NON-METRIC BIRD S EYE VIEW Prof. A. Georgopoulos, M. Modatsos Lab. of Photogrammetry, Dept. of Rural & Surv. Engineering, National Technical University of Athens, 9, Iroon Polytechniou, GR-15780 Greece - drag@central.ntua.gr Commission VI, WG V/4 KEY WORDS: Non-metric aerial convergent photography, aerotriangulation, self-calibration, cultural heritage ABSTRACT: The combination of analytical photogrammetric methods and suitable software are a powerful tool for achieving almost the impossible. For the geometric documentation of the Church of the Holy Sepulchre in Jerusalem a planimetric view of the rooftops was required, among numerous other drawings. The complex of the main church and the surrounding buildings presented a rather difficult object to survey either with classical survey methods. Hence a photogrammetric solution was sought. Experience gained from other similar projects called for helicopter photography from such an altitude to ensure the necessary image scale. As such a possibility was out of the question, oblique amateur non-metric photographs in colour slides were the only data available. From a rigorous photogrammetric point of view, these data were completely useless for metric work. However, they were forming a network of, mostly oblique, photos over the area of interest and at the same time a scientific challenge. At the same time the work of the past years had already produced drawings of elevations and cross-sections of the monument, part of which concerned the rooftops. Hence some distances between points in space could easily be extracted off these drawings. At the same time, the BINGO-F software was also available. This combination proved quite miraculous. Careful and suitable extraction of object distances, together with digitally measured image co-ordinates were the observation data, which when introduced into the BINGO-F software supported the adjustment of the whole network. The results of this adjustment were the exterior orientation elements of all photographs used, the geodetic coordinates of a large number of characteristic points, which played the role of tie points. Interior orientation parameters were also set as unknowns and the adjustment was able to produce their values. Several series of adjustments were performed in order to achieve the desired optimum result. Numerous mathematical and geometrical parameters were tested and they were assessed according to their effect. For the compensation of image errors the best self-calibration parametric model, different for each image available, was sought and applied. From the adjusted co-ordinates of the numerous tie points, it was possible to compile the desired planimetric drawing of the rooftops. In this paper the whole project is presented and the results are discussed for their accuracy and reliability. 1.1 History of the Project 1. INTRODUCTION For seven consecutive years the Laboratories of General Geodesy and Photogrammetry of the Dept. of Rural & Surveying Engineering of NTUA carried out the huge and really challenging project of geometrically documenting the Church of the Holy Sepulchre in Jerusalem. The project was supported by the University of Athens, as far as the historic and architectural documentation were concerned. This work was realised under the auspices of the Greek Orthodox Patriarchate of Jerusalem with the kind permissions of all other religious Communities present in the area. For the completion of fieldwork seven months, one each year, for the consequtive years were needed. In the meantime processing of the collected data was performed at home. The geometric documentation comprised a series of drawings at a scale of 1:50. Among them plan drawings at different levels and elevations and at different locations through the monument. One of the desired drawings was the horizontal plan of the roof tops of the whole complex. It should be noted that the Church of the Holy Sepulchre is situated in the Old Town of Jerusalem and is surrounded by numerous buildings of various uses, such as closters, mosques, shops, houses etc. The only façade exposed is part of the Southern elevation, where the main and only entrance to the Church is situated. 1.2 Administrative Problems The production of a roof top plan called for either aerial photography (Georgopoulos et al., 1999) or access to the roofs for intensive geodetic work. However, it was impossible to apply any of the above solutions. Access to a large proportion of the roofs of the Church was denied by the Muslims. This also made difficult the survey of several objects for the elevations, but it was rather easy to overcome the problem with terrestrial photography and suitable measurements from a distance. On the other hand, aerial photographs were only available, not without serious red tape problems, at very small scales, practically prohibiting the survey at the desired 1:200 scale. Moreover, permission was not granted for taking our own photographs from a helicopter, as local regulations would not
allow the craft to fly at heights lower than 1000ft. Hence it was thought to abandon the production of this particular drawing. 1.3 Available Photographs Fortunately a series of amateur colour 35 mm slides were made available to us by two Israeli archaeologists. They happenned to have recently flown over the Old City with a small handheld camera. They appreciated our problem and kindly made copies of their slides for us. A sample of one such amateur image is shown in Figure 1. taken with various and unknown focal lengths. Moreover, as the camera was handheld, the images were taken at completely uncontrollable angles. Additionally, the copies made available to us were made with unknown process, a fact which may have caused even worse geometry problems. However, a rough estimation of the mean image scale for these photos was possible with the help of some known distances appearing on them. 3. METHODOLOGY 3.1 Exploiting the available data Since the only information available were these particular images, it was decided to try and exploit them to the best of our abilities (Modatsos, 2000). Figure 1: An oblique photograph of Old City Jerusalem 2. DATA AVAILABLE 2.1 Geometric Documentation Products In order to achieve the desired result, all available data should be exploited. At our disposal were all drawings produced for the geometric documentation of the complex. They were plans and elevations at a scale of 1:50, both in analogue and digital form (Figure 2). It was decided to implement an adjustment method, which would be able to calculate and determine practically everything, under certain circumstances, of course. This method is none other than the bundle adjustment method. As output products one may receive co-ordinates of unknown points, co-ordinates of image stations, camera lens attitudes and, of course, the interior orientation parameters of the cameras used. In such an adjustment the additional information available would be of utmost importance. 3.2 Software Description For the adjustment the BINGO-F v.4 software was available. It is a well known bundle adjustment software with long presence in the market and very good reputation. The characteristics of this software are briefly the following: Complete parametrisation Full control of all unknowns and observations Possibility to perform self calibration Possibility for inclusion of geodetic measurements in the adjustment Ability to adjust images irrespective of their attitude No need for ground control points Complicated data snooping techniques No need for initial approximations, as the software calculates them automatically For the calculations BINGO-F uses the well known collinearity equations and as input data it requires the image co-ordinates of all known or unknown points appearing on the images, the coordinates of the ground control points, the eventually known geodetic measurements (e.g. distances) and all the necessary parameters for the interior geometry of the camera (Kruck, 1998). Figure 2: Sample of the geometric documentation drawings Moreover we also had access to all our relevant geodetic measurements and other technical data, such as point coordinates, angles, height differences and three dimensional distances. 2.2 Image Data Nothing was known, however, concerning the geometry of the 35mm slides available. They were taken with an amateur, but completely unknown, camera obviously equipped with a zoom lens. Hence the images were of different and unknown scales As output the software provides the co-ordinates of the perspective centres and the camera axes attitudes expressed with the help of the Euler angles, the co-ordinates of all unknown points involved in the adjustment and if so required by the user the parameters of the interior geometry of the cameras, i.e. the principal distance, the coefficients of the radial distortion curve and the image co-ordinates of the principal point.
3.3 Data preparation In order to implement the adjustment, a preparation stage was necessary. The images available were enlarged and used in order to determine those detail points which would be necessary to produce the roof top plan. This operation resulted to a detailed sketch of the roof tops which was constructed with the help of the already available drawings, but also with the help of the immediate knowledge of such a complicated monument. Hence a total of 242 points were determined, necessary to provide a firm basis for the final drawing. These points appeared on at least 2 images and at maximum on 12. The co-ordinates of these points could not be determined from the existing elevation drawing, as these were in rotated systems. Hence three dimensional distances between almost all of the points could only be determined from the work completed so far. It is obvious that in this way all possible geodetic measurements were made available for the adjustment. The above described image data were scanned at a resolution of 1200dpi on an AgfaScan desktop scanner, thus resulting to a pixel size of 21µm, which corresponds to approximately 85mm on the ground. It was thought that although the use of a simple off-the-shelf scanner could introduce geometry errors, these would be adjusted later. In order for the image co-ordinates to be measured a simple own developed software (Stambouloglou et al. 1999) was used. With this software one may perform all the necessary measurements within the AutoCAD environment and receive as output an ASCII file with the image co-ordinates referred to the principal point. All the determined points were marked on all images they appeared and then the measurements were performed. As for the interior orientation, the knowledge that the negative size was the standard 26x34 mm was used. Approximately 1200 measurements were necessary for this task. The RMS errors for each affine transformation and also the number of observations for each image are given in Table 1. 4.1 Image RMS error (µm) No of obs 1 26 59 3 34 91 4 20 64 5 10 116 6 18 78 7 15 129 8 6 120 9 37 46 10 37 66 11 9 111 12 3 86 13 7 56 15 41 117 16 2 67 Mean 17 1206 Table 1: RMS errors after the affine transformations and number of observations for all images used 4. DATA ADJUSTMENTS Input files BINGO-F requires two input files. One file, image.dat, contains the image co-ordinates as measured. The other file, geoin.dat, enables the user to fully control all parametrs involved. It was decided to variate several parameters for the adjustments. Firstly it was obvious that the images were taken with a zoom lens, which actually could be interpreted that practically every image was taken with a different camera. Hence the camera constant and the position of the principal point should definitely be included in the unknown parameters. As already mentioned, BINGO-F may adjust a photogrammetric network without any ground control points, under certain circumstances of course. Additionally either distances between points or geodetic co-ordinates would enhance the strength of the adjustment. Hence the kind and the quantity of the ground control was another interesting subject for variation during the adjustments. 4.2 Performing the adjustments The adjustment was performed dozens of times. As experience was gained, it was decided to group the calculations into mainly three groups. Firstly it was assumed that there was one single camera used throughout the project. Hence all photographs were included into the adjustment with one unknown principal distance. Approximately 25 known distances provided the necessary ground control. Successive minor variations to the data were required in order to exclude points giving unacceptably large residuals, or even exclude a couple of images, which would not fit into the adjusted network. The main problem encountered was the resulting reference system. As already mentioned, BINGO-F has the ability to calculate initial approximations automatically. This is carried out by the module RELAX, which actually assumes that the initial reference system is the one defined by the first two images in good geometry. If, later, known ground control points are fed into the adjustment, this system adjusts itself to the desired one. If, however, this is not the case, the initial reference system remains unchanged. Secondly the images were grouped according to their scale. Assuming that the camera was equipped with a zoom lens, it was decided to introduce to the adjustment two camera constants as unknowns. The point distances provided the necessary ground control. During the adjustments corrections were made to the initial approximation of the camera constants of the two unknown cameras, in order to achieve a more reliable solution. Again the problem of the uncontrolled determination of the co-ordinate reference system was a major problem. Finally it was decided to carefully choose three points and with the help of the corresponding distances assign to them rectangular co-ordinates, in order to force the software to provide adjusted co-ordinates in that particular system. Seven additional points were also used as vertical control, in order to ensure the horizontality of the system. In this way the resulting system was closer to reality and enabled the easier exploitation of the results.
4.3 Discussion of results The most important results of the adjustments are grouped and presented in Table 2. A B C Control distances dist. Distances + GCP s First best best low med. best Unknown 698 606 594 642 618 543 parameters Number of 2668 1620 1473 1738 1311 1076 observs Number of 199 181 176 186 181 161 points Number of 14 9 9 12 11 9 images σ ο (mm) 163.2 38.5 27.0 26.7 18.7 15.2 Number of cameras 1 1 2 4 3 2 Principal distance values (mm) Mean RMS for XYZ (m) 80.02 83.4 77.4 83.6 71.7 88.6 176.7 71.4 80.16 84.05 184.18 78.7 84.6 0.25 0.12 0.10 0.11 0.09 0.06 It is obvious from this table, that some of the results are just adequate for the required product. The adjustments in group A, i.e. those with the assumption that only one camera lens was used, are justifiably the worse. Although the overdetermination of the system is advantageous, the fact that the image scale presents such differences prohibits an accurate solution. One, however, may see from the best results in this group, that an RMS of 0.12m may be achieved, although 181 points were used in this case. Figure 3: The final drawing of the roof tops 5. CONCLUDING REMARKS It has been shown that it is possible to adjust even the most difficult configuration of images provided a suitable combination of ground control is applied. The completely unknown interior orientation was confronted with success, although one is not quite sure that the resulted values for the principal distances are exactly the true ones, as there were not enough control points available for a full self calibration. Moreover it was not possible, under these circumstances, to include radial distortion terms as unknowns. An important conclusion is that irrespective of the image geometry, a solution was almost always possible. The photos were taken from different heights with different inclinations. The sketch in Figure 4 shows the relationship of the camera stations and the axes attitudes in respect to the main object. As for group B, although two cameras are input as unknowns, the results, as far as accuracy is concerned, are not much better. The major improvement is observed in group C, where a few points provide more rigid information about the reference system. One may observe that the best results are achieved when two camera lenses are assumed, although it seems more logical that the second case (i.e. with three camera lenses as unknowns) is the most realistic one. 4.4 Final products The points determined were by no means enough for the final drawings. It was decided to keep 188 points in total, most of them (161) from the best adjustment of group C. For the production of the final drawings the following procedure was applied. Firstly the points determined were plotted at the desired scale in order to provide a rigid frame for the details to be added. By suitably inserting the already produced drawings in the AutoCAD environment and using simple descriptive geometry rules the various details could be determined, as crossections of perpendiculars from the corresponding points on the elevations. In Figure 3 the final plot is presented. References Figure 4: Camera axes attitudes Georgopoulos, A., Karras, G., Makris, G.N., 1999. The photogrammetric Survey of a Prehistoric Site undergoing
Removal. Photogrammetric Record 16(93): pp. 443-456, April 1999. Kruck, E., 1998. BINGO-F v. 4.0 User s Manual. Modatsos, M., 2000. Photogrammetric exploitation of non metric images with analytical methods. Diploma Thesis, Lab. of Photogrammetry, School of Rural & Surveying Eng., NTUA (in Greek). Stambouloglou, E., Chavakis, I., 1999. Adjusting terrestrial non-metric images using the BINGO-F software. Diploma Thesis, Lab. of Photogrammetry, School of Rural & Surveying Eng., NTUA (in Greek).