Experiments with matching in the object space for aerotriangulation

PHOTOGRAMMETRY & REMOTE SENSING ELSEVIER

ISPRS Journal of Photogrammetry& RemoteSensing 52 (1997) 160-168

Experiments with matching in the object space for aerotriangulation Amnon Krupnik a,,, Toni Schenk b a Department of Civil Engineering, Technion, Israel Institute of Technology, Haifa, 32000, Israel b Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, 2070 Neil Av., Columbus, OH 43210, USA

Received7 August 1996; accepted31 January 1997

Abstract A method for accurate and reliable image matching for aerotfiangulation is described and experimental results are reported. Most matching methods use small image patches because they assume that the object surface around the point is planar. However, in order to increase reliability, large image patches that are more likely to contain significant information are necessary. In the method presented here, the matching is performed in the object space in order to minimize the geometric distortion of the image patches due to the relief. As a result, much larger image patches can be used, which increases both the accuracy and the reliability. Experimental results obtained from six different datasets confirm these expectations. The accuracy varies between 1/5 and 1/12 of a pixel. Keywords: digital photogrammetry; automatic aerotriangulation; multiple-image matching; object-space matching

1. Introduction Aerotriangulation is a well-established procedure for obtaining the exterior (and possibly the interior) orientation parameters for a set of aerial photographs. Its main purpose is to determine enough control points for orienting every stereo model. This is accomplished by using a relatively small number of ground control points (see, e.g., Kraus, 1993) which in turn reduces the cost of a photogrammetric mapping project considerably. One of the major tasks in aerotriangulation is the measurement of conjugate points on two or more partially overlapping photographs. These points tie the photographs together. The exterior orientation parameters of all the photographs are then calculated

simultaneously according to a known mathematical model (see Ayeni, 1982 for an extensive review of aerotriangulation measurement and calculation techniques). With the current trend towards digital photogrammetry and the use of softcopy workstations, there is a growing interest in automating the aerotriangulation process. Several researchers have recently reported attempts to automate aerotriangulation, e.g., Tsingas (1991), Agouris (1992) and Ackermann and Tsingas (1994) (see Krupnik, 1994 for a more detailed description). The development of the fully automatic aerotriangulation system AATS is reported in Schenk (1995) and Toth and Krupnik (1996). Here the three major phases are summarized:

*Correspondingauthor. 0924-2716/97/$17.00 © 1997 ElsevierScienceB.V. All rights reserved. PII S0924-2716(97)00004-X

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• Strip and block formation, where all the photographs of a block are transformed into a common 3D coordinate system. The large number of tie points obtained automatically allows generation of a surface model of the entire block (DEM), which in turn leads to an accurate determination of the footprints of all photographs. • With the footprints the overlap configuration of the block is known. The location of small image patches in highly overlapping areas is computed with the exterior orientation parameters determined in the first phase. These image patches are registered, based on edge matching, and approximations for tie points are found. • Once approximations for tie points exist, multiple-patch matching is performed for accurately locating conjugate points. This paper is mainly concerned with the third phase. Although accurate matching has been the subject of numerous research studies in the fields of photogrammetry and computer vision (see, e.g., Hannah, 1988; Lemmens, 1988; Wrobel, 1988; Dhond and Aggarwal, 1989; Doom et al., 1990; Baltsavias, 1991), its application to aerotriangulation poses new problems. For example: • since the exterior orientation parameters are not known it is more difficult to constrain the search space by geometric conditions like epipolar lines; • to meet the high-accuracy requirements is much more challenging than in other applications such as automatic generation of DEMs; • usually more than two image patches are used at every matching location. For consistency and accuracy reasons, all image patches must be matched simultaneously. In this paper a solution to these problems is presented. Multiple-patch matching in the object space is based on hierarchically reconstructing a small surface that is centered around each matched tie point. Having these surface patches, two or more image patches are warped and simultaneously matched. In each iteration both the calculated orientation parameters and the surface patches are improved. In the following sections, the proposed algorithm is explained and experimental results are presented and discussed.

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2. Motivation and basic concepts The motivation for designing and developing this matching approach evolved from seeking a solution to the following key issues. 1. Reliable matching with single points

Failures in area-based matching are usually related to insufficient information within the matching windows. In order to improve the reliability, local and global constraints are used. For example, when generating DEMs automatically a local consistency check is performed by analyzing neighboring matches. The object surface is assumed to be smooth, or at least smooth between discontinuities. If the disparity at a certain point is considerably different from its surroundings, then the matched position is not accepted. However, in aerotriangulation only a single point is required at each location. Thus, it is not possible to use the smoothness constraint to check the reliability of the results. A possible remedy is to use larger matching windows that are more likely to contain sufficient information. However, large windows may lead to less accurate matching positions if conventional area-based matching techniques are used. These techniques assume that the ground surface is a tilted plane (if shape parameters are considered), or a horizontal plane otherwise. To alleviate this problem this method reconstructs a small surface patch around each point to be matched, embedded in a hierarchical approach. Thus, the ground surface is more realistically represented than by a plane. The image patches are warped with respect to the surface patch and the matching is performed between warped patches. Because the geometric distortions caused by the relief are now much smaller than those that occur when assuming a planar surface, windows of significantly larger size can be used in the least-squares matching procedure. As a result, the accuracy and the reliability increases. 2. Reducing numerical problems and correlation among parameters

As proposed by several authors, the most general solution to the matching problem includes the

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surface and the exterior orientation parameters (see, e.g., Wrobel, 1988; Ebner et al., 1993). However, various dependencies exist among the parameters, for example between the elevations and some of the exterior orientation parameters. This will cause an ill-conditioned normal equation system to the extent of obtaining a wrong solution. To circumvent the numerical problem a two-step procedure with two groups of unknowns has been adopted. First, the image patches at each tie point are warped and matched as described earlier. This is followed by determining the orientation parameters of all the photographs in the block by a standard block adjustment. With the improved exterior orientation and tie point locations, the surface is refined. Now, the procedure is repeated, either on the same level of the image pyramid or on the next finer-resolution level.

3. Avoiding correlation among observations In aerotriangulation it is a common practice that more than two image patches are to be matched. It is desirable to perform a simultaneous adjustment. One possibility is to use differences between gray values from each possible combination of a pair of images as observations (Agouris and Schenk, 1992). With this approach, there are correlations among the observations. Consider, for example, a matching between three image patches. After considering the differences between the first and the second image patches, and between the first and the third ones, the differences between the second and third image patches do not contribute any new information to determine the parameters. The proposed matching method uses gray values as observations, rather than gray-value differences. The 'true' intensities of the surface (referred to as the gray values of the surface elements) are introduced as unknowns in the adjustment. The mathematical model for this matching is explained in detail in Krupnik (1996).

2.1. Matching warped images Suppose the surface around a given tie point is known. It is then possible to rectify the corresponding image patches, resulting in orthophotos. Since the surface is only approximated in the case discussed here, the rectification does not render a true orthophoto. These 'wrong' orthophotos are called warped image patches. As the approximation of the surface improves, the warped image patches converge to orthophotos. In any case, the geometric differences between warped image patches of the same area are significantly smaller than those of the original image patches. For simplicity, the idea is explained here for the one-dimensional case with two images. The extension to the two-dimensional case with more than two images is obvious. Fig. 1 illustrates the geometric situation. For a given point Pl on the left image, the conjugate point P'r on the right image is sought. If point Pr is an approximation for p~, an object point P, which does not lie on the true surface, is obtained. Using the available surface elevations (which are not necessarily known a priori, but are approximated and modified during the iterative procedure), the image patches, centered on Pl and Pr, are warped. The corrected location/5 found by the matching is then projected back to the image (based, again, on the available surface elevations), and a better approximation is obtained for the matched point. Note that r ......

P,,, " In summary, the proposed method of multiplepatch matching in the object space employs two key components, namely, matching warped images (referred to as matching in object space) and matching more than two images simultaneously. The following subsections illuminate the concept further.

correctedlocation

approximate surface

true surface shift .......... (found by matching)

/

Fig, 1. Schematic description of the concept of matching warped images.

A. Krupnik, T. Schenk/ ISPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 160-168 as the differences between the approximate and the true surfaces become smaller, the correction will bring the location found by the matching closer to the true location.

2.2. Matching more than two image patches The mathematical model for matching multipleimage patches is an extension of the classical LSM algorithm. Although the proposed algorithm is suitable as a general image patch matcher, it is employed here for matching warped images, where only shift parameters are required and considered. Let S be a set of l warped image patches assumed to be scaled and shifted copies of the projection of the ground surface. Let the patch size be n × m pixels. If there were neither geometric nor radiometric distortions, the patches would be identical, and therefore, the following identity would hold for each pixel of every image patch in S:

gi(r, c) -- gt(r, c) = 0

(1)

where gi (r, c) is the observed gray value of the pixel in row r and column c of patch i 6 S and gt (r, c) is the gray value of the surface element. In reality, there are geometric and radiometric differences between the patches. Systematic radiometric differences are significantly reduced by a preliminary radiometric correction, for example, histogram equalization. Considering the geometric model and remaining random radiometric distortions, Eq. 1 is rewritten:

gi (r -b- Ar i, c

-I- A C i) --

gt (r, c) = e(r, c)

(2)

where

A r i and Ac i are the unknown horizontal shifts of patch i and e(r, c) is the random error vector. Linearizing Eq. 2 to the standard form of an observation equation results in:

gto(r, c ) - gi(r, c ) : g[(r, c)Ari + g~(r, c)Ac i - Agt(r, c)

(3)

where gto(r, c) is an approximation for the theoretical gray value of the surface element at location (r, c), g~(r, c) and gic(r, c) are the intensity gradients across the rows and columns, and A g t (r, c) is the unknown correction to the theoretical gray value of the surface element at (r, c). Note that the actual

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observations in this model are gray values and not gray-value differences as used in traditional LSM. Eq. 3 will be the same for all the image patches except one. In order to obtain from Eq. 3 a nonsingular equation system, the location of one of the image patches must be fixed, and its shifts are set to zero. The observation equations for the pixels of this patch are reduced to:

gto(r, c ) - gi(r, c ) = - - A g t ( r , c)

(4)

The unknowns of the model presented in Eqs. (3) and (4) consist of n • m theoretical gray values of the surface elements, and 2(l - 1) shifts of the image patches. Each image patch contributes n • m equations, which brings the total number of equations to l • n • m. The redundancy of this model is always sufficient. In Krupnik (1996) it is also shown that in the case of two image patches this mathematical model is equivalent to the classical LSM approach. The equation system is relatively large because of the large number of additional theoretical gray values of the surface elements. However, as shown in Krupnik (1996), it is easy to partition the model such that the normal equation system only contains the unknown shift parameters.

3. Outline of the proposed strategy Fig. 2 shows a diagram of the iterative procedure. Given approximate locations of tie points, approximate orientation parameters and an approximation of the surface around the tie points, image patches are warped and then matched. Resulting conjugate tie points constitute the input for a bundle block adjustment, which generates an improved set of orientation parameters. These parameters, together with other conjugate points obtained in the matching phase, are used for updating the surface around each tie point. In each iteration of the procedure, the following three phases (gray blocks in Fig. 2, described separately in Figs. 3-5) occur. • Warping and matching phase (Fig. 3): The image patches that are centered on every tie point are warped according to the available approximations of the orientation parameters and the surface around the point. At the first iteration, when no surface approximation is available, a horizontal plane is assumed. A multiple-patch matching of

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approximate tie points,orientationparameters surfacearoundtie points

tie pointand other ~... points on patch 1 19~'~

",..1

.......

......

, ,

pointson patch l "1

,

,

L

I

orientation parameters I conjugatetie points

, edpatc.,

.... l-warpeapatclla./J

I orientationparameters ]

conjugatetieand otherpoints Fig. 2. A block diagramof one iterationof the proposed matching scheme.The three phases of the schemeare presentedby the gray blocks. the resulted warped patches is performed to determine the image coordinates of the tie point. In all iterations except the last one, a grid is formed in the object space, centered on the approximate tie point. Multiple-patch matching is used (in the same manner as it is used for matching the tie point) to match each point on this grid. Each matched grid point is projected back through the available surface to the image space. This procedure provides a set of tie points for the bundle adjustment, and additional points around each tie points for generating an improved surface. • Block adjustmentphase (Fig. 4): The photo-coordinates of the center of the grid found in the 'warping and matching phase' constitute the input for a bundle block adjustment. The results of the block adjustment are new (improved) orientation parameters. • Surface update phase (Fig. 5): Using the new orientation parameters estimated in the 'block adjustment phase,' a surface is reconstructed around

Fig. 3. Warping and matchingphase. Image patches are warped and matchedto formimprovedtie and surfacepoints. each tie point by intersecting the photo-points (from the 'warping and matching phase') back to the object space and interpolating them into

approximateorientation parameters

conjugatetie point I ~ . . "~7l-conJugateue pomt..n..j

new orientation parameters Fig. 4. Block adjustmentphase. Improvedtie points are used for improvingorientationparameters.

A. Krupnik, T. Schenk / lSPRS Journal of Photogrammetry & Remote Sensing 52 (1997) 160-168 I

orientation parameters

i.

tie point and other h " . points on patch 1 19 I..[ r V"pom;son-patcd / ]

surface around tie point Fig. 5. Surface update phase. Matched points and improved orientation parameters are used for generating improved surfaces around tie points.

regular grids. The grid interval is half the interval that was used in the former iteration. Since each 'warping and matching' phase yields better locations for the conjugate points, the results of the block adjustment render improved orientation parameters. These orientation parameters, together with the improved conjugate points, lead to better approximations for the object surfaces around each tie point. The process converges iteratively to the desired solution.

4. Experiments and results In order to check the feasibility and effectiveness of the proposed concept of multiple-patch matching in the object space for aerotriangulation it has been implemented on a workstation. This section presents and analyzes the experimental results.

OSU, SWISS-2 and WY contain only one stereo model. This is useful for checking the effect of the object-space approach, without involving multiplepatch matching. The other three datasets, SWISS-3, TEXAS and OEEPE involve more than two images, lending themselves to multiple-patch matching. All examples have a relatively large image scale where matching procedures are challenged with foreshortening and surface discontinuity problems. At smaller scales these problems are less acute. The ground coverage varies: OSU and SWISS show heavily structured urban areas; OEEPE depicts a rural/suburban area; TEXAS shows an airfield (runways, no airplanes or vehicles); and WY shows a hilly, rural area. In order to verify the matching results a 'ground truth' for every dataset was established by measuring the conjugate points manually. In most cases the locations of the points were selected at the vonGruber locations. Around each location, several points were measured in order to facilitate the detection of incorrect matching results. The first column in Table 2 lists the total number of points that were measured in each dataset. The next five columns show the number of points that appear on 2, 3, 4, 5 and 6 photographs. The reference points of the OSU and SWISS datasets were measured on the Zeiss P1 analytical plotter, using the original diapositives. For the WY, TEXAS and OEEPE sets, only digital images were available. Therefore, measurements were performed on an Intergraph softcopy workstation. The resolutions of the images are specified in Table 2. Quality and consistency of the measurements were checked by a bundle block adjustment. To avoid any influence of errors in the coordinates of ground control points, a minimum-constraints block adjustment was performed. The datum defect was

Table 1 Number, configuration and scale of photographs in each dataset

4.1. Datasets and reference measurements

As summarized in Table 1, six datasets were used for the experiments 1. The first three datasets, 1 SWISS-2 is a subset of SWISS-3. When 'SWISS' is mentioned, it refers to both SWISS-2 and SWISS-3.

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OSU SWISS-2 WY SWISS-3 TEXAS OEEPE

No. of photographs

No. of strips

Forward/side overlap (%)

Image scale

2 2 2 3 6 8

1 1 1 1 2 2

60 60 60 60 60/25 60/50

1 : 4000 1 : 2500 1 : 6000 1 : 2500 1 : 4000 I : 4000

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Table 2 Tie point configuration of each dataset, and results of reference (manual) measurements No. of points measured OSU SWISS-2 WY SWISS-3 TEXAS OEEPE

24 24 24 36 68 109

Available resolution (/xm)

Coverage (images) 2

3

4

24 24 24 25 39 42

. . . . . . . . . 11 13 12 22 24

eliminated by identifying the block coordinate system with the photo coordinate system of the first photograph and by scaling the block to the photo scale. The results of the bundle adjustment are summafized in the last two columns of Table 2. The accuracy (or0), and the maximum residual for each dataset are shown. Table 2 shows that the accuracies of the TEXAS and OEEPE datasets are somewhat worse compared to the other sets. There are two possible explanations for this. First, measuring points across strips without marking them is difficult. An attempt was made to measure the points across strips as accurately as possible by creating 'models' with images from different strips. However, measuring exactly the same point on more than two images is not possible. The second reason is the lower resolution (22.5/zm and 30 Ixm) of these sets. Nevertheless, an overall accuracy of one-fifth of a pixel was obtained for the TEXAS set, and approximately one-third of a pixel for the OEEPE set. 4.2. Results

The manually measured reference points were used as approximations for the matching procedure. Normally, approximations that are obtained through an automated procedure (like AATS) are not as accurate as those considered here. However, preliminary experiments (see Krupnik, 1994) showed that the matching procedure has a pull-in range of 2-3 pixels. Approximations obtained from AATS are expected to be better than that. Therefore, the reference measurements can safely be used as approximations. For the iterative procedure, three levels were chosen. The pixel size, the size of the matching, win-

5

6

. . . 1 5

3 16

photos, 15 photos, 15 15 photos, 15 22.5 30

Results (/zm) q-g0

max. residual

2 3 2 4 5 12

2 4 3 7 12 40

Table 3 Parameter setting for each iteration level Iteration level

1

2

3

Pixel size (/zm) Size of matching window (pixels) Number of matched points Grid interval (/zm)

240/180 13 × 13

120/90 23 × 23

60/45 45 × 45

5×5 1920/1440

3×3 1 960/720 480/360

For pixel size and grid interval, right values refer to the TEXAS dataset, while left values refer to the other sets.

dows, the number of matched points and the grid interval for each iteration are listed in Table 3. Some entries contain two values, separated by a slash. The first value refers to the OSU, WY, SWISS and OEEPE datasets; the second value refers to the TEXAS dataset. It may be surprising that the last matching (level 3) was not performed with the highest resolution imagery. This was done purposely in order to allow an accuracy comparison with the manual measurements. The major results of the experiments with object-space matching are summarized in Table 4. For each dataset, the overall accuracy, the maximum residual, the total number of observations and the number of rejected observations are shown. In the case of blunders (i.e., the matching diverged or converged to a wrong location), all related observations were skipped. If only two images are involved then the results can be directly compared with traditional matching methods. Standard LSM was used for the OSU, WY and SWISS-2 datasets, with the same approximations and window size (45 pixels) as in object-space matching. Table 5 displays the comparison.

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Table 4 Results of the matching procedure

OSU SWISS-2 WY SWISS-3 TEXAS OEEPE

Overall accuracy a0 (/zm)

Max. residual (/zm)

Total No. of observations

No. of rejected observations

5 6 6 6 4 12

6 9 8 11 13 46

96 96 96 166 376 734

12 12 0 18 22 102

Table 5 Comparison between object-space and image-space approaches Object space

OSU SWISS-2 WY

Image space

overall accuracy tr0 (/zm)

max. residual (/zm)

rejected

overall accuracy tr0 (#m)

max. residual (/zm)

rejected

5 6 5

6 9 8

12 12 0

7 9 5

13 11 6

20 16 12

Table 6 Comparison between the matching results and reference (manual) measurements Matching results

OSU SWISS-2 wY SWISS-3 TEXAS OEEPE

Reference (manual) measurements

a0 (/zm)

max. residual (#m)

a0 (#m)

max. residual (#m)

5 6 6 6 4 12

6 9 8 11 14 40

2 3 5 4 5 11

2 4 3 7 12 31

For the first two datasets object-space matching produces superior results evidenced by tr0 and the m a x i m u m residuals. There is no significant difference between the two matching approaches for the W Y dataset. This does not come as a surprise since the ground is rather smooth. Although there are elevation differences, no significant discontinuities and gradient changes occur within a matching window. Therefore, the mathematical model o f image-space matching, such as approximating the object surface by a plane, still leads to satisfactory results. This is not the case for the first two datasets. Numerous m a n - m a d e features cause discontinuities and gradient changes in the surface within the matching window. Consequently, using a more realistic surface renders better results.

Finally, the results of all datasets were compared with those obtained from the manual measurements (see Table 6). For the OSU, S W I S S - 2 and W Y datasets, the results o f the manual measurements are better than the matching results. However, one should bear in mind that the matching was performed with 6 0 / x m resolution images, while for the manual measurements analog photographs with a resolution better than 1 0 / z m were available 2. For the SWISS-3, T E X A S and O E E P E datasets, the results o f the matching procedure are comparable to the manual measurements. This is remarkable because low-resolution images were used. Obviously, z The WY dataset was manually measured on a softcopy workstation using 15/zm resolution imagery.

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this disadvantage is compensated for by the simultaneous matching of all image patches - - a feat not possible when points are manually measured. The overall accuracy of the multiple-patch matching scheme is between 1/5 and 1/12 of a pixel. 5. C o n c l u d i n g r e m a r k s

A method for accurate and reliable image matching of points for aerotriangulation was developed and tested. In order to increase reliability, large image patches that are more likely to contain significant information are necessary. Most matching methods use small image patches because the object surface around the matching area is assumed planar. In the method presented here, the matching is performed in the object space which minimizes the geometric differences between the matched patches. Consequently, much larger image patches can be used and the accuracy and the reliability are increased. The method has been implemented on a workstation, and experiments with several different datasets have been performed to study the effects on accuracy and reliability. The results can be summarized as follows: • The accuracy of the matching results is between 1/12 and 1/5 of a pixel. Although images of relatively coarse resolution were used (60 and 45 /zm), the results compare favorably with manual aerotriangulation. If higher-resolution images were used for the matching, better results would have been expected. • The proposed matching scheme performs better than traditional matching methods in areas that include surface discontinuities. The results are similar to image-space matching when smooth surfaces are involved. • Since multiple images are simultaneously matched, the method is superior to manual measurements because a human operator cannot measure more than two images simultaneously. These encouraging results show that by employing multiple-patch matching in the object space, conjugate points for aerotriangulation with an accuracy that exceeds manual measurements may be obtained. Together with the increase in efficiency by an automated procedure, the method presented in

this paper improves the accuracy and reliability of digital aerotriangulation. References

Ackermann, E and Tsingas, V., 1994. Automatic digital aerial triangulation. In: Proceedings, ACSM/ASPRS Annual Convention, Reno, NV, Vol., 1, ASPRS, pp. 1-12. Agouris, E, 1992. Multiple Image Multipoint Matching for Automatic Aerotriangulation. PhD thesis, Department of Geodetic Science and Surveying, The Ohio State University, Columbus, OH. Agouris, E and Schenk, T., 1992. Multiple image matching. Int. Arch. Photugramm. Remote Sensing, 29(B3): 802-807. Ayeni, O.O., 1982. Phototriangulation: A review and bibliography. Photogramrn. Eng. Remote Sensing, 49(11): 1733-1759. Baltsavias, E.E, 1991. Multiphoto geometrically constrained matching. Mitteilungen 49, ETH-Ztirich. Dhond, U.R. and Aggarwal, J.K., 1989. Structure from stereo - - a review. IEEE Trans. Syst., Man, Cybernetics, 19(6): 1489-1510. Doom, B., Agouris, E, A1-Tahir, R., Stefanidis, T. and Zilberstein, O., 1990. Digital stereo matching in perspective. Technical Notes in Photogrammetry 10, Department of Geodetic Science and Surveying, The Ohio State University, Columbus. Ebner, H., Heipke, C. and Holm, M., 1993. Global image matching and surface reconstruction in object space using aerial images. In: E.B. Barrett and D.M. McKeown, Jr. (Editors), Integrating Photogrammetric Techniques with Scene Analysis and Machine Vision (Proceedings, SPIE 1944), Orlando, FL, April, pp. 44-58. Hannah, M.J., 1988. Digital stereo image matching techniques. Int. Arch. Photogramm. Remote Sensing, 27(B3): 280-293. Krans, K., 1993. Photogrammetry. Vol. 1. Diimmler, Bonn, 4th Ed. Krupnik, A., 1994. Multiple-patch matching in the object space for aerotriangulation. Technical Report 428, Department of Geodetic Science and Surveying, The Ohio State University, Columbus. Krupnik, A., 1996. Using theoretical intensity values as unknowns in multiple-patch least-squares matching. Photogramm. Eng. Remote Sensing, 62(10): 1151-1155. Lemmens, M.J.EM., 1988. A survey of stereo matching techniques. Int. Arch. Photogramm. Remote Sensing, 27(B8): V 11-V23. Schenk, T., 1995. Zur automatischen aerotriangulation. Z. Photogramm. Fernerknndung, 3/95: 137-144. Toth, C,K. and Krupnik, A., 1996. Concept, implementation, and results of an automatic aerotriangulation system. Photogramm. Eng. Remote Sensing, 62(6): 711-717. Tsingas, V., 1991. Automatische aerotfiangulaion. In: Proceedings, 43rd Photogrammetric Week, Stuttgart, pp. 253-268. Wrobel, B.E, 1988. Least-squares methods for surface reconstruction from images. Int. Arch. Photogramm. Remote Sensing, 27(B3): 806-821.