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Fig.10 Hydraulic Model in working conditions. The above-described method has been tested on a lab model: we made in the laboratory a model of the confluence in this portion of land. The following were the results of modeling displayed within the software Photo Modeler. Applying the photogrammetric technique, we reconstructed the 3D model.

Figure 10 Hydraulic Model in working conditions. The above-described method has been tested on a lab model: we made in the laboratory a model of the confluence in this portion of land. The following were the results of modeling displayed within the software Photo Modeler. Applying the photogrammetric technique, we reconstructed the 3D model.

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The photogrammetric technique is based on a transformation of a perspective (or a couple of perspectives) in a quoted orthogonal projection. In this transformation, we have non-linear equations and, before starting the plotting, we need information about the preliminary value of unknown parameters. Our main aim is to find expressions working with parameters easy to be obtained. In order to orient two images in the 3D space, we can choose two different procedures: a “one step” or a “two steps”. The first procedure is based on_ collinearity equations and needs 12 parameters: X,, Y,, Z;, Xo, Y>, Z, (coordinates of the two projection centers), and @, @1, Ki, @2, 2, Ky (attituded angles of the two sensor). The second one separates the model formation (Relative Orientation) from the object reconstruction (Absolute Orientation). In this procedure, we define the problem of Relative Orientation by means of 5 parameters: ©), Kj, @2, Q2, kK, (Symmetric Relative Orientation), or by, b ;, @2, 2, Ky (Asymmetric Relative Orientation). On the contrary, to define the problem of Absolute Orientation we need 7 parameters: t,, ty, t, (shift vector), A (scale factor), Q, ®, K (Cardanic angles). yarameters easy to be obtained. In order to orient perspectives) in a quoted orthogonal projection. In
The photogrammetric technique is based on a transformation of a perspective (or a couple of perspectives) in a quoted orthogonal projection. In this transformation, we have non-linear equations and, before starting the plotting, we need information about the preliminary value of unknown parameters. Our main aim is to find expressions working with parameters easy to be obtained. In order to orient two images in the 3D space, we can choose two different procedures: a “one step” or a “two steps”. The first procedure is based on_ collinearity equations and needs 12 parameters: X,, Y,, Z;, Xo, Y>, Z, (coordinates of the two projection centers), and @, @1, Ki, @2, 2, Ky (attituded angles of the two sensor). The second one separates the model formation (Relative Orientation) from the object reconstruction (Absolute Orientation). In this procedure, we define the problem of Relative Orientation by means of 5 parameters: ©), Kj, @2, Q2, kK, (Symmetric Relative Orientation), or by, b ;, @2, 2, Ky (Asymmetric Relative Orientation). On the contrary, to define the problem of Absolute Orientation we need 7 parameters: t,, ty, t, (shift vector), A (scale factor), Q, ®, K (Cardanic angles). yarameters easy to be obtained. In order to orient perspectives) in a quoted orthogonal projection. In
Table 1. Exhaustive Research for Symmetric Relative Orientation parameters. Examples were carried out in all the middle points of the possible configuration. Considering the 5 parameters of the Symmetric Relative Orientation, the angles «;, @2, k) are defined in a complete rotation (8 configurations), whilst ©), @2 are defined in a half rotation (5 configurations), which led to the above mentioned 12800 cases. As known, if the @ angle is around +II/2, we cannot individuate the k rotation, which is fixed equal to zero. Indeed in the polar zones (we assumed their range in a circle of one degree), the two angles are identical or quasi identical, and this fact produced singularity or ill-conditioning. Each linear system solution gave us the estimate parameters for the Symmetric Relative Orientation. The convergence to admissible values is when 6p is small enough. Considering only the distinct solutions, we found four analytical acceptable configurations.
Table 1. Exhaustive Research for Symmetric Relative Orientation parameters. Examples were carried out in all the middle points of the possible configuration. Considering the 5 parameters of the Symmetric Relative Orientation, the angles «;, @2, k) are defined in a complete rotation (8 configurations), whilst ©), @2 are defined in a half rotation (5 configurations), which led to the above mentioned 12800 cases. As known, if the @ angle is around +II/2, we cannot individuate the k rotation, which is fixed equal to zero. Indeed in the polar zones (we assumed their range in a circle of one degree), the two angles are identical or quasi identical, and this fact produced singularity or ill-conditioning. Each linear system solution gave us the estimate parameters for the Symmetric Relative Orientation. The convergence to admissible values is when 6p is small enough. Considering only the distinct solutions, we found four analytical acceptable configurations.
Fig.3 The four final possible configurations. 4 Object reconstruction Starting from a rototraslation in the space, a rational alternative to classical Rotation Matrix is the mde uresefe
Fig.3 The four final possible configurations. 4 Object reconstruction Starting from a rototraslation in the space, a rational alternative to classical Rotation Matrix is the mde uresefe
To verify precision, accuracy and reliability of these techniques, a program in Fortran 95 language (compiled and assembled with Lahey-Fujitsu Fortran 95 version 5.6) was written, implemented and tested. In all the examples, we introducec random errors, with standard deviation of 20 um, as usual in photogrammetry. In the following flowchar (Fig.5), we will summarize the global procedure fot the orientation of two images, then we will present ¢ brief explanation of these programs. Fig.5 Global procedure for the orientation of two images.
To verify precision, accuracy and reliability of these techniques, a program in Fortran 95 language (compiled and assembled with Lahey-Fujitsu Fortran 95 version 5.6) was written, implemented and tested. In all the examples, we introducec random errors, with standard deviation of 20 um, as usual in photogrammetry. In the following flowchar (Fig.5), we will summarize the global procedure fot the orientation of two images, then we will present ¢ brief explanation of these programs. Fig.5 Global procedure for the orientation of two images.
Fig.6 Absolute Orientation Results. The following tables and figures show the difference among the nominal values and the preliminary ones.
Fig.6 Absolute Orientation Results. The following tables and figures show the difference among the nominal values and the preliminary ones.
Fig.7 Symmetric Relative Orientation results.
Fig.7 Symmetric Relative Orientation results.
Fig.8 Symmetric Relative Orientation results (Polar regions). In the light of the proposed experiments, new programs, which would permit an easy solution for he Relative and Absolute Orientations, gave very satisfied expected results. This procedure has great potentiality for non-conventional data acquisition e.g. amatorial images, images coming from unknown and old sources, equipped vehicles, robots, and many other applications in close range photogrammetry). The advantage of a_ linear Absolute Orientation should also taken into account. Moreover, even if the solution achieved in the Relative Orientation requires an exhaustive research, it is again quick and easy, and seems to solve positively the problem how to acquire the preliminary values of the Relative Orientation parameters.
Fig.8 Symmetric Relative Orientation results (Polar regions). In the light of the proposed experiments, new programs, which would permit an easy solution for he Relative and Absolute Orientations, gave very satisfied expected results. This procedure has great potentiality for non-conventional data acquisition e.g. amatorial images, images coming from unknown and old sources, equipped vehicles, robots, and many other applications in close range photogrammetry). The advantage of a_ linear Absolute Orientation should also taken into account. Moreover, even if the solution achieved in the Relative Orientation requires an exhaustive research, it is again quick and easy, and seems to solve positively the problem how to acquire the preliminary values of the Relative Orientation parameters.
Fig.9 Image Orientation — Global Proced. (ORTRE Program).
Fig.9 Image Orientation — Global Proced. (ORTRE Program).
Fig.11 Visualization of 3D Model with Photo Modeler
Fig.11 Visualization of 3D Model with Photo Modeler
Fig. 12 Texture obtained with point shooting. The construction of the denser point cloud (dense cloud points) represents the second stage of processing, in which starting from the cloud of Sparse points we get a more detailed and dense cloud of points.
Fig. 12 Texture obtained with point shooting. The construction of the denser point cloud (dense cloud points) represents the second stage of processing, in which starting from the cloud of Sparse points we get a more detailed and dense cloud of points.
Fig.13 Detail of texture.
Fig.13 Detail of texture.
Table 2. Comparison of the values obtained from the two models Fig.16 shows comparisons between the two techniques in terms of accuracy obtained by setting the target positioned on the homologous elements, such as the edges of the reef and the “test” fixed points arranged appropriately on the sea surface.
Table 2. Comparison of the values obtained from the two models Fig.16 shows comparisons between the two techniques in terms of accuracy obtained by setting the target positioned on the homologous elements, such as the edges of the reef and the “test” fixed points arranged appropriately on the sea surface.
In terms of accuracy, estimation of the leading photogrammetric orientation parameters, accuracy of results, we found a substantial similarity of results of the two models.
In terms of accuracy, estimation of the leading photogrammetric orientation parameters, accuracy of results, we found a substantial similarity of results of the two models.
Fig.16 Comparison of the results obtained by the two techniques.
Fig.16 Comparison of the results obtained by the two techniques.
where its parameters generally have any physical meaning. — Moreover, because the rotation matrix is obviously unique, this matrix allows passing from the Cardanic angles to the Eulerian ones, and vice versa. -_ Appendix B This appendix wants to present, very shortly, the analytical definition of the coplanarity condition, both in the Asymmetric configuration and in the Symmetric one.
where its parameters generally have any physical meaning. — Moreover, because the rotation matrix is obviously unique, this matrix allows passing from the Cardanic angles to the Eulerian ones, and vice versa. -_ Appendix B This appendix wants to present, very shortly, the analytical definition of the coplanarity condition, both in the Asymmetric configuration and in the Symmetric one.
Related topics:
Analytical PhotogrammetryAbsolute OrientationRelative Orientation
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