Support for Precision Agriculture in Colombia using images acquired from Unmanned Aerial Vehicles (UAV’s)

Apoyo a la Agricultura de Precisión en Colombia utilizando imágenes adquiridas de vehículos aéreos no tripulados (UAV’s)

Juan Camilo Fajardo-Junco a

a Facultad de Ingeniería, Pontificia Universidad Javeriana, Colombia. fajardo-juan@javeriana.edu.co

Received: November 2th, 2012. Received in revised form: November 7th, 2013

AbstractThe document that follows is the result of a Graduation Project, in which it was developed a contribution to Precision Agriculture (PA) by

formulating a mathematical method that enables to get the crop's area from aerial photographs taken from an Unmanned Aerial Vehicle (UAV). Through the results gotten it of the measurements, it is possible to take decisions about the crops, as well as estimate its production. The validation of the developed method is given in the photogrammetric analysis of a crop of gooseberries in the Bogota savannah, Colombia.

Keywords: Precision Agriculture; photogrammetric; UAV; aerial photographs.

ResumenEl documento que se presenta a continuación es el resultado de un Trabajo de Grado, en el cual se desarrolló un aporte a la Agricultura de

Precisión (AP) mediante la formulación de un método matemático que permite realizar el dimensionamiento de áreas de cultivos a partir de fotografías aéreas tomadas desde un Vehículo Aéreo no Tripulado (UAV), a través de dicho dimensionamiento es posible tomar decisiones sobre el cultivo así como estimar su producción. La validación del método formulado se dio dentro del análisis fotogramétrico realizado a un cultivo de uchuvas en la Sabana de Bogotá, Colombia.

Palabras clave: Agricultura de Precisión; fotogrametría, UAV, fotografías aéreas.

1 Introduction

Precision Agriculture (PA) helps to manage and administer agricultural plantations efficiently. PA is an information system that requires the input data to generate decisions about resources to be managed in a crop.

In this article we demonstrate how to implement PA by obtaining relevant information from aerial photographs of crops purchased from an Unmanned Aerial Vehicle (UAV), to get this information is necessary a photogrammetric process (measurement on photographs) to identify the area of an agricultural plantation. The finding of this area is done by formulating a mathematical method that draws the crop inside irregular polygon, the crop is captured within an aerial photograph taken from a camera on the structure of a UAV.

2 Problematic

Precision Agriculture (PA) is an agricultural term used in the management of agricultural parcels, based on the constantly changing field. PA requires the use of Global Positioning System (GPS), sensors, satellite and aerial images together with the help of a Geographic Information System (GIS) to estimate, evaluate and understand changes [1]. These

changes are transformed into variables that estimate the amount of fertilizers, herbicides, pesticides, supplies, nutrients and products needed nutrients in a crop plantation.

In 2006 it was spent $ 119.2 billion in agricultural fertilizers worldwide. These applications are used on crops to fertilize, avoid pests and provide nutrients [2].

Fertilizers are compounds of nitrogen, phosphorus and potassium in contact with air gases emanating increasing pollution levels in the ecosystem.

According to official figures IGAC (Instituto Geográfico Agustín Codazzi) in 2013, of the 22.1 million of hectares for agricultural, Colombia uses only 5.3 million, which means that only 24.1% of its capacity is used. Colombia has a significant agricultural potential because it has tropical conditions and variety of climatic zones. DANE figures indicate that in 2012, 11,204,685 people live in rural areas [3] which has its basis in farming, as small producers with traditional practices work.

The crop management practices in Colombia, are still very traditional and not very technologically advanced. An example is the potato harvest in the Plateau Cundiboyacense, large areas of crops suffer inclement weather against low temperatures, where the farmers are exposed to losing production due to poor technological support. If they could have help from technology having a support it could be used to

© The authors; licensee Pontificia Universidad Javeriana, Colombia.

protect the crop. A preventive action to save the harvest is the application of fertilizers to crops, which often some parts of the crop do not require it because it is already healthy and rich soil, but the poor spatial vision of the agronomists leads them to these actions to protect the plantations.

3 Alternatives

Innovative ways to use the satellite images in PA proposals have emerged in recent years; however, this alternative has several drawbacks, particularly the cost and the quality of the images. This images consume a lot of time to take and when you see the crop, the spatial and spectral resolutions of these images is not optimal [4].

Recently it has begun using Unmanned Aerial Vehicles (UAVs) equipped with sensors and with the ability to fly at low altitude and acquire images with high spatial resolution [5]. However normally the images taken are not perpendicular to the ground but oblique, which prevents a uniform scale and difficult to measure objects on the ground. The conditions for making these images require consideration of a large number of parameters if it is to perform measurements on the ground. Aerial images taken perpendicularly are suitable for composing and superimpose (find common and unifying image) with each other allowing to create digital maps, these can be ideal for capturing detail agricultural planting and features.

4 Emerging techniques – UAV’s

Modern techniques to capture photographs in air are the Unmanned Aerial Vehicles (UAV's), these are flight systems without pilot aboard, with the ability to be controlled from the ground or flying in automatic mode with a flight plan georeferenced by GPS. They have the ability to fly at low altitude and maintain a real-time communication with the ground station [6].

Within UAVs for educational and commercial environments there are several structural configurations, one way is by having a front-rotor UAV similar to an aircraft, another is a UAV with parallel rotor like a helicopter, this last one could have configurations of 4 and 6 rotors. They can reach altitudes of up to 150m, with data transfer to the ground station of about 20km radius [7].

The UAV can have sensors, this may be a camera with high resolution. It could also have image stabilization for aerial pictures that are taken properly regardless of movement or turbulence. The UAV has a set of sensors that support remote sensing of aerial photography such as GPS (provides geographical coordinates, altitude and time), barometer (air pressure gauge), electronic compass (indicates the cardinality), accelerometers (measures acceleration in the XYZ), axis gyroscopes (measured XYZ rotation), hygrometer (humidity measured) and altimeter (height measured with respect to ground) [6], all these sensors collect data which become variables for geographic information system and allow aerial photographs georeferenced. The spatial resolution of a UAV flying at 20m height can be 18mm.

5 About the solution

The geographical expansion of agriculture through crop plants leads to focus on close spaces for the use of soil nutrients, crop maintainability by applying fertilizers and pesticides and these spatial concentrations of plants can appreciate as polygons [8].

Moreover, most of the objects we have in our environment we can consider the irregular polygons, which are plane figures that are composed of infinite segments where the sides and interior angles are not similar to each other. These polygons are composed of vertices and joining two vertices form a line segment, inside a coordinate system is possible to register an irregular polygon.

5.1 Mathematical method

Taking in consideration the coordinates of the vertices of the polygon inscribed in a Cartesian plane and calculating the determinant between a couples of points, you may find the area of irregular polygon. The sum of the determinants gives the area of the regular polygon.

In the Fig 1. you can appreciate an irregular polygon in a coordinate system, with travel clockwise points (x1,y1), (x2,y2)… (xn,yn)

Figure 1. Polygon inscribed in a Cartesian plane

The determinant of the first pair of vertices is given by the cross product matrix, see eq. (1) and eq. (2)

det ¿[ x1 y1

x2 y2] (1)

det ¿x1 ∙ y2−x2∙ y1 (2)

The determinant to calculate the product between the base and height of the triangle formed between the coordinate points (x1,y1) and (x2,y2), for an irregular polygon with n vertices area can be calculated as in eq. (3)

A ¿ 12 |([ x1 y1

x2 y2]+[ x2 y2

x3 y3]+…+[ xn yn

x1 y1])| (3)

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The point (x1,y1) is repeated at the end to indicate the coordinates segment closes the figure, in the determinant the products that adds, add the internal area of irregular polygon, the products with negative sign suppress the external area to the irregular polygon, finally the method is established by the eq. (4)

A=12 |( ∑i=1

i=n−1

(x i ∙ y i+1− yi ∙ x i+1))+( xn ∙ y1− yn∙ x1 )|(4)

5.2 Variables

The variables listed below are important for properly sizing a geographic feature, which is required to be measured through aerial photograph taken from a photography system that will board the UAV.

5.2.1 Nadir

Corresponds to the point on the ground vertically beneath the perspective center of the camera lens [9] for appropriate decision in this picture should ensure that the camera lens is perpendicular to the surface.

Therefore if the photograph is made obliquely and not perpendicularly, cannot be considered as valid to perform a photogrammetric process to estimate the sizing of surface area through aerial photography, since it would measure about a geographic feature in perspective.

Consequently, making this aerial photograph is done through a camera GoPro Hero 3+ supported on an image stabilizer Tarot T-2D with IMU (Inertial Measurement Unit) which allows you to keep the camera perpendicular to the surface, said stabilizer is attached to the UAV flying in the GPS flight mode (flight mode that allows you to suspend a geographic point the UAV position corrections via GPS).

5.2.2. Height

The scale of an aerial photograph may depend on the height [10] to which the sample is taken, the UAVs have a GPS which gives the height in the marked geographic coordinate, also have the atmospheric pressure sensor to estimate the height. Regarding the use of this variable in the photogrammetric analysis performed on the Aerial Capture, will be taken a pattern measurement standard ashore, this allows discontinue the use of this variable.

5.2.2 Scale

This concept is an important dimension in reference the geographic objects because it indicates the ratio between the picture to be obtained and the ground reality of the object.

To control this variable regardless of the height can be done using a pattern, this is an object which you have certainty that its extent, the photogrammetry in aerial photographs can make use of patterns to identify sizing of the objects.

5.3 Software application

The function of this software application is to help develop the concept of photogrammetry (measurement on photographs) so that the technique can support the decisions made from Precision Agriculture, in addition to supporting the method developed in section 5.

This application receives as input an aerial photograph taken from the UAV, this photograph is an image of the aerial view of an area covered by an agricultural plantation area, with a pattern. Through the software application can draw two polygons, the first to enroll in an irregular polygon crop area displayed in the photograph and the second corresponds to the drawing of a square polygon that represents the area of the pattern, later the user must enter the actual size of the pattern and the software application will calculate the actual area of the crop by applying mathematical modeling method. Finally, the software provides the user the area and perimeter of the crop and an estimate of the total production of the crop.

This software application provides a visual interaction between what the user is looking at on the screen and what may be drawing with the mouse.

The software was developed in Java following the paradigm of object oriented programming, the application runs in stand-alone mode. The software was developed under the guidelines of Software Engineering that include conception of SRS (Software Requirements Specification) and SDD (Software Design Description), the software presents a MVC architecture and Fig 2. shows the analysis of a crop in an aerial photograph.

Figure 2. Software development

6 Testing

In the previous chapter was realized the analysis, design and development of a mathematical method for calculating the area of a crop from an aerial photograph captured from a UAV, this development ended with presenting a software application that implements the mathematical formulation, this chapter presents four tests framed within a pilot project that allows to verify the method and developed software.

In these tests we will check the error obtained in the calculation of sizing areas within a controlled environment, in

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addition to produce an analysis related to the field of view (FOV) depending on the height of the photo capture. Another study is about the spatial resolution of aerial photographs taken and finally concludes with a test in a crop to capture and deliver the relevant results on their sizing.6.1 Mean Squared Error (MSE)

The development of the test was to analyze the area of 5 samples of an image. The image size was 1280 x 960 px, this image had 4:3 ratio, it is valid as input to the software application developed. The picture is diagrammed with a rectangle 3.8 x 2.5m where cultivation is recorded and another rectangle of 1.5 x 0.9m with enrolled pattern. To develop the test we take 5 samples of the results produced by the software, in order to get the data of area and perimeter. To analyze the samples, we used of Mean Squared Error (MSE) with the following guidelines for each variable [11].

a. The 5 samples were performed due to the need to find an average value of the variable, as the user of the software can change your observation [12] and interaction with the application every time a scan is performed.

b. The average value of the variable x, is as in eq. (5)

¿ x>¿x1+x2+…+xn

n=∑

1

n

x i

n(5)

c. Once the average value was found, to find the MSE makes use of eq. (6)

∆ x=√∑1

n

¿¿¿¿¿ (6)

d. The analysis of the extent of the variable is expressed as follows in eq. (7)

¿ x>± ∆ x (7)

The actual size of area and perimeter giving the image is 9.50m2 and 12.60m respectively, the five samples taken and analyzed with the software developed and then calculating the mean value and the MSE, the results are:

Crop area9.53 ± 0.01m2

Crop perimeter12.63 ± 0.01m

6.2 Coverage area

The objective of this test is to determine the maximum coverage area according to the height of the UAV. The development of this test was to capture an aerial photograph in

a range of 10-14 meters of height, finally the aerial photography was taken to 11m of height.

In the picture was captured the pattern with dimensions of 1.49 x 0.8m. The photograph was pre-processed by the fisheye effect, this is produced by the wide angle lens GoPro Hero 3+. The result can be appreciate in Fig 3.

Figure 3. Aerial photography to 11m of height

This camera has the option to panoramic capture (wide), with a focal length of 14mm to a horizontal FOV of 122.6 ° and a vertical FOV of 94.4 °.

With the FOV and the flight height, it possible to calculate the maximum area that contains the aerial photography. The procedure uses the camera projection to the ground through a triangle [13], see the Fig 4.

Figure 4. Photography coverage

Coverage of the horizontal image is given by twice the height of the camera above the soil line and the tangent of the horizontal FOV divided in two. Once you have the coverage, you can calculate the area and perimeter of the image, see Fig 5

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Figure 5. Area and perimeter maxim in the photographyBy obtaining the width (C) and height (L), you can find the

perimeter (P) and maximum area (A) that will provide the image according to the height from which it was captured. The results for the first 20 meters in height are shown below in Table 1.

D C L A PUAV Height Coverage H Coverage V Area Perimeter

(m) (m) (m) (m2) (m)0,0 0,00 0,00 0,00 0,001,0 3,65 2,74 10,01 12,792,0 7,31 5,48 40,03 25,573,0 10,96 8,22 90,08 38,364,0 14,61 10,96 160,14 51,145,0 18,27 13,70 250,22 63,936,0 21,92 16,44 360,31 76,717,0 25,57 19,18 490,43 89,508,0 29,22 21,92 640,56 102,299,0 32,88 24,66 810,71 115,0710,0 36,53 27,40 1.000,87 127,8611,0 40,18 30,14 1.211,05 140,6412,0 43,84 32,88 1.441,26 153,4313,0 47,49 35,62 1.691,47 166,2114,0 51,14 38,36 1.961,71 179,0015,0 54,80 41,10 2.251,96 191,7916,0 58,45 43,84 2.562,23 204,5717,0 62,10 46,58 2.892,52 217,3618,0 65,76 49,32 3.242,82 230,1419,0 69,41 52,06 3.613,15 242,9320,0 73,06 54,80 4.003,49 255,72

Table 1. Area and perimeter to the first 20m

6.3 Spatial resolution

The development of this test is proposed to identify the spatial resolution (dimension that represents each pixel in reality), the aerial photo was taken in the format of 4000 x 3000 px for 12MP resolution. The following formulation shows the spatial resolution from the maxim area calculated in the previous test. See the eq. (8)

re=√ Ap

×1000 (8)

Generally the spatial resolution is given in meters, this length unit is widely used in the satellite images, for purposes of this test was evaluated from 0 to 100m high, so the spatial resolution is express in millimeters (mm), the number 1000 in

the formula is due to the latter assertion. The formulation is given as follows:

re: Spatial resolution in millimeters (mm) A: Maximum area present in the aerial photograph in

meters (m) p: number of pixels of aerial photography

For a 12MP resolution aerial photograph taken at a variable height from 0 to 100 m, the spatial resolution is the following, see Table 2.

D A Hectares SpatialUAV Height Area covered resolution

(m) (m2) (mm)0,0 0,00 0,0000 0,0010,0 1.000,87 0,1001 9,1320,0 4.003,49 0,4003 18,2730,0 9.007,84 0,9008 27,4040,0 16.013,95 1,6014 36,5350,0 25.021,79 2,5022 45,6660,0 36.031,38 3,6031 54,8070,0 49.042,71 4,9043 63,9380,0 64.055,78 6,4056 73,0690,0 81.070,60 8,1071 82,19100,0 100.087,16 10,0087 91,33

Table 2. Spatial resolution from 0 to 100m

Making an aerial photograph from the UAV to a height of 50 meters above the nadir, can cover an area close to 25,000m2

covering about 2.5 hectares and with a spatial resolution of about 46mm, the latter means that each pixel has a length of 4.6cm of reality, which allows to see precise details of the photographed item.

Currently the QuickBird satellite provides a spatial resolution of 61cm for panchromatic images, compared with previous data on the spatial resolution of 50m height, aerial photography from UAV's is a good alternative, in addition to being inexpensive, with catches in real time and better spatial resolution.

6.4 The crop of study

This last test supports the verification of the mathematical method developed to size the crop area by analyzing aerial photographs, the resulting image can be seen in Fig. 9

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Figure 6. Crop aerial photography

The analysis corresponds to growing a crop of gooseberries, this plant has fallen foliage and has yellow flowers and posteriorly it become the fruit of the plant, is characterized by having a height between 1m and 2m.

The crop is located at the geographical coordinates 5 ° 3 '53.9 "N, 73 ° 45' 31.1" W between 2750 m.a.s.l at its lowest point and 2760 m.a.s.l. at its highest point, this coordinate corresponds to the village of San Vicente in the municipality of Suesca, Cundinamarca, Colombia. The average temperature is 12 ° C with winds of 12 km/h.

We drew the plane of the crop, which has shaped like a "L" letter, the crop was measurement by the perimeter of it, using a tape measure 30 meters long, the diagram can be seen in Fig. 7

Figure 7. Crop diagram

Using a Cartesian plane and applying the mathematical method in Section 5, we can calculate the value of the variables, see Fig. 8. The area of this irregular polygon is 2.491m2 and their perimeter is the sum of the sides of the previous figure, it is a value of 238.5m.

Figure 8. Crop into a Cartesian plane

Once finished sizing the crop, the decision to perform a square pattern of side 20m was taken, because the area of this pattern accounts for 16% of the area of crop and for this we used four squares of 0.75m from the side, these materials was white interlining. Each square represents a vertex of the square of 20m.

Figure 9. Size and location of the pattern

The flight was performed with a UAV Hexacopter from 3DRobotics with a camera GoPro Hero3+ and with image stabilizer Tarot T-2D, the aerial photography was perpendicular to the surface in the ratio 4:3 and with a resolution of 4000 x 3000 pixels, finally the aerial photography was taken to 44.3m, with a coverage of 2 hectares. See Fig. 6.

With the software application developed, see Fig. 10, we analyzed five samples of area and perimeter of the crop, each data set was analyzed by the MSE.

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Figure 10. Analysis the crop with the software development

Sizing by ground (Metric tape and draw the crop)

o Crop area 2.491 m2

o Crop perimeter 238.5m

Sizing by aerial photography (UAV flight) and use software development and applying MSE.

o Crop area 2.498,5 ± 3.6m2

o Crop perimeter 242,1.5 ± 0.35m

Earlier results compared one to one that achieved in lifting the plane and taking aerial photographs show close values with small and irrelevant errors, which is important to note that the field of crop may have depression and had an inclination of 9.6°, imperfections may exist when drawing the pattern and the crop measurement instruments have errors and finally the aerial photography was taken at 44m of height. The spatial resolution was 40,2mm per pixel and a maximum coverage area of 1.9 hectares.

7 Conclusions

During this study it was shown that it is possible to use UAVs as a means to obtain aerial photographs, highlighting the photographs acquired from these aerial vehicles represent a cheaper alternative to satellite images or photographs taken from airplanes. It is also important to note that aerial photographs obtained from UAV's are available in places with topography inaccessible and with difficult weather conditions, as it is cloud cover or haze.

In this study was developed a mathematical method that is useful and valid for sizing the area and perimeter of a geographic object used a photogrammetric analysis of aerial photographs taken from a UAV.

This study supports data generation from a crop such as area, perimeter and estimated production, the data are

converted into input values to be considered and analyzed to generate decisions and solutions from the perspective of Precision Agriculture.

References

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[1] Marote, «Agricultura de Precisión,» Ciencia y Tecnología, ISEU, 2010.[2] D. Schimmelpfennig, «On the Doorstep of the Information AgeRecent Adoption of Precision Agriculture,» Economic Information Bulletin

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 47, NO. 3, 2009.[5] K. N. T. W. S. U. K. A. H. N. D. M. H. Anuar Ahmad, «Digital Aerial Imagery of Unmanned Aerial Vehicle for Various Applications,»

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resolution-test/.

J. C. Fajardo-Junco, student of last semester in System Engineering from the Pontificia Universidad Javeriana. Bogota, Colombia. From 2007 to 2009, he studied a Mechatronics Technologists in SENA. His research interests include: UAV’s, Robotics, Design, Intangible interfaces and physics computing.

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