## 4 Results
### Data Processing
#### 4.2.4 Generation of Historical 3D/4D Models  
For buildings where a sufficient number of historical photographs were available, we created higher-resolution 3D models from imagery. This approach has currently been tested with data from single buildings in Jena and Dresden and for a larger area in the inner city of Budapest.  
The presented automatic image orientation allows time-dependent 3D models (4D models) to be generated using image content. For this purpose, the textures of the georeferenced images are projected onto the respective LoD2 models. Depending on the selected time period, one or multiple images are used. In the case of multiple images, we developed a shader for smart selection of image content depending on the image angle and distance to the object, as explained in the visualization section.  
This approach is useful for real-time applications where heavy data traffic should be avoided. However, textured models usually lack complexity due to the simplicity of LoD2 (Figure 12).  
Figure 11: Example roof shapes from the parametric generator for buildings with four faces (**left**), implementation in the 4D City application for larger numbers of faces (**right**).  
Figure 12: A reconstruction of the National Maritime Museum in Amsterdam using an oriented image, texture projection, and an LoD2 building model.  
More detailed 3D models from SfM workflows are usually generated using dense matching with its most widespread technology, semi-global matching. As a result of the extremely inhomogeneous nature of historical images, and consequently the large radiometric and geometric differences between image pairs, the result of conventional dense matching is often unusable (Figure 13).  
This is why initial experiments on using neural rendering strategies like NeRF [136] have been carried out in the research group. Detailed tests and results [80] are summarized in the following.  
The sparse point cloud derived using advanced SfM techniques is transferred into SDFStudio [301], which is a modular framework for neural implicit surface reconstruction. In our experiments, NeuS Facto yielded the best results, even for a small number of historical terrestrial images. However, rendering may also produce artifacts, and the results are still far from perfect detailed representations of the historical buildings (Figure 14).  
Consequently, more experiments have to be carried out to improve the automatic generation of high-quality 3D building models. Improvements may be obtained by using and adapting even more recent neural rendering methods such as [302; 303], as we think that there is high potential when using these approaches for automatic 3D and 4D modelling.  
Figure 13: Two photographs of the Semperoper, Dresden, from 1953 (**top left**) and 1954 (**top right**). The change in appearance of the roof is translated into inaccuracies and artifacts in the final dense cloud (**bottom**) calculated in Agisoft Metashape.  
To test this pipeline on a larger scale, we selected, from \(\sim\)200 k historic images, 10 k images as belonging to the same continuous city model of Budapest. Figure 15 depicts an SfM reconstruction using SOTA it isand -content-based image retrieval (EigenPlaces) and neural matching algorithms (DISK + LightGlue). Although the overall topology of the city is clearly visible, although partially mirrored, it contains many degenerate cameras (long red lines) and incorrect matches; also, the repetition of structures such as the two sides of the bridge in the center of the view causes problems.