Accuracy Assessment of Horizontal Measurements from LiDAR Available in Mobile Phones

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Accuracy Assessment of Horizontal Measurements from LiDAR Available in Mobile Phones

Nasr Sabaa

Oct 6 University, Faculty of Engineering, Department of Civil Engineering,

Giza, Egypt

Abstract: The Apple Company has added LiDAR to mobile phones for the iPhone 12 Pro and iPhone 12 Pro Max camera systems. This addition makes various applications, including Measure and Photos, run better and faster. A typical LiDAR sensor sends out pulsed light waves into the surrounding environment. These impulses bounce off surrounding objects and return to the sensor. The sensor uses the time it takes each pulse to return to the sensor to calculate the distance traveled.

In this study, LiDAR technology added to Iphone Pro-Max 12 was used to measures interior 2D plan of small building, nearly 85 square meters using polycam software which is commercial software available in apple store, interior scanning for the building walls done using LiDAR in Iphone mobile in kinematic mode, while moving in hand, at distance nearly 3m far from each wall side. The same building was observed by Leica total station for its partition corners getting their coordinates. 4 minutes is the duration to scan all building partitions using Iphone LiDAR scanner, while the same job took 2 hours using Leica total station. After scanning by iPhone LiDAR and measuring coordinates by total station instrument for building interior, a 2D plan was draw from the produced point cloud from Iphone LiDAR after exporting into PTS, Position and Trunk Scanner, which imported to Autodesk Recap, RCP, real capture project. Also, another 2D plane was illustrates from the total station measurements. The two 2D plans were compared together against, partition side lengths, Areas, and angles. Taking the time of observation into consideration, and the resulted used statistical parameters, it is remarkable that, horizontal measurements using the available LiDAR technology in iPhone mobiles is acceptable to some extent especially in limited extension jobs. Side lengths and areas measurements have root mean square error 0.08m and

    1. m² respectively. While little differences in angle occur, the calculated root mean square error was 2.02 degrees. Measurement resulting from iPhone scanner was little errors compared with measurements by Leica total station. Therefore, the measurements using this technique are useful, at least for projects like that selected in the research as study area.

      Keywords: iPhone, LiDAR, total station, Accuracy, Assessment:

      1. INTRODUCTION

        Since the 2000s, ground laser scanning has become an increasingly important method of recording a detailed feature like historic buildings in protected areas. This is to reduce the difficulty of working in large areas, save time, and at the same time better understand the details of the area [1]. Laser scanner instruments are based on the principal of light detection and ranging LiDAR. LiDAR is a popular remote sensing method used for measuring the exact dimensions of an object on the earths surface. Even though

        it was first used in the 1960s when laser scanners were mounted to aero planes, LiDAR didnt get the popularity it deserved until twenty years later [2]. Today it has become a very important technology in many engineering and non- engineering fields. Even though it was first used in the 1960s when laser scanners were mounted to airplanes, LiDAR didnt get the popularity it deserved until twenty years later [3]. Today, LiDAR popularity has increased and obtained the importance it deserves; now it is available in mobile phones; giving more chance to public users for simple and quick access to measurements and calculating the distances between objects. LiDAR also become important key factor in gamming because it simulates nature and makes the objects and tools used more realistic.

        Terrestrial laser scanner devices today represent one of the most widely and important instruments in the field of surveying engineering and environmental applications. Laser scanner instruments can collect irregular 3D point clouds of land areas, rivers, and roads, constructions, analyzing infrastructure or

        even collecting point clouds from the inside and outside of buildings in a fast and cheap way.

        With LiDAR technology, it is possible to acquired 3D point data (point cloud) on surface of an object with high accuracy. In addition, this 3D point group data can be transformed into 3D mapping, modeling and quantitative using appropriate software, this products may be useful in several applications. LiDAR systems are classified into two types based on its functionality Airborne LiDAR & Terrestrial LiDAR. Airborne LiDAR is installed on a helicopter or drone for collecting 3D data. As soon as its turned on, Airborne LiDAR send light towards the objects on the ground surface, and then, this emitted light returns to the sensor immediately after hitting the object, giving an exact measurement of its true dimensions. Airborne LiDAR divided into two types Topological LiDAR and Bathymetric LiDAR. Unlike Airborne, Terrestrial LiDAR systems are installed on moving vehicles or fixed in static mode on tripods on the earth surface for collecting accurate 3D data points.

        LiDAR principal has followed a simple idea emitting laser light at an object on the earth's surface then calculating the time it takes to return to the emitting source of LiDAR. Given the speed at which the light travels (approximately 300,000 km per second), the process of measuring the exact distance through LiDAR appears to be incredibly fast. However, its very technical. The formula that analysts use

        to arrive at the precise distance of the object is as follows: the surface of the object then reflects the laser beam [4].

        =

        Equation (1)

        Using the principles of pulse time of flight, the distance to

        2

        The distance of the object = (Speed of Light x Time of

        Flight) / 2, where,

        D, is distance of the object to the emitting source C, is the Speed of Light in space

        T, is time of Flight

        A laser scanner consists of an emitting pulses that produces a light source at a specific frequency. A mirror directs the laser beam horizontally and vertically towards

        the object can be determined by the transit time, with a precision of 4 mm [5]. The result of a scan produces a collection of points in space, 3D, commonly known as point clouds,

        Which can be processed and combined into accurate 3D models; figure 1 shows the principle of the laser scanners.

        Figure 1: principal of laser scanner

        LiDAR can be used to accomplish many developmental objectives, some of which are: depth of the oceans surface to locate any object submerged in oceans or seas due to accident or for research purposes, they use LiDAR technology to accomplish their mission. Terrain elevations play a crucial role during the construction of roads. Small and large buildings and bridges. LiDAR technology has 3D coordinates, which makes it incredibly easy to produce the 3D representation of elevations or 2D plans to ensure that concerned parties can draw necessary conclusions more easily. Typical applications of LiDAR technology in agriculture are used. Besides this, it is also used for campaign planning, mapping under the forest canopy.

      2. DATA SETS

        Three tools were used in this experiment, iPhone pro-max mobile provided with LiDAR scanner, polycam software used in data collection, and Leica total station instrument. IPhone 12 pro max has 8GB RAM and 256GB storage. The rear camera consists of a 12MP (wide) + 12MP (telephoto) 5x otical zoom + 12MP (ultra-wide) sensors and a LiDAR scanner for night mode. The front camera has a 12 MP (wide) + SL 3D (depth/biometrics) camera sensor. An image is posted showing a diagram of the rear of an iPhone in figure 2, sniped to show the camera bump and the standby button. As shown in the figure 2, three of the camera lenses are normal, while a fourth is indicated to be different, something the tweet describes as LiDAR in the "iPhone 12 Pro" and "iPhone 12 Pro Max" models [6].

        Figure 2: LiDAR scanner location in Iphone mobile.

        Polycam software is a leading 3D capture application for iPhone Creates high-quality 3D models from photos, and rapidly generates scans of spaces with the LiDAR sensor. Polycam software has the capability to export 3D capture to many extensions [7]. in this paper, polycam software used in scanning the interior walls for the building and then used to process the collected point cloud for producing the 3D modeling.

        Leica total station instrument TS03 model with 3 seconds accuracy and distance accuracy 1mm +1.5ppm used to measure the x,y coordinates for the interior of the building using single laser beam reflector less option without using any prism. Figure 3 shows the Leica TS03 instrument. The study area is chosen to be a small building (apartment), its area is about 85 square meters, 8m by 10.5 m, it contains 8 partitions.

        Figure 3: TS03 Leica instrument

      3. METHODOLOGY

        iPhone ProMax 12 used to collect measurements data for the small building. 3D Point cloud was collection using Kinematic mode as the mobile phone handheld. Using the polycam software, interior scanning for the building were done. Raw data in the form of point cloud were collected while the mobile phone moving nears the walls, nearly 3 meters apart. Raw data from mobile phone in the form of Point cloud (174.6 MB) exported to dxf formal to be used by Autodesk software, the storage capacity after exportation is 262.2 MB included 389,500- 3D points. The collected data was 2*2 mm to 5*5 mm grids using iPhone mobile (ProMax 12) with the aid of polycam software. As described, the 3D data were collected in kinematic mode, the mobile phone moving near the walls catching in hand, so, lidar beam transmitted directed to the objects (walls) surrounding it by mesh, then the raw data (point cloud) were transformed to 3D object using the same software. Data process by polycam taking about 3 minutes to transform. The lidar rays are emitted from the mobile, and within the range of three to five meters, they can surround the targets with a two- dimensional mesh, this mesh appears clearly on the mobile screen, and the person conducting the survey can move in the direction of the scanning line when all the visible targets are covered by this mesh. it is remarkable that, during the collection of LiDAR data from the mobile phone, the 2D mesh traced on the mobile screen more extensively and density in the corners and deep places, as well as on the ground line of all walls elevations. Figure 4 shows the collected LiDAR mesh size compared with a fixed target has 8 * 8 centimeters. Also, the traced mesh was uniform; twice the size of the fixed target for the objects has the same pattern, nearly, sixteen centimeters. In all cases, after the data process with polycam software, the final mesh size of the produced point cloud was 2*2 mm to 5*5 mm with different pattern as measured from AutoCAD program, figure 5.

        figure 4: LiDAR mesh while data collecting with a fixed target.

        figure 5: Point cloud as obtained from iPhone Mobile LiDAR scanner

        The same raw data point cloud- figure 6 are then proceeding using the same software polycam – to be visualized in 3D modeling as object. Figure 7 shows the 3D modeling produced from the point cloud after process. The dxf file then used by AutoCAD software and all walls are manually digitized and traced as 2D plane using AutoCAD software.

        Measurements obtained from LiDAR

        iPhone mobile was used to know at what extent this measurement useful and the possibility of using them for simple tasks quickly without affecting the accuracy, this is the objectives of this paper. Therefore, scanning wall faces of the sectors or partitions forming the whole building also, the openings represented in doors and windows only

        without taking into consideration any internal details are followed. Nearly 3 meter was the distance from which all walls were scanned without affecting any problems in coverage. Therefore, 3m apart was the planed distance that was followed in data collection throughout. The scanning duration for all partitions with an approximately 85 square meters was nearly four minutes using iPhone LiDAR. The product from this process is a three-dimensional point cloud represents a detailed survey of the component parts of the building walls. The obtained 3D point cloud was used by AutoCAD program to produce 2D plan for the building. Polyline tool command from AutoCAD tools was used manually to digitize building walls which appeared clearly in the 3D point cloud. walls appear somewhat clearly represented by dense points on both sides of the walls, and the width of these walls ranged from 12 to 20 cm. Figure 8 shows the methodology flowchart, while, Figure 9 shows the extracted 2D map from both iPhone and total station measurements included partition areas. Figure 10 shows the extracted 2D map included side lengths. Figure 11 shows the extracted 2D map included point numbers for the selected angles and coordinates. After finalizing tracing the 2D plan for the building, dimensions and angels for the building walls were extracted, and the areas of all partitions are calculated. The same building was observed using Leica instrument total station. Building corners for all partitions were observed and x,y coordinates are collected, then the 2D plan was traced by AutoCAD, then dimensions and partitions interior angles were extracted from the drawing

        also the partition areas were calculated. The two 2D plans are then identically Geo-referencing together using one common point as a base point has the same coordinates and the coordinates of corner for all building were extracted. Four items were computed and compared from the two 2D planes, angels, side lengths, areas, and coordinates of all points forming the model. The methodology that was followed in the research starts from using LiDAR on the iPhone for scanning the interior parts of the selected building represented in included door openings and windows, as well as making a two-dimensional survey observation using the Total Station device. The raw data generated by the iPhone are then exported to 3D point cloud. The 3D point cloud was processed to produce a 3D modeling for the building. The point cloud was used by the AutoCAD program to draw the two-dimensional plan by deducing the outer limits of the partitions of the building, as it appears in the form of dense point clouds ranging in width from 12 cm to 20 cm and is easy to distinguish and draw using the Polyline tool from AutoCAD. Also, the observations from the Total Station device were used directly to draw a two-dimensional horizontal plan. The two 2D plans resulting from the hand-held iPhone mobile scanning and the Total Station observations were used together to in evaluation process. The elements of evaluations were, areas of the partitions, the lengths of the sides for the entire walls of the building, the interior angles, and the point's coordinates of the 2D plan corners.

        Figure 6: 3D point cloud as produced from iPhone scanning

        Figure 7: 3D modeling produced from point cloud after process.

        Figure 8: Methodology flowchart

        Figure 9: 2D plan indicates partitions areas, (a) produced from I phone and (b) produced from total station.

        Figure 10: 2D plan indicates side lengths, (a) produced from I phone and (b) produced from total station.

        Figure 11: 2D plan indicates selected points id for coordinates and angles.

      4. RESULTS

<>The evaluation of the data produced from total station observations and iPhone measurements are done using four elements. The two 2D plans from the two equipments are used for elements extraction the following, (1) Area of each partition, (2) side lengths, (3) interior angles, and (4) corner coordinates. Four statistical parameters were used; (1) the minimum error, (2) maximum error, (3) the mean error, and

(4) root mean square error. The coordinates of 35 selected points and interior angle around these points were measured from the two 2D planes of the total station observations and LiDAR scanning from iPhone mobile. The coordinates and the interior angles are tabulated in table 1. The differences in angles and coordinates between the two equipment are given in the same table, table 1. RMSE, the most widely used statistics as a measure of accuracy was calculated and used to evaluate the quality of iPhone mobile measurements against total station measurements, equation 2. RMSE can be given by,

(min, max, mean and RMSE) for coordinates of the 2D plan of iPhone and total station are given in table 3, it is remarkable from this table that, the maximum error in x- coordinates is 0.02m, while it is 0.04 m for y-coordinates, the RMSE are 0.05 and 0.06 meters for x and y-coordinates respectively. The mean error was 0.02 and 0.01 for x and y- coordinates respectively. Little deformation in the shape of the 2D plan produced from iPhone was remarkable. It was also noticeable that there was a big distortion in angle 8. The value of the distortion was 4.854 degrees, the reason maybe it was considered as obtuse angle. Angles 19,29, and

31 are also have big errors to some extent, the errors included in these angle ranges 4 to 6 degrees the reason maybe existing these angles in small partitions. All the remaining angles has differences not exceeds 2 degrees, table 1. Overall, the minimum, maximum and mean errors in angles of the 2D plan are (-6.88, 3.35, and -0.42) degrees while the root mean square error was 2.01-degree, table 4. Statistics for the side lengths of the 2D plan of iPhone and

RMSE =

( )

( 2)

total station are given in table 5, form this table, it is noted

Where,

.

.

=

n, is the number of

=

checkpoints

that small differences exist between the two types of the data, few centimeters differences exist between side lengths in the two plans. The minimum, maximum and mean error for 27 side are (-0.18, 0.18, and 0.01) m with RMSE 0.08 m.

Hk Are iPhone measurements of point k,

Hk Are the total station measurements of point the point k.

error in Areas are small like the error in lengths, there was little differences between the two sources of the data, the

.

Table

2 descripts the values of partitions area and their

minimum, maximum and mean error for 8 partitions were (- 0.31, 0.54, and 0.04) m² with RMSE 0.28 square meters,

differences produced from the two data sources. The

partition areas range 38.55 to 1.76 square meters. Statistics

table 6.

TABLE 1: Coordinates and angels of the 2D plan measured from the two data sources.

Po-id

(coordinates)

angles/degrees

Side- length /m

I phone

T.S

Diff /m

x

y

x

y

dx

dy

I phone

T.S

Diff

I phone

T.S

Diff

1

5353.52

4089.5

5353.48

4089.47

0.042

0.02

90.296

90.19

-0.10

3.46

3.49

-0.03

2

5353.55

4087.355

5353.49

4087.32

0.055

0.02

89.908

90.66

0.75

0.79

0.86

-0.07

3

5357.66

4087.321

5357.60

4087.26

0.055

0.05

91.677

90.93

-0.74

8.68

8.68

0

4

5357.69

4089.641

5357.65

4089.58

0.04

0.05

90.593

89.81

-0.78

1.08

1.06

0.02

5

5354.44

4089.839

5354.40

4089.80

0.04

0.03

90.118

90.19

0.072

1.73

1.71

0.02

6

5355.58

4089.797

5355.54

4089.75

0.04

0.04

89.898

89.26

-0.629

2.47

2.48

-0.01

7

5355.57

4090.788

5355.54

4090.74

0.034

0.04

134.7

135.0

0.36

11.19

11.23

-0.04

8

5354.44

4090.803

5354.41

4090.76

0.034

0.03

139.994

135.1

-4.854

2.33

2.35

-0.02

9

5355.75

4089.798

5355.71

4089.75

0.04

0.04

87.998

89.62

1.622

5.21

5.03

0.18

10

5357.70

4089.815

5357.66

4089.76

0.039

0.05

92.447

91.51

-0.933

1.67

1.7

-0.03

11

5357.69

4090.777

5357.66

4090.72

0.034

0.05

89.526

89.52

0.002

0.61

0.58

0.03

12

5354.62

4092.857

5354.60

4092.82

0.021

0.03

90.819

89.81

-1.007

2.28

2.21

0.07

13

5354.60

4090.96

5354.57

4090.92

0.033

0.03

90.169

90.77

0.608

2.56

2.58

-0.02

14

5357.68

4090.948

5357.64

4090.89

0.032

0.05

88.071

89.4

1.329

1.12

0.96

0.16

15

5357.67

4092.846

5357.65

4092.79

0.021

0.05

90.941

91.15

0.215

1.05

1.14

/td>

-0.09

16

5354.67

4093.037

5354.65

4093.00

0.02

0.03

92.17

90.19

-2.041

1.05

1.07

-0.02

17

5355.68

4093.023

5355.66

4092.98

0.02

0.04

88.076

88.68

0.604

2.29

2.47

-0.18

18

5355.72

4095.337

5355.71

4095.29

0.006

0.04

91.881

90.20

-1.679

2.31

2.47

-0.16

19

5354.66

4095.331

5354.66

4095.29

0.006

0.03

97.873

90.98

-6.884

1.01

1.08

-0.07

20

5355.90

4096.438

5355.90

4096.39

-0.00

0.04

91.357

90.26

-1.096

3.41

3.44

-0.03

21

5355.84

4093.026

5355.82

4092.98

0.021

0.04

89.744

89.70

-0.039

3.71

3.67

0.04

22

5359.46

4093.001

5359.44

4092.93

0.02

0.06

90.045

89.80

-0.238

3.45

3.38

0.07

23

5359.55

4096.448

5359.55

4096.38

-0.00

0.06

88.855

90.22

1.373

3.06

2.97

0.09

24

5354.66

4095.487

5354.66

4095.45

0.006

0.03

87.446

89.07

1.625

1.9

1.8

0.1

25

5355.71

4095.503

5355.71

4095.46

0.005

0.04

90.277

90.41

0.133

1.9

1.74

0.16

26

5358.29

4096.62

5358.29

4096.56

-0.00

0.05

90.97

90.38

-0.581

1.13

1.13

0

27

5358.13

4099.513

5358.15

4099.45

-0.02

0.05

91.307

90.13

-1.177

0.96

0.94

0.02

28

5356.96

4100.698

5356.98

4100.65

-0.02

0.04

89.685

89.54

-0.141

0.99

0.91

0.08

29

5354.63

4100.712

5354.66

4100.67

-0.02

0.03

96.109

91.38

-4.724

1.95

1.87

0.08

30

5350.88

4088.109

5350.83

4088.09

0.051

0.01

85.723

87.24

1.519

0.96

0.93

0.03

31

5353.36

4088.101

5353.31

4088.07

0.051

0.02

88.482

91.82

3.347

2.15

2.17

-0.02

32

5354.44

4089.839

5354.40

4089.80

0.04

0.03

89.138

88.96

-0.176

2.32

2.33

-0.01

33

5354.34

4099.308

5354.36

4099.27

-0.01

0.03

89.646

90.35

0.706

4.11

4.05

0.06

34

5350.88

4099.308

5350.90

4099.29

-0.01

0.01

91.388

91.21

-0.172

2.15

2.17

-0.02

35

5353.52

4089.5

5353.52

4089.5

0

0

88.702

89.33

0.633

3.08

3.09

-0.01

TABLE 2: Area from 2D plan measured from the two data sources and their differences.

partition / Area

Area / m²(T.S)

Area/ m² – I phone LiDAR

Difference / m²

partition 1

38.235

38.558

-0.314

partition 2

15.067

15.213

-0.151

partition 3

12.688

12.308

0.226

partition 4

2.374

2.658

-0.283

partition 5

5.815

5.274

0.541

partition 6

1.896

1.761

0.024

partition 7

9.251

9.221

0.137

Total Area

85.326

84.993

0.324

TABLE 3: Statistics for coordinates of the 2D plan measured from the two data sources.

Statistics (coordinates)

X,m

Y,m

Min error

-0.027

0.011

RMSE

0.055

0.064

Max error

0.02

0.04

Mean error

0.02

0.01

TABLE 4: Statistics for angels of the 2D plan measured from the two data sources.

Statistics (angels)

Angle difference (degree)

Min error

-6.88

Max error

3.35

Mean error

-0.42

RMSE

2.01

TABLE 5: Statistics for side length of the 2D plan measured from the two data sources.

Statistics (side length)

side length difference (m)

Min error

-0.18

Max error

0.18

Mean error

0.01

RMSE

0.08

TABLE 6: Statistics Areas of the 2D plan measured from the two data sources.

Statistics (partition area)

partition area difference (m²)

Min error

-0.31

Max error

0.54

Mean error

0.04

RMSE

0.28

Profiles for some verification elements were illustrated in figure 12 and 13; figure 12 shows the relation between the two types of the data from total station and iPhone LiDAR

for partition areas, side lengths and angels. Regarding this figure, areas and side lengths profiles are systematic and same pattern, while the angle

40 AREAS

30

20

10

0

1 2 3 4 5 6 7 8

T.S I phone

SIDE LENGTHES

12

10

8

6

4

2

0

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

TS I phone

ANGLES

140

120

100

80

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

I phone T.S

Fig. 12: A profiles for Areas, Side lengths and Angles for the 2D plan produced from TS and iPhone LiDAR.

40 AREAS

30

20

10

0

1 2 3 4 5 6 7 8

T.S I phone

SIDE LENGTHES

12

10

8

6

4

2

0

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

TS I phone

ANGLES

140

120

100

80

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

I phone T.S

Fig. 12: A profiles for Areas, Side lengths and Angles for the 2D plan produced from TS and iPhone LiDAR.

0.6

0.4

0.2

0

-0.2

0.2

0.2

0.1

0

0.1

0

-0.4

-0.1

-0.2

-0.1

-0.2

4

2

0

-2

-4

-6

-8

AREA DIFFERENCE

1

2

3

4

5

6

7

8

SIDE LENGTHES

DIFFERENCE

SIDE LENGTHES

DIFFERENCE

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

ANGLES DIFFERENCE

1

3

5

7

9

11

13

15

17

19

21

23

25

27

29

31

33

35

Fig. 13: A profiles of differences for Areas, Side lengths and Angles for the 2D plan produced from TS and iPhone LiDAR.

  1. CONCLOUSION

    The availability of LiDAR technology in mobile phones became very important to know the extent of reliance on this technology without making serious mistakes. Where it is considered as new technology added in Mobil phones nowadays, also it is very saving time and effort as well as cost. Therefore, the aim of the research was to evaluate the performance of LiDAR available in these mobile phones for simple surveying work need in our daily life to show is this technology useful or not and at what extent can use it? To answer these questions, Two-dimensional interior 2D plans for a small building with an area of approximately 85 square meters were observed by total station instrument and used as reference data to evaluate the same production from LiDAR scanner available in iPhone Mobiles. Some statistical parameters were used to achieve this evaluation. The mean, minimum, maximum differences and the root mean square error (RMSE) used as four assessment parameters. While the evaluation items used were, the angles, the side lengths, the areas and the point coordinates from the 2D plans produced from the two equipment. Results showed that the measurements accuracies from iPhone are useful to some extent at least for the study case. Measurements using liDAR available in mobile iPhones were compatible with the corresponding measurements from total station instrument. RMSE were (2.01degree, 0.08 m, 0.28m²) for angles, side lengths and partition areas respectively. While the RMSE for point coordinates were (0.02 m and 0.01 m) for x and y coordinates respectively. Therefore, based on the obtained results, measurement error getting from iPhone scanner was little compared with measurements by Leica total station. Therefore, the measurements using this technique are useful, at least for projects like that selected in the research as study area.

  2. REFERENCES

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