Creating Stereomodels with Aerial Triangulation by Bundle Block Adjustment

In praxis, photogrammetric analysis is mostly done using not one, but several or even many stereopairs for covering larger areas. In order to avoid the individual orientation of each stereomodel with accordingly large numbers of ground control points, multiple overlapping images forming a so-called block (see Fig. 3-8 and 3-9) can be oriented simultaneously with fewer ground control points using aerial triangulation techniques. One of the most commonly used and most rigorous aerial triangulation methods is the bundle adjustment or bundle-block adjustment.

In theory, bundle-block adjustment allows the absolute orientation of an entire block of an unlimited number of photographs using only three GCPs. This requires that the relative orientation of the individual images within the block first be established by additional tie points—image points with unknown ground coordinates which appear on two or more images and serve as connections between them (Fig. 3-13). These tie points can be identified either manually or (in digital photogrammetry) with automatic image matching procedures. The term bundle refers to the bundle of light rays passing from the image points through the perspective center L to the object points. The bundles from all photos are adjusted simultaneously so that the remaining errors at the image points, GCPs and perspective centers are distributed and minimized. Thus, the ground coordinates of the tie points as well as the six exterior orientation parameters of each image can be calculated in a single solution for the entire block. The stereomodels may now serve for further quantitative analysis, i.e. manual or automated measuring and mapping of unknown object point coordinates, heights, distances, areas, or volumes.

Regarding the accuracy of bundle-block adjustment, several equations for accuracy estimations are given in the photogrammetric textbooks (e.g. Kraus, 2004; Kraus et al., 2007). However, they are not easily assignable for the SFAP case, as accuracy is a function not only of scale and flying height, but also of the quality of interior orientation, base-height ratio, etc. Table 3-1 summarizes typical results for bundle-block adjustment carried out with the type of vertical SFAP appearing throughout this book. Nine images, taken with an 8 megapixel DSLR (Canon EOS 350D)

Aerial Triangulation

FIGURE 3-13 Principle of bundle-block adjustment; example of a possible SFAP survey. The relative orientation of the images in the block is established by both tie points and GCPs, the absolute orientation of the block within the ground coordinate system is realized using the GCP coordinates. After Kraus (2004, fig. 5.3.1, adapted).

FIGURE 3-13 Principle of bundle-block adjustment; example of a possible SFAP survey. The relative orientation of the images in the block is established by both tie points and GCPs, the absolute orientation of the block within the ground coordinate system is realized using the GCP coordinates. After Kraus (2004, fig. 5.3.1, adapted).

TABLE 3-1 Summary of bundle-block adjustment results for nine digital images taken at Gully Bardenas 1, Province of Navarra, Spain;image GSDs 1.9-2.6 cm. Triangulation performed without camera calibration, with self-calibration and with precedent test-field calibration, using varying numbers of control and check points. Photogrammetric processing by IM.

TABLE 3-1 Summary of bundle-block adjustment results for nine digital images taken at Gully Bardenas 1, Province of Navarra, Spain;image GSDs 1.9-2.6 cm. Triangulation performed without camera calibration, with self-calibration and with precedent test-field calibration, using varying numbers of control and check points. Photogrammetric processing by IM.

Bundle-block adjustment

No calibration

Self-calibration

Test-field calibration

GCP number (control/check)

6/45

12/39

26/25

6/45

12/39

26/25

6/45

12/39

26/25

Total image unit-weight RMSE

0.907

1.154

1.227

0.458

0.453

0.462

0.480

0.482

0.480

Control point RMSE

Ground X (cm)

4.10

6.36

4.83

0.21

0.51

0.61

0.22

0.54

0.50

Ground Y (cm)

2.90

5.09

3.73

0.45

0.41

0.62

0.45

0.55

0.57

Ground Z (cm)

11.70

14.94

11.65

0.84

0.55

0.92

0.67

0.70

0.63

Image (pixels)

5.34

5.91

4.16

0.69

0.67

0.62

0.62

0.67

0.58

Check point RMSE

Ground X (cm)

8.68

11.00

14.95

2.05

1.64

2.44

1.55

1.23

1.66

Ground Y (cm)

14.61

10.65

21.51

3.04

2.33

2.01

2.88

2.36

1.80

Ground Z (cm)

91.87

46.19

76.74

7.11

5.14

6.66

7.18

5.25

5.05

Image (pixels)

3.72

2.01

1.05

0.45

0.44

0.40

0.45

0.44

0.41

Mean exterior orientation error

Position (cm)

6.21

5.61

4.78

4.73

6.24

3.48

3.45

2.44

1.94

Angle (°)

0.04

0.04

0.03

0.03

0.02

0.01

0.02

0.02

0.01

w w camera at flying heights between 60 and 82 m above ground, were triangulated using a total of 51 GCPs in Leica Photogrammetry Suite.

The study site was an agricultural area with an erosion gully, in parts densely vegetated, cutting between two fallow fields (see Fig. 11-1). Of the GCPs, six, 12 or 26 were used as control points, the rest as check points for error assessment. The interior orientation of the camera was not defined (nominal focal length of lens only; "no calibration"), determined by the software in a self-calibrating approach (correction of focal length and principal point position, lens-distortion model applied; "self-calibration"), or determined by previous test-field calibration (see Chapter 6.6.5).

Results show that bundle adjustment without any camera calibration performs by far the poorest. The nonlinear fluctuation of error values with increasing control point number (12 control points are better than 26) indicates that no satisfactory solution can be found for the adjustment. Errors at the independent check points are around 10-20 cm for horizontal and up to 92 cm for vertical position which must be considered intolerable. Both the self-calibration and the precedent test-field calibration show much better results, with the latter only slightly superior to the former. All residuals at the control points are well below 1 cm, and the horizontal errors are within the range of image GSDs (1.9-2.6 cm). Z errors are, as to be expected with aerial triangulations, somewhat poorer but decrease just as horizontal errors with the number of control points employed. Altogether, the accuracies achieved in this study benefit from the large number of tie points (900) generated for improved image-block stabilization.

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  • AFFIANO
    Why does a stereomodel need 3 gcp?
    6 years ago

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