Accuracy analysis of measuring close-range image points using manual and stereo modes.

Suziedelyte-Visockiene, Jurate

Introduction

The photogrammetric method of object measurement processes consists of taking images of an object employing a professional calibrated photo-camera and processing these images applying appropriate software. To obtain highly accurate and reliable results, it is necessary to control the capture of photo images and processing accuracy. The processes of photogrammetric images cover relative and absolute orientation, bundle adjustment, stereo-digitalisation, digital terrain model generation and orthophoto creation. A geometric model of the object is made of relative orientation that embraces the interior orientation of the image and matching the image. The point measurements of the images can be divided into two methods: stereo mode and manual mode. When the geometric model of the object is produced using stereo mode, an operator can measure the points (control (CP) and Tie points) with special glasses. The operator can observe a three-dimensional object through the image view on the computer screen and carry out measurements in both photo images at the same time. During manual measurements, the points are estimated separately in each of the images and then processed adopting a correlation approach or applying to least-square adjustment techniques. The value of correlation coefficients shows how accuracy at that particular point is measured. The quality of the obtained results is estimated by vertical parallax residuals in the measured points and root mean square (RMS) geometric models.

The goal of the carried out experiments is to respond to the below introduced questions:

1. What available and acceptable maximum value of the correlation coefficient will be used for measuring the points employing manual methods in overlapping images?

2. What errors of vertical parallax residuals and RMS will be used for measuring manual or stereo modes in overlapping images?

1. Calculation of the correlation coefficient

The correlation coefficient is used for a close range photogrammetric application of image point measurements.

Applications include a comparison of two overlapping images for the purposes of image registration, CP or Tie point recognition and measurement. The correlation coefficient (q) is calculated according to the formula (Potuckova 2004; Mileskaite 2011)

q = [q.sub.LR] / [q.sub.L] x [q.sub.R], (1)

where [q.sub.LR]--the covariance of left and right image patches; [q.sub.L]--the standard deviation of image patch L (left image); [q.sub.R]--the standard deviation of image patch R (right image).

The correlation coefficient (q) has value -1 [less than or equal to] q [greater than or equal to] 1. q = 1 if two overlapping images are absolutely identical, q = 0 if they are completely uncorrelated (stereo point measurement) and q = -1 if they are completely anti-correlated when the let image is a negative right image.

For digital colour image processing, an equation for the correlation coefficient can be modified using a mean value of three channels as a single similarity measure (Potuckova 2004; Mileskaite 2011):

q = [q.sup.red] + [q.sup.green] + [q.sup.blue] / 3. (2)

Correlation coefficients are calculated considering two overlapping images during the relative orientation of photogrammetric processes in the following way (Hanke, Grussenmeyer Corfu 2002):

1. Measuring Tie points of stereo pairs (models) in overlapping areas and triplet zone (in case we have more than two images) images.

2. Input value of coordinates and measuring CP in the overlapping image.

3. Accuracy control using the correlation coefficient that is calculated applying the manual point measurement method in overlapping images. When the points are measured by stereo mode, the correlation coefficient is not calculated (q = 0).

4. Accuracy control using vertical parallax residual. After measuring the points on the images, the relative orientation parameters of the images are calculated. They are the maximum error of vertical parallax residuals ([E.sub.max]) and the root mean squared error (RMS) (Kiseleva 2002):

[E.sub.max] = 2 X [E.sub.mean], RMS = [square root of 2] X [E.sub.mean]. (3)

where [E.sub.mean]--is a mean error of measurement points on overlapping images. [E.sub.mean] error should not be greater than a half of pixel size in a camera matrix.

After measuring Tie and CP in stereo pairs (models), they should be transferred to the geodetic coordinate system. Relative orientation accuracy can be checked comparing the discrepancies of point measurements in adjacent models (triplets). Triplet errors [E.sub.X], [E.sub.Y], [E.sub.Z] in their coordinates X, Y and Z were calculated for two adjacent models. The mean errors of measurement points in the XY plane and Z coordinates are calculated by the following formulas (Kiseleva 2002):

[E.sub.xy(mean)] = [square root of 2] X 0.5 X pxl, [E.sub.z(mean)] = c / [b.sub.x] [E.sub.xy(mean)], (4)

where pxl--pixel size in a camera matrix; c--the focal length of the camera; [b.sub.x]--photographic base in the image scale.

2. Experimental works

To evaluate the possibilities of point matching methods creating the 3D model, the fragment of two heritage objects was chosen. The first one is a church built in 1881 in the settlement of Raudenai, Siauliai municipality, Lithuania. The second object is a farm building in Arnioniai manor, Moletai municipality, Lithuania. Both objects were reconstructed last year. During reconstruction, it was necessary to have photogrammetric ixation of the object facade.

Thus, colour digital images of two objects were taken by the professional digital photo-camera Canon EOS 1D Mark III (Figs. 1 and 2) that was calibrated (optical distortions were determined and evaluated) using Tcc sotware at the Institute of Photogrammetry in the University of Bohn (Germany) in 2008 and 2012 (Suziedelyte-Visockiene, Brucas 2009a, b; Suziedelyte-Visockiene 2012). The focal length of the camera is 50.76 mm and pixel size in a camera matrix pxl = 6.4 [micro]m.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The facade of the first object (house) has a smooth surface (Fig. 1). The facade of the second object is advanced and has two different point measurement levels of the surface (Fig. 2). CP and Tie points are marked on the facade. All these points are used for the relative orientation of photogrammetric processes. CP have been measured considering the images of the manual (mono) and stereo modes of the first object. The correlation coefficients (q) and vertical parallax residual (E) of the measured points have been calculated following the measurement. Accuracy results are shown in Table 1.

The correlation coefficients (q) of the measured points have not been calculated in stereo mode. The results of vertical parallax residuals are shown in Table 2.

The results of the first object show that the relative orientation and image adjustment of measuring manual and stereo points (Tables 1 and 2) are of similar and good quality. Consequently, if an object has a smooth surface, it is possible to measure the points manually or by stereo mode. The correlation coefficient (q) is 0.992-1.00.

As for the second object, two overlapping images (Model 549/547) have also been measured using CP manual and stereo modes. Accuracy results are shown in Tables 3 and 4.

The results of the second object indicate that the relative orientation and image adjustment of manual and stereo point measurements (Tables 3 and 4) are different. The results of the points measured in stereo mode are good enough; the mean errors of measurement points in the XY plane and Z coordinates are small. The results of point measurements and image adjustment applying

manual mode disclose big blunders ranging from 0.03 to 0.08 m. Consequently, if the points are measured on more than one surface, it must be done in stereo mode. The correlation coefficients of the image adjustment of manual mode are 0.960-0.991.

A comparison of the point vertical parallax [E.sub.mean] of measurement points on overlapping images and RMS image processing in manual and stereo modes are shown in Figs. 3 and 4.

A comparison of the results of image adjustment ([E.sub.xy(mean)], [E.sub.z(mean)]) in the images of manual and stereo modes are shown in Figs. 5 and 6.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

Figures 3-6 clearly indicate that the point measurements of the second object using manual (mono) mode has unacceptable errors, whereas the point measurements of the first object has been done using manual or stereo mode.

Conclusions

The images of two heritage objects have been taken for experimental investigation. Control points and tie points have been measured using stereo and manual mode. The control points of the first object are distributed on the surface of the smooth facade and on the surface of different (a few) levels.

The process of image matching of the smooth surface object points to the value of the determined correlation coefficient, which makes 0.992-1.00. The mean error of the vertical parallaxes of the measured points makes [E.sub.mean] = 0.07-0.15 pxl and root mean squared RMS = 0.01-0.21 pxl. After image transformation (adjustment processes) to the 3D model, the accuracy of the measured points has reached 0.001-0.003 m and satisfies the requirement for creating an accurate digital terrain model and orthophoto generation.

Within the process of matching an image with an object having a different surface, the value of the correlation coefficient, which is 0.960-0.991, has been determined. The mean error of the vertical parallax of the measured points is [E.sub.mean] = 1.4 pxl and RMS = 5 pxl when points are measured manually. The result of image adjustment makes 0.04-0.08 m. When the points are measured by stereo mode, vertical parallax [E.sub.mean] = 0.15 pxl and RMS = 0.28 pxl and image adjustment result is 0.03-0.05 m. The results of stereo mode are more precise than those of manual mode.

Considering close-range photogrammetry during relative orientation, it is recommended that the value of the correlation coefficient should be not smaller 0.990. The precise results of point measurements are obtained using stereo mode.

doi:10.3846/20296991.2013.786881

References

Hanke, K.; Grussenmeyer Corfu, P. 2002. Architectural Photogrammetry: Basic Theory, Procedures, Tools [online], [cited 20 January 2013]. Available from Internet: http://www.isprs. org/commission5/tutorial02/gruss/tut_gruss.pdf

Kiseleva, A. S. 2002. Accuracy Control at Various Stages of Photogrammetric Processing in PhotoMod System. Moscow: Racurs.

Mileskaite, J. 2011. The application of the covariance method analysing the digital images of land surface, Geodesy and

Cartography 37(3): 105-110. http://dx.doi.org/10.3846/139 21541.2011.626260

Potuckova, M. 2004. Image Matching and Its Applications in Photogrammetry: Ph.D. thesis [online], [cited 25 January 2013]. Available from Internet: http://www.plan.aau.dk/digitalAssets/5/5516_314.pdf

Suziedelyte-Visockiene, J.; Brucas, D. 2009a. Digital photogrammetry for building measurements and reverse-engineering, Geodezija ir kartografija [Geodesy and Cartography] 35(2): 61-65. http://dx.doi.org/10.3846/1392-1541.2009.35.61-65

Suziedelyte-Visockiene, J.; Brucas, D. 2009b. Influence of digital camera errors on the photogrammetric image processing, Geodezija ir kartografija [Geodesy and Cartography] 35(1): 29-33. http://dx.doi.org/10.3846/1392-1541.2009.35.29-33

Suziedelyte-Visockiene, J. 2012. Photogrammetry requirements for digital camera calibration applying Tcc and MatLab software, Geodesy and Cartography 38(3): 106-110. http://dx.doi.org/10.3846/20296991.2012.728895

Jurate Suziedelyte-Visockiene

Department of Geodesy and Cadastre, Faculty of Environmental Engineering, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania E-mail: jurate.visockiene@vgtu.lt

Received 02 February 2013; accepted 26 February 2013

Jurate SUZIEDELYTE-VISOCKIENE. Assoc. Prof., Dr at the Department of Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania. Ph +370 5 2744703, fax +370 5 2744705.

Doctor Vilnius Gediminas Technical University, 2003.

Research interests: digital photogrammetry, land management.

Table 1. Accuracy analysis of point measurements using manual
modes of the first object

No of CP q E, pxl q E, pxl
points

 Model of 593/587 Model of 587/591

803 0.996 -0.011 0.997 0.002
901 -- -- 0.998 0.040
902 0.994 0.014 0.997 0.006
903 0.992 -0.012 -- -
904 0.996 -0.133 0.996 0.148
910 0.994 0.018 0.997 -0.014
913 -- -- 0.998 -0.067
914 0.995 0.019 0.997 -0.024
915 0.995 -0.001 -- -
916 0.997 0.070 0.997 0.094
917 0.995 -0.130 -- -
927 0.995 -0.026 0.998 0.006
928 0.994 0.006 0.996 0.009
929 -- -- 0.997 -0.078
930 0.995 0.184 0.997 -0.119

[E.sub.mean] = 0.079 pxl [E.sub.mean] = 0.070 pxl
RMS = 0.111 pxl RMS = 0.099 pxl

The result of image adjustment

[E.sub.xy(mean)] = 0.003 m [E.sub.z(mean)] = 0.001 m

Table 2. Accuracy analysis of point measurements using stereo
modes of the first object

No of CP E, pxl E, pxl
points Model of593/587 Model of587/591

803 -0.084 -0.513
901 -- 0.229
902 0.140 0.017
903 -
904 0.161 -0.196
910 -0.056 0.084
913 -- 0.334
914 0.037 -0.744
915 0.133 0.827
916 -0.068 0.154
917 0.012 -
927 0.000 -0.106
928 -0.193 -0.008
929 -
930 -0.281 0.060

 [E.sub.mean] = 0.148 pxl [E.sub.mean] = 0.369 pxl
 RMS = 0.209 pxl RMS = 0.522 pxl

The result of image adjustment

[E.sub.xy(mean)] = 0.003 m [E.sub.z(mean)] = 0.001 m

Table 3. Accuracy analysis of point measurements using manual
modes of the second object

No of CP q E, pxl
points
 Model of549/547

701 0.991 -1.962
720 0.987 -0.407
703 0.994 -1.238
702 0.990 0.126
114 0.989 2.254
113 0.956 1.904
895 0.963 -0.066
894 0.974 1.061

[E.sub.mean] = 1.387 pxl
RMS = 4.997 pxl

The result of image adjustment

[E.sub.xy(mean)] = 0.035 m [E.sub.z(mean)] = 0.082 m

Table 4. Accuracy analysis of point measurements using stereo
modes of the second object

No of CP E, pxl
points Model of 549/547

701 -0.304
720 0.435
703 0.308
702 -0.063
114 -0.408
113 0.115
895 -0.160
894 0.127

[E.sub.mean] = 0.148 pxl; RMS = 0.284 pxl

The result of image adjustment

[E.sub.xy(mean)] = 0.003 m, [E.sub.z(mean)] = 0.005 m