[IEEE its Applications (CSPA) - Penang, Malaysia (2011.03.4-2011.03.6)] 2011 IEEE 7th International Colloquium on Signal Processing and its Applications - Calibration of high resolution

Calibration of High Resolution Digital Camera using Self-Calibration Bundle Adjustment Method

Wani Sofia Udin *1, Anuar Ahmad #2

*1Faculty of Agro Industry & Natural Resources Universiti Malaysia Kelantan

Lock Beg 36, Pengkalan Chepa, 16100 Kota Bharu, Kelantan, Malaysia

[email protected]

#2Department of Geoinformatics, Faculty of Geoinformation & Real Estate Universiti Teknologi Malaysia

81310 UTM Johor Bahru, Johor, Malaysia [email protected]

Abstract - Currently, the price of digital camera is decreasing and many users afford to purchase it. The digital camera can be used for many applications. The digital camera can also be used for accurate measurement such as determination of three dimensional (3D) coordinates, production of accurate measurement and generation of 3D model of objects. However, the digital camera need to be calibrated to obtain accurate results. The aim of this study is to calibrate the digital camera so that it could be used for accurate measurement. In this study, close range photogrammetric technique was used to calibrate three high resolution digital cameras. The digital cameras used comprise of Rollei D30, Nikon D60 SLR and compact Nikon Coolpix S560. The three digital cameras were used to acquire photographs of three different sizes of testfield that are equipped with retro-reflective targets. The approximate 3D coordinates of the different testfield were estimated by measuring it manually. The three digital cameras were calibrated using self-calibration bundle adjustment method. The photographs of the testfield were acquired using potrait and landscape setup for each camera location in 3D space. After the acquisition of the photographs of the testfield, they were downloaded into the computer for the measurement process of the retro-reflective targets and subsequently the final 3D coordinates of the retro-reflective targets were determined using the self-calibration bundle adjustment method. The coordinates of the retro-reflective targets were also determined using intersection method of total station which were used as referenced value. The 3D coordinates from the digital camera were then compared with the 3D coordinates of the total station. Results showed that the Nikon D60 SLR digital camera is superior than the other two digital cameras in term of accuracy and network precision. The next best result is shown by the Nikon Coolpix S560 compact digital camera and finally the Rollei D30. For the Rollei D30, the results are less accurate than the Nikon D60 SLR. However, the interior orientation parameters of this camera are very stable. In conclusion, all the three high resolution digital cameras have the potential to be used for various close range applications. Keywords- digital cameras; camera calibration; retro-reflective target; close range photogrammetry; test field

I. INTRODUCTION Close range photogrammetry has been used in various applications such as industrial applications, medicine, archeology, architecture, and so forth. Close range photogrammetry has many advantages including the measurement accuracy; short acquisition time and cost effective. The use of digital camera of different resolutions for different applications has an impact in terms of accuracy and precision of 3D measurement data. It is well established that to achieve accurate results, the camera must be calibrated.The aim of this study is to calibrate the digital camera so that it could be used for accurate measurement. The digital cameras used are the Rollei D30, Nikon Coolpix S560 and Nikon D60 as illustrated in Figs.1(a), 1(b) and 1(c). Several methods of calibrating digital camera are available which include on the job calibration, self-calibration bundle adjustment and plumb line calibration. The most widely used method is the self-calibration bundle adjustment which is adopted in this study. Fig.1(a) ROLLEI D30 Fig..1(b) NIKON COOLPIX Fig.1(c) NIKON S560 D60

2011 IEEE 7th International Colloquium on Signal Processing and its Applications

137978-1-61284-413-8/11/$26.00 ©2011 IEEE

II. METHODOLOGY

In this study, the methodology is divided into several stages: A. Literature Review

The literatures have been reviewed in order to understand the background of the study that has been made by previous researchers related to camera calibration. From the literature, it was found that usually some form of targets with known coordinates and also a scale is required for calibration process. As mentioned in Section 1, there are at least three methods commonly used for calibrating camera in close range photogrammetry. The most popular method that should be used is the self-calibration bundle adjustment method and it is suitable for calibrating film based camera or digital camera [2], [3], [12]. Also to obtain accurate results the convergent configuration of photography must be used. For the test field, it is recommended to use 3D test field which could provide the best result. In this study, this approach is used to calibrate the three digital cameras.

B. Planning Measurement In this study, three sizes of 3D test fields were constructed.

The total targets for the three calibration plates are the same. The first calibration plate has a dimension of 0.4 meter x 0.4 meter and consists of 36 screws of different height and arranged in matrix form of 6 x 6 units. Fig.2 shows an example of the calibration plate or test field. Notice that a scale bar is also placed in the test field to provide some form of control to the photograph. On top of each screw, retro-reflective target is stick on it. The second calibration plate has the same setup as the first calibration plate but the dimension is bigger i.e 0.6 meter x 0.6 meter. The third dimension of the calibration plate is 0.8 meter x 0.8 meter and both calibration plates also have the same total number of 36 retro-reflective targets.

Fig. 2 Test field of 0.4m x 0.4m

C. Field Data Collection The three digital cameras were each used to acquire photographs of the photogrammetric test fields at a constant distance (1 meter) from the camera to the midpoint of the calibration plate. Before taking any photograph, a scale bar of known value is placed in the calibration plate or the test field (Fig. 2). The retro-reflective targets were illuminated by built

in flash on every digital camera. Convergent photographs were taken with eight pieces of photographs for each camera. The photographs were taken with the camera in normal landscape position and then rolled it at 90°; and the photographs were acquired from four different camera locations in space. The digital camera need to be rotate 90° with the purpose to recover the principle point [2], [3]. The coordinates of the retro-reflective targets were also determined using total station which are used as reference or known value for accuracy assessment. For accuracy assessment, the 3D coordinates obtained from self-calibration bundle adjustment process (i.e photogrammetric method) are compared with their respective values determined from the total station, hence, network accuracy could be computed (Table 10, 11 and 12).

D. Image Measurement The acquired digital images for each digital camera of different dimension of calibration plate were downloaded one by one into a PC using appropriate software for image measurement. Targeted points were then measured automatically using Australis software. Then Australis perform the self-calibration bundle adjustment process and generate 3D coordinates of all the retro-reflective targets [5]. Australis also provides the value of camera calibration parameters of each digital camera. This software can produce a value of precision known as posteriori variance factor (Sigma nought). The smallest value reflects the highest precision. The digital cameras were calibrated one at a time.

E. Data Processing Self-calibration bundle adjustment method in the

Australis software produces five calibration files [5]. Additional files such as residual image coordinates, camera parameters and adjusted correlation matrix data, depending on the processing option.

III. RESULTS This study was conducted to evaluate the accuracy and

precision of measurement for different types of digital cameras and the 3D data obtained from Self-calibration bundle adjustment method. One of the important outputs produced from self-calibration bundle adjustment is the 3D coordinates of the object points. Other significant outputs include the camera calibration parameters, measurement residuals, precision and accuracy of calibration system, characteristic of stochastic coordinates and discrepancies of targeted coordinates. The results produced from a self-calibration bundle adjustment for the three digital cameras are tabulated in the following sections.

Scale bar


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NIKON NIKON ROLLEI COOLPIX D60 (SLR) D30

S560c (mm) 7.7749 6.931E-03 21.2012 2.093E-02 10.6429 9.480E-03xp (mm) -0.0649 7.359E-03 0.0836 1.891E-02 0.2783 1.062E-02yp (mm) -0.1536 7.060E-03 0.1860 1.728E-02 -0.0498 1.061E-02

k1 7.10100E-03 2.502E-04 1.83254E-04 9.243E-05 1.25882E-03 3.778E-03k2 -7.27032E-04 1.141E-04 -1.36159E-06 7.052E-06 2.81396E-05 3.692E-05k3 7.87930E-05 1.600E-05 3.59516E-08 1.721E-07 -2.91047E-06 2.938E-06p1 1.66967E-07 4.763E-05 -1.38283E-05 1.542E-05 -2.49500E-04 3.567E-05p2 1.32639E-04 4.654E-05 -1.49795E-05 1.515E-05 3.59760E-05 3.530E-05b1 3.16261E-04 1.109E-04 5.33903E-05 9.381E-05 5.23934E-05 1.208E-04b2 -1.34998E-04 1.292E-04 3.09247E-06 1.081E-04 9.42648E-05 1.383E-04

DIGITAL CAMERA

Std DevParameter Std Dev Std Dev


S560c (mm) 7.7938 7.035E-03 21.2423 1.024E-02 10.6712 6.716E-03xp (mm) -0.0600 4.985E-03 0.0678 8.411E-03 0.2664 7.221E-03yp (mm) -0.1378 5.094E-03 0.2171 8.111E-03 -0.0385 7.204E-03

k1 5.89760E-03 1.661E-04 2.06302E-04 3.361E-05 1.30710E-03 1.026E-04k2 -1.92982E-04 4.843E-05 -9.61525E-07 1.265E-06 -8.10300E-07 1.832E-05k3 1.04475E-05 4.222E-06 1.93634E-08 1.440E-08 -5.90363E-07 9.997E-07p1 -1.66240E-05 3.005E-05 -1.36190E-05 6.624E-06 -2.62903E-04 2.304E-05p2 1.31673E-04 3.071E-05 -2.20261E-05 6.364E-06 3.98000E-06 2.282E-05b1 3.06344E-04 8.675E-05 1.24916E-04 4.985E-05 5.35382E-05 8.639E-05b2 -3.72817E-05 1.082E-04 -1.03768E-04 6.308E-05 -6.82402E-01 1.063E-04

Std Dev

DIGITAL CAMERA

Parameter Std Dev Std Dev


S560c (mm) 7.7668 4.967E-03 21.2316 1.050E-02 10.4103 7.439E-03xp (mm) -0.0700 1.195E+00 0.0974 7.660E-03 0.2667 5.638E-03yp (mm) -0.1441 3.453E-03 0.2294 7.658E-03 -0.0449 5.844E-03

k1 5.09189E-03 9.649E-05 1.74598E-04 1.699E-05 1.56250E-03 8.342E-05k2 1.16136E-05 1.596E-05 2.28916E-07 3.448E-07 -1.35557E-05 8.979E-06k3 -6.60092E-06 8.288E-07 -4.18695E-10 2.126E-09 -3.16953E-07 3.043E-07p1 -2.58613E-05 1.837E-05 -1.58766E-05 5.031E-06 -2.98044E-04 1.662E-05p2 2.63763E-04 1.860E-05 -3.19870E-05 5.036E-06 -3.85991E-06 1.672E-05b1 2.10634E-04 6.929E-05 9.41291E-05 5.556E-05 4.14820E-05 8.863E-05b2 -2.56598E-04 1.428E-04 3.22892E-05 1.300E-04 -4.68888E-04 1.808E-04

Parameter

DIGITAL CAMERA

Std Dev Std Dev Std Dev

COOLPIX S560 ±0.30 ±0.31 96.51 x 72.38 3648 x 2736 ±0.15 ±0.16 0.731 412NIKON D60 ±0.64 ±0.62 102.43 x 68.57 3872 x 2592 ±0.09 ±0.09 1.538 331ROLLEI D30 ±0.42 ±0.40 67.51 x 50.79 2552 x 1920 ±0.11 ±0.10 0.971 423

Variance Factor (VF)

Degree Of

Freedom

Camera Std Dev. photocoord x

(µm)

Std Dev. Photocoord y

(µm)

Image Dimension

(cm)

Image Dimension

(pixel)

Std Dev. photocoord x

(pixel)

Std Dev. photocoord y

(pixel)

A. Camera Calibration Parameters Table 1, 2 and 3 showed the estimates and standard deviation for the camera calibration parameters used in the self- calibration bundle adjustment procedure for the 0.4m x 0.4m, 0.6m x 0.6m and 0.8m x 0.8m test fields respectively. It demonstrates that similar inner orientation parameters, comprising focal length (c), principal point offset (Xp, Yp), and correction terms for radial lens distortion (k 1, k 2, k 3), tangential lens distortion (p 1, p 2), affinity (b 1) and the differences in scale factor (b 2) were recovered for the three digital cameras. By using the convergent configuration network, additional parameters for all the three cameras can be obtained. These parameters should be tested to determine whether it is necessary to compare with stochastical properties. If the estimated value is smaller than the standard deviation, statistically parameter estimation is not required. Typically, additional parameters that are not necessary and associate with a high correlation between estimate parameters, they contribute to poor geometry. In this study, only a slightly difference of focal length derived for the three cameras based on the observed dataset every time the camera is calibrated. However, the focal length of Rollei D30 camera is more stable.

B. Measurement Residuals, Precision and accuracy of System Calibration. Table 4, 5 and 6 showed the stochastic qualities of the

measurements of photocordinates used in the self-calibration bundle adjustment, the computed a posteriori variance factors and accuracy of system calibration for each calibration plate or test field (0.4m x 0.4m, 0.6m x 0.6m and 0.8m x 0.8m). Standard deviation of x and y photocoordinates in micron unit (µm) for the three cameras were obtained using the self-calibration bundle adjustment processing option. The lowest Root Mean Square (RMS) residuals for different size of test field is given by Nikon Coolpix S560 compact camera, followed by Rollei D30 and finally Nikon D60 SLR camera. Posteriori variance factor is large in some cases which indicate that systematic errors exist in the calibration process.

TABLE 1: CAMERA CALIBRATION PARAMETERS FOR THE TEST FIELD 0.4m x 0.4m.

TABLE 2: CAMERA CALIBRATION PARAMETERS FOR THE TEST FIELD 0.6m x 0.6m

TABLE 3: CAMERA CALIBRATION PARAMETERS FOR THE TEST FIELD 0.8m x 0.8m.

TABLE 4: MEASUREMENT RESIDUALS, PRECISION AND ACCURACY OF SYSTEM CALIBRATION

(TEST FIELD 0.4 m x 0.4m)


(TEST FIELD 0.6m x 0.6m)





Degree Of

Freedom

Camera Std Dev. photocoord x

(µm)

Std Dev. Photocoord y

(µm)

Image Dimension

(cm)

Image Dimension

(pixel)


(pixel)


(pixel)


139


Std Dev. Photocoord x

(µm)


(pixel)


Degree Of

Freedom

Camera Std Dev. Photocoord y

(µm)

Image Dimension

(cm)

Image Dimension

(pixel)


(pixel)



C. Stochastical Characteristics of Coordinates Figure 3 shows a bar graph of overall network precision for Nikon Coolpix S560, Nikon D60 and Rollei D30 digital cameras of 0.4m x 0.4 m, 0.6 m x 0.6m and 0.8m x 0.8m test fields. The precision of all estimated coordinates and the overall network precision derived between two points widely separated by a longest distance in three different sizes of the test field. The figure also showed the variation of network precision for the three digital cameras with different types and resolutions. Results showed that the Nikon D60 SLR digital camera is superior than the other two digital cameras in term of accuracy and network precision. The next best result is shown by the Nikon Coolpix S560 compact digital camera and finally the Rollei D30. From this finding, it is clearly seen that there is a relationship between the resolution and the precison and accuracy of the camera. If the resolutions of the digital cameras increase, the accuracy also increases.

Fig. 3 Camera Precision

D. Discrepancies in Target Coordinates The estimated coordinates from the control survey of the

retroreflective targets derived from Leica Total Station TCR307 were accepted as the best estimate or true value and were used as check points. These accepted values were compared with the estimated coordinates from the self-calibration bundle adjustment to determine discrepancies and

hence to obtain a measure of the accuracy of each camera network and processing option. Fig. 4 shows a bar graph of the entire network accuracy for Nikon Coolpix S560, Nikon D60 and Rollei D30 digital cameras of 0.4 mx 0.4 m, 0.6 mx 0.8 mx 0.6 m and 0.8 m test fields. Results showed that the Nikon D60 SLR digital camera is superior than the other two digital cameras in term of accuracy and network precision. The difference of accuracy and precison of digital cameras is depending on several systematic errors such as camera calibration, convergence distortion, main points displacement, optical aberrations and others.

Fig. 4 Camera Accuracy

CONCLUSIONS

This study shows that the Nikon D60 digital SLR camera produces the best results in terms of accuracy and precision of the network and followed by a Nikon Coolpix digital camera and Rollei D30 camera after calibrating them based on the self-calibration bundle adjustment method. Generally, the Rollei D30 camera gives more stable internal orientation parameters and produces better results than the Nikon Coolpix digital camera. However, environmental factors such as lighting when acquiring photographs, the camera distance to the midpoint of the test fields, the camera position, the resolution and also pixel size of the digital camera could affect the final result. This study also shows that the compact digital camera Nikon Coolpix and Nikon D60 can be used for close range photogrammetric applications and other applications in different field. All the digital cameras used in this study have the potential to be used for various applications where high accuracy is not required and when the budget is minimal. Finally, this study also provides a guideline to digital camera users to select the appropriate digital camera any applications and the most important lesson learned from this study is that it must be calibrated every time to obtain quality output in term of precision and accuracy.


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ACKNOWLEDGMENT The authors wish to acknowledge use of the Australis self- calibrating bundle adjustment program developed by Professor Clive Fraser at University of Melbourne, Australia. The Rollei D30, Nikon SLR D60 and Nikon Coolpix S560 digital cameras used in this study were obtained from the Department of Geoinformatic, Faculty of Geoinformation and Real Estate, Universiti Teknologi Malaysia, Malaysia.

BIBLIOGRAPHY [1] Abdul Hamid Mohd Tahir. Basic Photogrammetry. Johor: Academic

Publications Unit of Universiti Teknologi Malaysia, 1990. [2] A. Ahmad, A and J.H. Chandler. Photogrammetric Capabilities of the

Kodak DC 40, DCS 420, DCS 460 And Digital Cameras. Photogrammetric Record. 16 (94): 601-615, 1999.

[3] Anuar Ahmad, Ibrahim Busu and Ghazali Desa. Digital Close Range photogrammetry: Calibration of Different Digital Sensor Using Different Field Test And Application.International Symposium and Exhibition on Geoinformation 2003, 13-14 October. 2003, Shah Alam, Selangor, MALAYSIA, 2003.

[4] Anuar Ahmad. An Investigation of Photogrammetric Systems Using Low Cost Small Format Photography For Use In The Recording Of Buildings. University Of Newcastle Upon Tyne. MPhil Thesis, 1992.

[5] Australis. User manual. Department of Geomatic Engineering, University of Melbourne, Australia. November 2001.

[6] T.A. Clarke and J.G. Fryer. 1998. The Development of Camera Calibration Methods and Models. Photogrammetric Record. 16 (1991): 51-66. 1998

[7] T.A. Clarke, J.G. Fryer and X. Wang. The Principal Point and CCD Cameras. Photogrammetric Record 16 (1992): 293-312, 1998.

[8] I.J. Dowman. Fundamentals of Digital photogrammetry INSIDE. Atkinson, KB ed. Close Range photogrammetry and Machine Vision. Scotland: Whittles Publishing. 1996

[9] C.S. Fraser. Some Thoughts on the Emergence of Digital Close Range photogrammetry. Photogrammetric Record, 16 (1991): 37-50, 1998.

[10] C.S. Fraser and S. Al-Ajlouni. Zoom-Dependent Camera Calibration in Digital Close-Range photogrammetry. Photogrammetric Engineering & Remote Sensing Vol. 72, No. 9, September 2006, pp. 1017-1026, 2006.

[11] Geodetic Services Inc., V-STAR, [online], [http://www.geodetic.com]. 2006.

[12] F. Remondino and C.S. Fraser. Digital Camera Calibration Methods: Comparisons and considerations. ISPRS Commission V Symposium 'Image Engineering and Vision Metrology', Volume XXXVI, Part 5, Dresden 25 to 27 September 2006.


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[IEEE its Applications (CSPA) - Penang, Malaysia (2011.03.4-2011.03.6)] 2011 IEEE 7th International Colloquium on Signal Processing and its Applications - Calibration of high resolution