965 0.962 0.966 0.958 3 0.973 0.975 0.961 0.973 4 0.978 0.976 0.978 0.971 5 0.981 0.972 0.971 0.973 Cylinder 2 0.972 0.964 0.976 0.967 3 0.975 0.985 0.984 0.987 4 0.984 0.977 0.977 0.984 5 0.977 0.964 0.975 0.985 Artificial tree 1 2 0.944 0.930 0.936 0.938 3 0.928 0.937 0.941 0.940 4 0.955 0.969 0.968 0.962 5 0.939 0.962 0.948 0.953 Artificial tree 2 2 0.913 0.899 0.916 0.905 3 0.906 0.911 0.917 0.921 4 0.900 0.900 0.910 0.906 5 0.904 0.883 0.883 0.885 Field tree 1 2 0.850 0.861 0.881 0.873 Field tree 2 2 0.926 0.924 0.937 0.937 Field tree 3 2 0.850 0.872 0.859 0.855
The measurement accuracy of the 270° radial range laser scanning sensor was evaluated with actual measurements of three beach balls at three heights, a rectangular box, a cylinder, two artificial trees, and three field-grown trees at four travel speeds and four detection distances. The dimensions of the objects and trees with complex shapes and sizes measured with the laser sensor agreed well with the actual dimensions of these objects and trees under indoor and outdoor conditions. For the eight objects detected at travel speeds ranging from 3.2 to 8.0 km h-1 and detection distances ranging from 2 to 5 m, the average CV was not greater than 6.1% in the X direction (travel direction), 8.6% in the Y direction (depth direction), and 7.0% in the Z direction (height direc-tion). Similarly, the average RMSE was not greater than 60 mm for horizontal width detection, 50 mm for depth detection, and 68 mm for detection of vertical height ranging from 0.58 to 3.35 m. For every object, the contour similarity between paired images from the laser sensor and the camera was greater than 0.85.
The test results demonstrated that the 270° radial range laser sensor and the specifically designed algorithm were able to accurately measure object surfaces with complex shapes and sizes at differentsensor travel speeds and detection distances between the sensor and the object. Subsequently, six air-assisted variable-rate prototype sprayers with integration of the laser sensor and algorithm were developed to deliver the required amounts of spray to target plants based on the plant canopy structure and sprayer travel speed in real time. The sprayers were successfully tested for precision spray applications and biological control efficacy under commercial field conditions.
The authors acknowledge invaluable technical assistance from Adam Clark, Barry Nudd, Keith Williams, Dr. Erdal Ozkan, Dr. Yu Chen, and Dr. Yue Shen. We are also grateful to the USDA-NIFA Specialty Crop Research Initiative (Grant No. 2015-51181-24253), the National Natural Science Foundation of China (Grant No. 51505195), and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130501) for funding this research.
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