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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LiDAR **points** of buildings are extracted **from** the scene using previously available 2D **building** bound- ary polygons. Nearby **points** **from** terrain and vegetation are removed using filtering procedures. For roof segmentation, a robust region growing technique is developed. A unique feature of the segmentation method is the growing of triangles of a Triangulated Irregular Network (TIN) instead of LiDAR **points**. This minimizes the gaps between segments, because LiDAR **points** at segment intersections can be assigned multiple segment labels. Additionally, robust adaptive thresholds are introduced as region growing criteria. These enable the region growing procedure to stop at weak edges, while also segmenting non-planar roof segments. Results show that the proposed segmentation outperforms other methods concerning undersegmentation, and that it recognizes even weak edges. Evaluation and an extensive analysis of the input parameters’ effects on the results have shown that the segmentation is very robust against LiDAR point cloud characteristics and segment shape. Segment boundaries are cretated by collapsing the convex hull of segment **points**. Point density variations in across-track and along-track directions are considered in the collapsing procedure. For **building** modeling, the 2.5D dual contouring approach of Zhou and Neumann [2010] is adapted to **model** complex roofs. After overlying a 2D grid to the segmented point cloud, vertices of the 3D **building** **model** are estimated for each grid cell by minimizing a Quadratic Error Function (QEF). Each QEF minimization results in a hyperpoint, which consists of one or more vertices of the **building** **model** at the same x-y-coordinates. This 2.5D-characteristic enables the connection of **building** ver- tices at step edges with vertical walls. In contrast to Zhou and Neumann [2010], the proposed method

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2.3.2.3.4 Edge-Based Technique Edge-detection technique is a technique to detect edge pix- els using Gradient, Laplacian or Canny filtering and then link those pixels to form contours at the end. Linking of edges, in a predefined neighborhood, depends on two criteria. The **first** one is the magnitude of the gradient and the second is the direction of the gradient vector. Since edges are important features in an image to separate regions, a large variety of edge detection algo- rithms have been developed for image segmentation in computer vision area (Shapiro u. Stockman [2001]). (Heath u. a. [1998]) demonstrate a proposed experimental strategy by comparing four well- known edge detectors: Canny, Nalwa–Binford, Sarkar–Boyer, and Sobel. (Jiang u. Bunke [1999]) presented a novel edge detection algorithm for range images based on a scan line approximation technique. LiDAR data are converted into range image, e.g. DSM (Digital Surface **Model**) to make it suitable to image edge-detection methods. The performance of segmentation is largely dependent on the edge detector. However, the operation of converting 3D point **clouds** to 2.5D range images inevitably causes information loss. For airborne LiDAR data, the overlapping surface such as multi- layer **building** roofs, bridges, and tree branches on top of roofs cause buildings and bridges either under segmented or wrongly classified. The point **clouds** obtained by terrestrial LiDAR are usually combined **from** the scans in several different positions, converting such kind of true 3D data into 2.5D would cause great loss of information (Wang u. Shan [2009]).

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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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A novel method for creating detailed **building** models with com- plex roof shapes **from** LiDAR point **clouds** is proposed in this paper. The 2.5D Dual Contouring method of Zhou and Neumann (2010) is used and adapted in a way that step edges and inter- section edges can be created between roof segments. A main contribution of this work is the modification and weighting of the Quadratic Error Function (QEF) for modeling step edges and intersection edges. The modeling depends on the step edge prob- abilities of local height layers. A prerequisite for adaptive 2.5D Dual Contouring is a roof segmentation technique which stops at smooth edges. The applied robust TIN-based region growing reli- ably stops at smooth edges. Consequently, undersegmentation is significantly reduced. The resulting **building** models show a very high fit to the input LiDAR **points**. Each roof segment is repre- sented by a triangulation, thus also non-planar roof shapes can be modelled. Subsequent **model** regularization is recommended, because buildings are represented by a large number of vertices. Errors in **reconstruction** result mostly **from** wrong or missing con- nections of the vertices. Thus, the way the connections of the ver- tices to the **building** **model** should be more robust. Wrong con- nections could be avoided by checking for the consistency of the **model** with the **building** footprint. Under assumption that build- ing edges are mostly orthogonal or parallel to the main build-

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In this paper, we propose an approach for façade detection and **reconstruction** **from** such point **clouds**. Firstly, the façade region is extracted by thresholding the point density on the ground plane. The extracted façades **points** are then clustered into segments corresponding to individual façades by means of slope analysis. Surface (flat or curved) **model** parameters of the segmented **building** façades are further estimated. Finally, the elevation estimates of each raw **TomoSAR** point is refined by using its more accurate azimuth and range coordinates, and the corresponding reconstructed surface **model** of the façade. The proposed approach is illustrated and validated by examples using **TomoSAR** point **clouds** generated **from** a stack of 25 TerraSAR-X high spotlight images

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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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There are different challenges relevant to 3D **building** **model** generation as well as an accuracy evaluation of the produced **model** which should be discussed. Firstly, the heights located in an outline of a **building** should be consistent. Some incon- sistencies come **from** noise produced during the SAR-optical dense matching process. Moreover, regarding shapes of roofs particularly inclined types, the location of **points** differs **from** the topmost toward the lowest part. Then, making a decision, which cluster of **points** are suitable for 3D **reconstruction** in the LOD 1 level is a challenge. In this research, we simply used median as a robust estimator against the large heights changes of reconstructed **points** located in a footprint of **building**.

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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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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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Presegmentation typically classifies the point cloud into **building** **points** and other **points**, mainly terrain and vegetation in LiDAR point **clouds**. If 2D **building** footprints are avail- able beforehand, **building** point **clouds** can be directly extracted [Rau and Lin, 2011]. A popular way is ground filtering method, in which a Digital Terrain **Model** (DTM) is pro- duced by morphological filter operations [Morgan and Tempfli, 2000] [Zhang et al., 2003] [Pingel et al., 2013], then a height threshold is set on the DTM. Another approach is to fit planes to **points** **clouds**, and clustering **points**. The largest cluster is assumed to be ground [Verma et al., 2006]. [Lafarge and Mallet, 2012] defineed expectation values for buildings, vegetation, ground and clutter by combining different covariance-based measures and height information by energy optimization. [Dorninger and Pfeifer, 2008] extracted all planar regions of the scene using region growing method in feature space and group the extracted **points** to buildings with a mean-shift algorithm.

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world coordinates enable the generation of high quality **TomoSAR** point **clouds**, containing not only the 3D positions of the scatterer location but also estimates of seasonal/temporal deformation, that are very attractive for generating 4-D city models **from** space. However there are some special considerations associated to these point **clouds** that are worth to mention [1]: 1) **TomoSAR** point **clouds** deliver moderate 3D positioning accuracy on the order of 1 m; 2) few number of images and limited orbit spread render the location error of **TomoSAR** **points** highly anisotropic, with an elevation error typically one or two orders of magnitude higher than in range and azimuth [2]; 3) Due to the coherent imaging nature, temporally incoherent objects such as trees cannot be reconstructed **from** multipass spaceborne SAR image stacks; and 4) **TomoSAR** point **clouds** possess much higher density of **points** on the **building** façades due to side looking SAR geometry enabling systematic **reconstruction** of buildings footprint via façade **points** analysis. As depicted over smaller and larger areas in [1] and [3], façade **reconstruction** turns out to be an appropriate **first** step to detect and reconstruct **building** shape **from** these point **clouds** when dense **points** on the façade are available. Especially, when data **from** multiple views e.g., **from** both ascending and descending orbits, are available, the

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In this paper we propose a method which aims at simplifying the 3D **reconstruction** of the **building** blocks by decomposing the overall **model** into several smaller ones corresponding to each **building** part. A similar method has been already reported by the author (Arefi, 2009) for **reconstruction** of high resolution LI- DAR data. In this paper due to a lower quality of the DEM pro- duced by stereo matching of satellite data (Worldview–2) com- paring to the LIDAR data, an additional data source is employed. Accordingly, the Worldview orthorectified image is employed for a better extraction of the ridge lines. According to each ridge line a projection-based algorithm is employed to transfer the 3D **points** into 2D space by projecting the corresponding pixels of each **building** part onto a 2D plane that is defined based on the orientation of the ridge line. According to the type of the roof, a predefined 2D **model** is fitted to the data and in the next step, the 2D **model** in extended to 3D by analyzing the third dimen- sion of the **points**. A final **model** regarding the parametric roof structures of the **building** block is defined by merging all the indi- vidual models and employing some post processing refinements regarding the coinciding nodes and corners to shape the appro- priate **model**. Additionally **prismatic** models with flat roof are provided regarding to the remaining areas that are not contain- ing ridge lines. Finally, all parametric and **prismatic** models are merged to form a final 3D **model** of the **building**.

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Roof **model** selection is the process of fitting models into point **clouds** and selecting the most appropriate **model** **from** a library which minimize a cost function. Mass and Vosselman [ 46 ] proposed a new method for gable roof **reconstruction** by computing their parameters using the analysis of invariant moments of the 3-D point **clouds** of LiDAR data. The information on the roof type and shape parameters is computed by using the heights of the point **clouds** as weight functions in moment equations. Haala et al. [ 47 ] estimated roof plane parameters by segmenting the DSM of aerial images and by analyzing the surface normals and ground plane orientations of the segments. A similar approach was presented in Kada and McKinley [ 40 ] using LiDAR **points** of each cell. They determined the roof types according to the number of segments. Zheng et al. [ 23 ] also used a similar approach for roof type identification, in which the root mean square error (RMSE) between the DSM and corresponding **points** **from** the candidate roof **model** determines the quality of **reconstruction**. Poullis and You [ 48 ] computed the roof **model** parameters using a nonlinear bound-constraint minimization. During this optimization, a Gaussian mixture **model** (GMM) was used to detect and exclude outliers **from** the fitting plane, where the parameters of GMM were estimated using an expectation-maximization (EM) algorithm. Lafarge et al. [ 2 ] proposed a stochastic method for reconstructing 3-D **building** models **from** the DSM of satellite imagery (PLEIADES satellite data simulations with resolutions of 0.7 m). They used a Bayesian algorithm based on RJMCMC to decide the **building** **model** which best fitted the DSM data. Huang et al. [ 49 ] utilized generative statistical models to reconstruct 3-D **building** models **from** LiDAR data. The method finds the optimal combination of parameters by a stochastic search. Henn et al. [ 41 ] proposed a strategy for 3-D **building** **reconstruction** **from** a small number of LiDAR data **points**. This method estimates roof parameters by fitting the roof models and by estimating their parameters by M-estimator sample consensus (MSAC). It determines the most probable roof **model** by a support vector machines (SVM). Zheng and Weng [ 42 ] proposed a method based on LiDAR data and **building** footprints. They computed some morphological and physical parameters **from** a decomposed footprint. They then applied a decision tree-based classifier to these statistical features to classify the **building** footprints into seven roof types. According to the roof type, they calculated the roof **model** parameters based on the statistical moments of the **points** within the cells.

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L-shape is the most common **building** outline appearing in **TomoSAR** point **clouds**. For each **building** segment, one or zero L-shape is detected. The detection is achieved by catching two interconnected line segment using gray-scale Hough transform [7]. Each pixel in the Hough transform matrix represents a line. In our algorithm, the pixel with the highest amplitude is firstly extracted, representing the **first** line of the L-shape. The second one is the pixel with highest amplitude away **from** the **first** one larger than a certain angle. To reject irregular L-shapes, constraints have to be put on this angle, the minimum pixel amplitude, and the minimum length of the line segments. For example, Figure 5 is the L-shape detection result of the test area near the Berlin central station. The detected L- shapes are overlaid on the binary façade image. The end **points** of L-shapes are marked with red and yellow dots.

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Suveg and Vosselman (2004) developed a method for 3D **reconstruction** of buildings by integrating 3D information **from** stereo images and a large scale GIS map. **First** a **building** on ground plan is subdivided into primitives. Optimum schemes of partitioning are determined by minimum description length criteria and a search tree. Then the **building** primitives are verified by a least square fitting algorithm. The approximated values of the fitting method are obtained **from** map and 3D information **from** the stereo images. Kada and McKinley (2009) proposed a method for decomposition of the footprint by cell decomposition. In this method, the buildings are partitioned into non-intersecting cells along its façade polygons using vertical planes. The roof shapes are determined by directions generated **from** LiDAR **points**. Then models of buildings blocks are reconstructed using a library of parameterized standard shapes of **model**. Arefi and Reinartz (2013) proposed a **model**-driven approach based on the analysis of the 3D **points** of DSM **from** satellite images in a 2D projection plane. In this method parametric models are generated through single ridgeline **reconstruction** and subsequent merging of all ridgelines for a **building**. The edge information is extracted **from** the orthorectified image.

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Automatic generation of 3D **building** models is an essential pre- requisite in a wide variety of applications such as tourism, urban planning and automatic navigation. Although over the last decades, many approaches of **building** detection and **reconstruction** **from** 3D point **clouds** and high resolution aerial images have been reported. The fully 3D **building** **reconstruction** is still a challenging issue due to the complexity of urban scenes. There are basically two strategies for **building** roof **reconstruction**: bottom-up/data-driven and top- down/**model**-driven methods. The bottom-up methods (e.g. region growing (Rottensteiner and Briese, 2003), Hough transform (Vosselman and Dijkman, 2001), RANSAC (Tarsha- Kurdi et al., 2008)) extract roof planes and other geometrical information **from** the point **clouds**. For roof **reconstruction**, the corresponding planes are assembled and vertices, ridges and eaves are determined (Sohn and Huang, 2008). Sampath and Shan (2010) used a bottom-up approach to segment the LiDAR **points** to planar and non-planar planes using eigenvalues of the covariance matrix in a small neighborhood. Then, the normal vectors of planar **points** are clustered by fuzzy k-means clustering. Afterwards, an adjacency matrix is considered to obtain the breaklines and roof vertices of corresponding planes. This method is used for **reconstruction** of moderately complex buildings. Rottensteiner et al. (2005), presents an algorithm to delineate **building** roof boundaries **from** LIDAR data with high level of detail. In this method, roof planes are initially extracted

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In order to validate our approach, we run the algorithm over **TomoSAR** point **clouds** generated **from** TerraSAR-X high spotlight images. Fig. 1(b) shows the result of applying SD estimation procedure. The two parameters r (radius of the neighborhood cylinder) and d are empirically set to 5m and 2m respectively according to the point density of the data set. One can observe that TH value influences the number of extracted façade **points**. Lower TH value results in higher completeness but lower correctness. To extract lower façades and to automate the procedure, the threshold TH is set to the maximum of SD histogram value. This includes not only the façade **points** but additionally also some nonfaçade **points** with relative high SD, e.g., roof **points**. To reject these **points** **from** the set of extracted **points** after SD thresholding, surface normals information is utilized. Fig. 1(c) shows the extracted façade **points** by retaining only those **points** having normals between ±15 degrees **from** the horizontal axis.

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With improved sensor resolution and advanced multi-pass interferometric techniques such as SAR tomographic inversion (**TomoSAR**), it is now possible to reconstruct both shape and motion of urban infrastructures. These sophisticated techniques not only opens up new possibilities to monitor and visualize the dynamics of urban infrastructure in very high level of details but also allows us to take a step further towards generation of 4D (space-time) or even higher dimensional dynamic city models that can potentially incorporate temporal (motion) behaviour along with the 3D information. Motivated by these chances, this paper presents a post processing approach that systematically allows automatic **reconstruction** of **building** façades **from** 4D point cloud generated **from** tomographic SAR processing and put the particular focus on robust **reconstruction** of large areas. The approach is modular and consists of extracting facade **points** via point density estimation procedure based on directional window approach. Segmentation of facades into individual segments is then carried out using an unsupervised clustering procedure combining both the density-based clustering and the mean-shift algorithm. Subsequently, **points** of individual facade segments are identified as belonging to flat or curved surface and general 1st and 2nd order polynomials are used to **model** the facade geometry. Finally, intersection **points** of the adjacent façades describing the vertex **points** are determined to complete the **reconstruction** process. The proposed approach is illustrated and validated by examples using **TomoSAR** point **clouds** over the city of Las Vegas generated **from** a stack of TerraSAR- X high resolution spotlight images.

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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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