In this Chapter a new method is proposed for generating **3D** **building** **models** on different levels of detail (LOD). The proposed work flow is presented in Figure 6.1. The **3D** **models** on differ- ent LOD follow the standard definition of the City Geography Markup Language (CityGML) described in (Kolbe et al., 2005). CityGML defines five LOD for multi-scale modeling: LOD0 – Regional model consisting of the 2.5D Digital Terrain Model (DTM), LOD1 – **Building** block model without roof structures, LOD2 – **Building** model including roof structures, LOD3 – **Building** model including architectural details, LOD4 – **Building** model including the interior. Algorithms for producing the first three levels of the LOD are explained in this chapter. Accord- ing **to** the above categorization, the first LOD corresponds **to** the digital terrain model (DTM). The non-ground regions are filtered using geodesic reconstruction **to** produce the DTM **from** **LIDAR** DSM (Arefi and Hahn, 2005; Arefi et al., 2007b). The LOD1 consists of a **3D** representation of buildings using prismatic **models**, i.e., the **building** roof is approximated by a horizontal plane. Two techniques are implemented for the approximation of the detected **building** outline: hierarchical fitting of Minimum Bounding Rectangles and RANSAC-based straight line fitting and merging (Arefi et al., 2007a). For the third level of detail (LOD2), a projection-based approach is proposed resulting in a **building** model with roof structures. The algorithm is fast, because 2D data are analyzed instead of **3D** data, i.e., lines are extracted rather than planes. The algorithm begins with extracting the **building** ridge lines thought **to** represent **building** parts. According **to** the location and orientation of each ridge line one para- metric model is generated. The **models** of the **building** parts are merged **to** form the overall **building** model.

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With data provided by modern meter-resolution SAR sensors and advanced multi-pass interferometric techniques such as tomographic SAR inversion (TomoSAR), it is now possible **to** generate 4-D (space-time) **point** **clouds** of the illuminated area with **point** density of approx. 1 million points/km 2 . However, due **to** side looking geometry, these **point** **clouds** exhibit much higher density of points on **building** façades in contrast **to** nadir looking **LiDAR** geometry (typically used for object reconstruction). Moreover, temporally incoherent objects such as trees cannot be reconstructed **from** multi-pass spaceborne SAR image stacks and provide moderate 3-D positioning accuracy in the order of 1m as compared **to** airborne **LiDAR** systems (around 0.1m). Despite of these special considerations, object reconstruction **from** these high quality **point** **clouds** can greatly support the reconstruction of dynamic city **models** that could be potentially used **to** monitor and visualize the dynamics of urban infrastructure in very high level of details. Motivated by these chances, earlier approaches have been proposed **to** reconstruct **building** façades **from** this class of data. E.g., experimental results provided in (Zhu, 2014) and (Shahzad, 2014) over smaller and larger areas demonstrate that façade reconstruction is an appropriate first step **to** detect and reconstruct **building** shape when dense points on the façade are available. In particular, when data **from** multiple views e.g., **from** both ascending and descending orbits, are available, the full shape of buildings can be reconstructed using extracted façade points. However, there are cases when no or only few

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This paper compares two generic approaches for the reconstruction of buildings. Synthesized and real oblique and vertical aerial imagery is transformed on the one hand into a dense photogrammetric **3D** **point** cloud and on the other hand into photogrammetric 2.5D surface **models** depicting a scene **from** different cardinal directions. One approach evaluates the **3D** **point** cloud statistically in order **to** extract the hull of structures, while the other approach makes use of salient line segments in 2.5D surface **models**, so that the hull of **3D** structures can be recovered. With orders of magnitudes more analyzed **3D** points, the **point** cloud based approach is an order of magnitude more accurate for the synthetic dataset compared **to** the lower dimensioned, but therefor orders of magnitude faster, image processing based approach. For real world data the difference in accuracy between both approaches is not significant anymore. In both cases the reconstructed polyhedra supply information about their inherent semantic and can be used for subsequent and more differentiated semantic annotations through exploitation of texture information.

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of two Gaussian functions **to** reduce the noise without affecting high-frequency details (Tomasi and Manduchi, 1998). Further- more, under the assumption that city buildings appear as ele- vated regions surrounded by lower ground, those DSM pixels that form the terrain are identified and removed by repeatedly moving windows of varying size over the DSM bitmaps as described in (Mayer, 2004). This process that basically creates a digital eleva- tion model also eliminates most of the vegetation that is likely **to** disturb any upcoming processing steps and provides an estimate for the ground height around the buildings as a by-product. After preprocessing the remaining DSM pixels are transformed into genuine **3D** points and merged into a single **point** cloud. The resulting high-resolution samples are reduced **to** limit the mem- ory consumption and projected onto the XY plane subdivided by a regular grid. The spacing of the grid needs **to** be adjusted empirically with respect **to** the residual noise of the points. For each grid cell its density, spatial distribution and characteristic height histogram is computed and evaluated **to** identify potential fac¸ade pieces (Linkiewicz, 2012). On the set of cell elements C = {p i = (x i , y i )} that is considered a part of the fac¸ade the

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Once the façade model parameters are estimated, the final step is **to** describe the overall shape of the **building** footprint by further identifying adjacent façades pairs and determining the intersection of the façade surfaces. The adjacency of facades is usually described by an adjacency matrix that is built up via connectivity analysis. Identified adjacent façade segments are then used **to** determine the vertex points (i.e., façade intersection lines in **3D**). They are found by computing the intersection points between any adjacent façade pair. Since polynomial **models** are used for façade parameter estimation, the problem of finding vertex points boils down **to** find the intersection **point** between the two polynomials corresponding **to** the two adjacent façades. The computed vertex points and the estimated model parameters are then used **to** finally reconstruct the **3D** model of the buildings façades.

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The problem of estimating the pose of an object **from** a scan **point** cloud is equivalent with calculating the trans- formation between two **point** **clouds** representing the ob- ject **from** different perspectives. This task is referred **to** as range image registration. Usually, the term is associ- ated with constructing three-dimensional **models** of real objects based on range image data which give a partial view of the object **from** different viewpoints. Following the categorization of [SMFF07], fine and coarse registra- tion methods can be distinguished. The former calculate very accurate solutions based on initial transformations (e.g. ICP). The latter do not need any initial informa- tion and achieve a lower accuracy. The coarse type is exactly what is needed for pose initialization. Common methods include spin image, principal component anal- ysis, genetic algorithms and RANSAC-based DARCES [SMFF07]. However, at least without any adaptation, these methods are only of limited suitability in the con- text of spacecraft relative navigation.

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Figure 9 illustrates the results of the verification process. Therefore, 16 datasets **from** Wujanz et al. [18] were used featuring planar panels that were captured under random survey configurations and varying radiometric properties. The corresponding data was then processed in a least squares adjustment using three different stochastic **models** yielding in different weights for individual ranges and, consequently, different empirical standard deviations s 0 . The horizontal axis shows intensity values on a logarithmic scale. The vertical green lines highlight the smallest and largest intensity values that were captured in the experiments for the generation of the stochastic **models**. The vertical axis graphs the empirical standard deviations s 0 that stem **from** the plane adjustments. The first model was generated based on repetitive range measurements according **to** Wujanz et al. [18] while the corresponding results are depicted by blue circles. For the red circles the stochastic model generated in Section 2.1 was used, while the green circles stem **from** Section 2.2. All green and red circles fall into the specified interval of 0.7 < s 0 < 1.3. Hence, this outcome verifies the two suggested procedures for the generation of intensity-based stochastic **models** based on capturing **3D**-**point** **clouds** instead of repeated range measurements. Note that the empirical standard deviations drift apart for higher intensities while a higher degree of conformity was apparent for the remaining parts.

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Typical data sources for reconstructing 3-D **building** **models** in- clude optical images (airborne or spaceborne), airborne **LiDAR** **point** **clouds**, terrestrial **LiDAR** **point** **clouds** and close range im- ages. In addition **to** them, recent advances in very high resolution synthetic aperture radar imaging together with its key attributes such as self-illumination and all-weather capability, have also at- tracted attention of many remote sensing analysts in character- izing urban objects such as buildings. However, SAR projects a 3-D scene onto two native coordinates i.e., “range” and “az- imuth”. In order **to** fully localize a **point** in 3-D, advanced in- terferometric SAR (InSAR) techniques are required that process stack(s) of complex-valued SAR images **to** retrieve the lost third dimension (i.e., the “elevation” coordinate). Among other InSAR methods, SAR tomography (TomoSAR) is the ultimate way of 3- D SAR imaging. By exploiting stack(s) of SAR images taken **from** slightly different positions, it builds up a synthetic aperture in elevation that enables the retrieval of precise 3-D position of dominant scatterers within one azimuth-range SAR image pixel. TomoSAR processing of very high resolution data of urban ar- eas provided by modern satellites (e.g., TerraSAR-X, TanDEM-X

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The Hough transform is a feature extraction technique used in image analysis, computer vision, and digital image processing (Shapiro u. Stockman [2001]). It estimates the parameters of a shape **from** its points. The purpose of the technique is **to** find imperfect instances of objects within a certain class of shapes by a voting procedure. This voting procedure is carried out in a parameter space, **from** which object candidates are obtained as local maxima in a so-called accumulator space that is explicitly constructed by the algorithm for computing the Hough transform. It can be used **to** detect lines, circles and other primitive shapes if their parametric equation is known. In principle, it works by mapping every **point** in the data **to** a manifold in the parameter space. This manifold describes all possible variants of the parametrized primitive. Making the parametrizing simpler or limit the parameter space speed up the algorithm. This is especially true for **3D** shape detection, where for example **to** detect a plane using the plane equation ax+by+cz+d=0 requires **3D** Hough space, which will quickly occupy large space of memory and performance since all possible planes in every transformed **point** **clouds** need **to** be examined. A plane can also be fitted based on normalized normal vectors using only two of the Euler angles and distance **from** origin, α, β and d. There is no need **to** the third Euler angle since the information when transforming around the axis in redundant (Hulik u. a. [2014]).

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shaped footprint could be reconstructed. Also, the approach utilizes roof points in determining the complete shape of the buildings and therefore resolves problems, as mentioned in (Shahzad and Zhu, 2015a), related **to** the visibility of the façades mainly pointing towards the azimuth direction of the SAR sensor. However, few points still need **to** be addressed. For instance, the reconstruction accuracy is restricted due **to** less number of available points and data gaps in the TomoSAR **point** cloud. This could be improved by incorporating data **from** other viewing angles and/or adding more constraints such as parallelism or using a model based approaches based on a library of low level feature sets. Also, we have compared our results **to** the OSM data which is regularly updated but not yet fully complete. Therefore, a more accurate ground truth would be needed for assessing the exact performance of the approach. Nevertheless, this paper presents the first demonstration of automatic reconstruction of 2-D/3-D **building** footprints **from** this class of data. Moreover, the developed methods are not strictly applicable **to** TomoSAR **point** **clouds** only but are also applicable **to** work on unstructured 3-D **point** **clouds** generated **from** a different sensor with similar configuration (i.e., oblique geometry) with both low and high **point** densities. In the future, we will explore the potential of extending the algorithm towards generation of automatically reconstructed complete watertight prismatic (or polyhedral) 3-D/4-D **building** **models** **from** space.

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Station dependent effects remain, such as observation noise, hardware delays, multipath, or antenna PCCs. These effects have **to** be considered with appropriate correction **models** by the user. PCCs result **from** the fact that the actual phase measurements are related **to** the electrical phase centre of the receiver antenna while within the adjustment, measurements are modelled with respect **to** the geometrically well defined Antenna Reference **Point** (ARP). This difference is described by the PCC (Fig. 2.3). An example stereographic plot of absolute PCC for a standard rover antenna (Javad GrAnt G3T) is shown in Fig. 2.4. The PCCs are obtained by abso- lute robot calibration (named the Hannover concept (Wübbena et al., 2000)) at the Institut für Erdmessung (IfE), Leibniz Universität Hannover, Germany. Further determination approaches are calibration in an anechoic chamber (Zeimetz and Kuhlmann, 2008) and relative calibration with respect **to** a Nullantenna (Mader, 1999). While GNSS signals are right-hand circular polarised electro-magnetic waves (cf. Fig. 2.5) the relative orien- tation of receiver and satellite antennas has **to** be taken into account, as described in, e. g., Wu et al. (1993). The polarisation of the satellite signal is determined by the electric field vector E = [ E X E Y ] T which is

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ence. Many approaches have been reported over the last decades. Sophisticated classification algorithms, e.g., support vector ma- chines (SVM) and random forests (RF), data modeling methods, e.g., hierarchical **models**, and graphical **models** such as condi- tional random fields (CRF), are well studied. Overviews are given in (Schindler, 2012) and (Vosselman, 2013). (Guo et al., 2011) present an urban scene classification on airborne **LiDAR** and mul- tispectral imagery studying the relevance of different features of multi-source data. An RF classifier is employed for feature evalu- ation. (Niemeyer et al., 2013) proposes a contextual classification of airborne **LiDAR** **point** **clouds**. An RF classifier is integrated into a CRF model and multi-scale features are employed. Recent work includes (Schmidt et al., 2014), in which full wave- form **LiDAR** is used **to** classify a mixed area of land and water body. Again, a framework combining RF and CRF is employed for classification and feature analysis. (Hoberg et al., 2015) presents a multi-scale classification of satellite imagery based also on a CRF model and extends the latter **to** multi-temporal classification. Concerning the use of more detailed **3D** geome- try, (Zhang et al., 2014) presents roof type classification based on aerial **LiDAR** **point** **clouds**.

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In our experiments, we show that our pipeline can create geometrically regularized **3D** **models** **from** buildings which finally consist of smooth and clean surfaces instead of a noisy mesh, as in the input data. It can handle input meshes with different quality and input density, where especially on meshed **point** **clouds** including some errors (e.g., a **point** cloud created **from** SfM) our novel, line-based smoothness term improves the quality of the resulting **3D** model com- pared **to** the approach presented in [ 6 ] (which will be de- noted as mesh-based smoothing method in this section). Fi- nally, we deliver textured output **models**, which can be vari- ably regularized and contain smooth surfaces where meshed **point** **clouds**, in contrast, contain a lot of noise and clutter.

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value is then determined at the location of the aforementioned **point** through spatial and temporal interpolation of the TEC maps [ 27 , 31 , 32 ]. Subsequently, the vertical TEC value at the **point** is projected onto the line of sight of the SAR satellite using a proper mapping function [ 31 ]. The path delay caused by troposphere is computed through the 4D integration of numerical weather data **from** European Centre for Medium-Range Weather Forecasts (ECMWF). The method extracts the dataset **from** a local database, converts it **to** a conventional geographic coordinate system, performs a **3D** interpolation for defined integration points and eventually integrates the refractivity index along the integration path in the slant-range direction **from** the **point** of interest **to** the satellite [ 15 , 26 ]. The geodynamic effects are removed based on the state-of-the-art **models** according **to** the International Earth Rotation and Reference Systems Service (IERS) guidelines [ 33 ]. The effects are reported in the horizontal and the radial coordinate components, which are transformed **to** the radar timing coordinate system [ 9 ]. The coordinate transformation residuals between object and sensor coordinate systems are compensated for by taking into account the plate tectonics effect and referring the observation **to** a reference epoch [ 26 ]. Finally, the geometric calibration constants in range and azimuth are updated based on the most recent studies concerning long-term corner reflector experiments [ 34 ]. For this purpose, all the aforementioned effects are initially mitigated using the described methods and then the median of offsets between the expected position of the corner reflector, surveyed with GNSS, and its corresponding position in a time series of SAR images is considered as new re-calibration constants [ 34 ]. All of the mentioned corrections are computed for a coarse grid and are further interpolated for targets inside the grid [ 35 ]. The corrections are subtracted **from** the annotated SAR measurements **to** achieve absolute t az and τ rg . For more information regarding SAR imaging geodesy and its operational implementation, the reader is referred **to** [ 9 , 26 , 34 , 35 ].

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algorithms, **3D** objects are reconstructed by surface fitting in the segmented **building** regions [10]. Numerous methods are employed for **building** roof segmentation and reconstruction such as unsupervised clustering approaches [11], region growing algorithms [12] and graph based matching techniques [13]. These techniques, however, cannot be directly applied **to** TomoSAR **point** **clouds** due **to** different object contents illuminated by the side looking SAR. In this paper, we propose an approach for **building** façade detection and reconstruction **from** TomoSAR **point** **clouds**. The proposed approach is illustrated and validated by examples using TomoSAR **point** **clouds** generated **from** a stack of 25 TerraSAR-X high spotlight images reported in [6]. Our test **building** is the Bellagio hotel in Las Vegas. Fig. 1 (b) shows the TerraSAR-X mean intensity map of the area of interest while Fig. 1 (a) is the corresponding optical image. Fig. 1 (c) gives an overview of the input TomoSAR **point** **clouds** in UTM coordinates.

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Recent advances in very high resolution synthetic aperture radar (SAR) imagery and its key attributes—self-illumination and all-weather capability—have attracted the attention of many remote sensing analysts in the characterization of urban environments. Various techniques have been developed that make use of SAR imagery for **building** detection and recon- struction. Complex **building** shapes surrounded by roads and other structures make **building** detection a challenging problem. One possible solution is **to** discriminate buildings **from** other objects using the **building** height and width measurements extracted **from** SAR imagery [6]. The key issue is then the **building** height retrieval. For this purpose, various methods have been developed, including using sound electromagnetic **models** [7], layover [8] or shadow analysis [9] and simulation- based methods [10]. In [11], an approach particularly suited for the detection and extraction of large buildings based on information acquired **from** interferometric SAR (InSAR) data is proposed. Stochastic model-based and low level feature-based approaches for extracting and reconstructing buildings **from** a single SAR intensity image are presented in [12] and [13], respectively. Wang et al. [14] presented an approach for build- ing extraction **from** high-resolution single-aspect polarimetric SAR data. Since, in urban areas, the structures are densely packed, the appearance of one particular **building** is dependent on the viewing angle of the sensor. Using a single-view SAR image, it is difficult **to** detect buildings that have no orientation component in the sensor’s azimuth direction [15]. **To** overcome this limit, multiview SAR acquisitions are required. In [16], an approach for estimating **building** dimensions using multi- view SAR images is presented. Bolter and Leberl [17] and Thiele et al. [18] proposed methods for **building** reconstruction based on multiview InSAR data. **Building** reconstruction in context **to** stereoscopic SAR radargrammetric and multiview polarimetric SAR acquisitions has also been used in [19] and [20], respectively.

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Different platforms and sensors are used **to** derive **3d** **models** of urban scenes. **3d** reconstruction **from** satellite and aerial images are used **to** derive sparse **models** mainly showing ground and roof surfaces of entire cities. In contrast **to** such sparse **models**, **3d** reconstructions **from** UAV or ground images are much denser and show **building** facades and street furniture as traffic signs and garbage bins. Furthermore, **point** **clouds** may also get acquired with **LiDAR** sensors. **Point** **clouds** do not only differ in the viewpoints, but also in their scales and **point** densities. Consequently, the fusion of such heterogeneous **point** **clouds** is highly challenging. Regarding urban scenes, another challenge is the occurence of only a few parallel planes where it is difficult **to** find the correct rotation parameters. We discuss the limitations of the general fusion methodology based on an initial alignment step followed by a local coregistration using ICP and present strategies **to** overcome them.

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FIGURE 2. RoIFusion framework. As a whole, the proposed architecture contains three parts: (a) a Fused Keypoints Generation (FKG) layer which uses the raw **point** **clouds** and the images as input and aggregates the keypoints generated **from** both the **point** cloud set abstract (SA) network and the image segmentation network respectively. (b) The keypoints are then used **to** estimate the center points of the potential objects and the **3D** Region of Interests (RoIs), which are projected **to** the image **to** obtain the 2D RoIs. (c) The **3D**/2D RoI pooling layers are employed **to** capture the respective local features, which are finally fused together for **3D** bounding box prediction. (d) The inputs of the SA module are the **3D** points N 1 × 3 and the corresponding features N 1 × F 1 . We simultaneously downsample the points, extract the corresponding deep features in the orange block, and obtain the downsampled **3D** points N 1 × 3 and corresponding features N 2 × F 2 . N 1, F1, N2, F2 are the dimension number of the input points/features, output points/features respectively. (e) Feature Propagation (FP) module: after applying a SA module, the number of the points is downsampled **from** N 1 **to** N 2 . Successively, the FP module takes layer1 with N 1 points and layer2 with N 2 points as input. After that, the number of points N 2 in the layer2 is firstly interpolated **to** N 1 , the output of which is then concatenated **to** layer1 **to** obtain the layer3 with the number of points N 1 .

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errors caused by the incompleteness of data arising, for instance, **from** missed faces due **to** insufficient points, occlusion or vegetation clutter. It is said that having increased the **point** density of modern ALS, the data-driven approach allows **to** have a more accurate and robust result than that through the model-driven approach (Oude Elberink, 2008). A number of methods for doing the reconstruction, based on either model-driven or data-driven approaches using ALS data have been presented in the literature. When reviewing relevant literature, it is observed that the major problem is the efficient manipulation of the topology and roof primitives. **From** recent literature, it is seen that roof topology graphs (RTG) are widely used in both data-driven and model-driven approaches, especially for the efficient manipulation of topology and roof primitives (e.g. Verma et al., 2006; Milde et al., 2008; Oude Elberink and Vosselman, 2009), and in many cases, accurate results have been obtained. However, many unsolved problems need **to** be addressed within the processing chain of **building** reconstruction. This will be discussed in detail under Section 1.2.

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