After the BBA is done successfully, the optimal positions and orientations of the images and the geometry of the cameras (in a global coordinate system) are provided with the desired accuracy. Now you can use the obtained information to produce the following outputs
1- Multi-image spatial intersection of any desired point: Using the information obtained from bundle adjustment, the 3D position of any point seen in more than one photo could be extracted by spatial intersection. It is obvious that the accuracy of the obtained coordinates completely depends on the geometric strength of the intersection.
2- Brightness values for each ground/model point: by using exterior orientation parameters, by applying the collinearity condition, it is possible to calculate the corresponding brightness values in the images for each model or ground point.
3- Internal geometry of the camera: one of the by-products of the bundle analysis is the internal geometry of the sensor and also the estimation of the interior orientation parameters of the cameras. This product is used in various industries such as internal design of composite cameras, self-driving cars, and mobile mapping systems.
4- Metric panoramic images: In a multi-camera that includes a set of cameras with projective geometry, one of the most important users of the geometry extracted from the bundle adjustment is the formation of metric panoramic images by combining multiple images. These images have many applications in various sections.
5- Photogrammetric point cloud: if high-density image correspondences between all possible pairs of stereo images could be obtained, then multi-image intersection could be used to find all possible model points that are visible in more than one photo. This is one of the most attractive photogrammetry applications for many various industry sections. A photogrammetric point cloud could have the same or even greater density and accuracy than other methods of point cloud formations such as LiDAR.
6- Orthophoto generation: one of the most important outputs that can be produced from the results of bundle adjustment is orthophoto which is an artificial image that is obtained by combining BBA results, images, and geometric information of the target object. To form an orthophoto, an imaginary plane is considered. In the case of aerial photogrammetry, this plane is usually assumed at the average height of the area. Then, the length of each pixel of this image is obtained by analyzing the values of the ground sampling distances of the photos, and the same length and width of the image as well as its coverage are obtained by analyzing the point cloud. In the last step, a height for each pixel is extracted by the interpolation method, and the collinearity equation is used to obtain grayscale values from the photographs. Elevations in an orthophoto are corrected by taking into account the projective geometry, so an orthophoto will have a map-like function.
The first case: Below we see an example of the process of using photogrammetry technology to extract a point cloud from aerial images. In this example, 49 images are taken from a mountainous area. In the figure below, 6 images out of 49 initial images are shown as examples.
In the first step, the tie points are automatically extracted from the images and the basic structure of the network is estimated using the coplanarity equations. Note that there are a considerable number of blunder points that must be removed. In the next step for this network, a BBA is performed by considering a minimum constraint. In the figure below, we can see the final structure of the network and 95% 3D error ellipses for images and ground points.
Pay attention that in the right figure, the rotational ellipses of the error are displayed with a multiplication factor of 100x. In the last step, the exact elements of the photo’s position and periods are used to extract a point cloud from the obtained images.
We can see the point cloud extracted from the images in above figure. it can be seen that the point cloud has considerable geometric accuracy and can be used for applications such as map generation, orthophoto production, as well as extracting elevation curves, or forming a digital elevation model. This example is an effective application of the use of photogrammetry technique in the preparation of aerial maps.
Second case: In the example below, 246 vertical images are taken from a field. 6 images can be seen as an example in the collection of images below.
In a process similar to the first example, tie points are automatically extracted from aerial images, network structure is estimated, and BBA is done as follows.
In the right figure, the rotational ellipses of the error are displayed with a scale of 10x. We can see a non-dense point cloud from the obtained images below. In this example, BBA has been done using the minimal constraint coordinate system. As it is clear from the observation of the 3D error ellipses, the sizes of the 3D error ellipses increase by moving away from the first image.
Finally, the results of BBA are used to extract a point cloud with a higher density based on automatic image tie points. In this example, the image residuals as well as the estimation of uncertainty about the model points are used to filter out the blunder points. The digital height model obtained from the point cloud is calculated as follows
The third case: Here we point out an important application of BBA in extracting the internal geometry of the camera and forming metric panoramic images. In this example, we want to estimate the internal geometry of a multi camera consisting of 6 cameras that are installed on the side and top faces with high accuracy by using BBA. For this purpose, we initially form a three-dimensional calibration object by installing coded-targets on the walls of a photogrammetric calibration room. Then, we accurately estimate the geometry of the calibration object using bundle adjustment. We use spatial resection to extract the approximate positions of multi images, and in the last step, we estimate the internal geometry of the camera with high accuracy, taking into account the internal constraints of the multi camera.
In the above figure, we see an example of images taken by a multi camera
In the figure above, we see the calibrated geometry of the multi camera on the left.
In the figure above, we see a view of a metric panoramic compilation of the calibration room, which was calculated using the calibrated geometry of the multi-camera.
It should be noted here that the formation of panoramic images is mainly possible in two ways: 1- by connecting images with an automatic approach for some artistic purposes 2- by using the photogrammetric method in such a way that the spatial position of each pixel of the final 360 image compilation is known using the calibrated geometry of the camera. Unfortunately, the artistic panoramic image has no metric value and is only used for visual appealing applications, while a metric panorama can be used for photogrammetric operations such as spatial intersection, resection, and BBA.
In the figure below, we can see the footprints of individual cameras on the final metric panorama for the multi-camera of the previous example. Here, it is clear that some points in the final compilation could be seen in more than one images. If we use an appropriate criteria such as best viewing angle, we can convert this information into a map to create a metric panoramic image.
In the figure below, we can see a map for creating a metric panoramic image for a multi-camera
