The segmentation is supported by in

The segmentation is supported by introducing ground plan information. Of course the given ground plan restricts the extension of the DSM area which has to be examined.More important, the implemented segmentationwithin each ground plan area can be based on the direction of the surface normals of the DSM, since possible orientations of planar surfaces to be extracted are predefined by the outline of the building. This is motivated by the observation that the direction of the unit normal vector of a possible roof plane emerging from an element of the ground plan has to be perpendicular to this segment. Hence, the different segments of the ground plan polygon are used to trigger the segmentation of a planar surface with a projected normal vector perpendicular to this element. For reasons of simplicity this step is discussed using a building, which can be represented by a single CSG primitive.
In figure 6 a ground plan provided by the digital cadastral map is projected to the corresponding section of the ortho image. The corresponding DSM is shown in figure 7. The implemented segmentation is based on the direction of the surface normals of the DSM, which are represented by the small white lines in figure 6. Since direct numerical differentiation tends to amplify noise and obscure signal content,a local least squares fit is computed within a small window around each element of the DSM. The derivatives of thecontinuous function then can be determined analytically at the corresponding discrete DSM points in order to calculate the surface normals.
The distribution of the surface normal directions corresponds to the four major axes of the ground plan. Even though these directions can also be calculated by analyzing the histogram of the surface normal directions, they are obtained by parsing the given ground plan, which is much more reliable. All points with a surface normal corresponding to the examined ground plan direction are combined to a region. This results in the segmentation represented by the shaded regions in figure 6. The result of the segmentation process can be used to define so-called compatibility regions for the estimation of each roof, i.e. only DSM segments with a direction of the normal vector compatible to the ground plan segment are utilized while estimating the parameters of the corresponding roof plane. The segmentation of figure 6 triggers the reconstruction of a building with hip roof, since this model (roof consisting of 4 faces) is the only one which fits to the result of the segmentation process.
For the more complex building shown in figure 5 the segmentation is presented in figure 8. Figure 9 shows the building primitives which are reconstructed based on the ground plan decomposition and the segmentation discussed above. Figure 10 gives the result of the automatic 3D building reconstruction for the complete test area. For visualization the reconstructed buildings were put on the map of scale 1:5000, which was used to digitize the ground plans.

3.4 Interactive refinement of initial reconstructions
In our approach the reconstruction is constrained by the assumption that
all walls defined by the ground polygon lead to a planarroof face of variable slope and
all eaves lines have the same height.
These assumptions are fairly general. However, one must keep in mind that any roof construction based on this approach provides incorrect results if the roof structure inside the ground polygon does not follow the cues that can be obtained from the ground polygon. This can e.g. happen if more than one plane emerges from a single polygon element or if parts of the building which are contained in a roof surface like a bay are not represented by the ground plan.
Figure 11 shows the reconstructed building with the original DSM surface overlaid. The difference between the DSM surface and the corresponding points at the roof planes provide a reliable test on the quality of a reconstruction. For this reason RMS values are calculated for each building and its sub-parts. Remaining regions, which are incompatible with the final reconstruction give an additional hint, if manual interaction is required for further refinement. Since these regions are determined by the previous segmentation, they can be visualized together with the calculated
RMS values in a final operator based evaluation step.
Up to now all buildings were reconstructed fully automati-cally. The ground plans used so far were digitized merely from the map. No care has been taken to digitize the ground plans with respect to the reconstruction algorithm.Even though the reconstruction is sufficient for many levels of detail, due to the problems of the algorithm mentionedabove a further improvement of the reconstruction can be necessary for very complex buildings. This can be obtained if the initial reconstruction is analyzed in order to refine the capture of ground plans. Figure 8 shows the original ground plan and the segmentation of the DSM into planar regions.For this example the two segmented regions contained in the black rectangle are incompatible to their surrounding roof plane and therefore are not used to reconstruct the parameters of the corresponding building primitive. Based on this information the black polygon was generated inter-
actively by an operator. This rectangle then automatically triggers the reconstruction of an additional building primitive, which represents the bay of the roof. The result of the final reconstruction is shown in figure 12. For this visualization the CSG representation was transformed to a boundary representation of the building. This step is required for all buildings if wire frames have to be presented adequately. Therefore the union of the set of CSG primitives has to be computed. Within this process the primitives are intersected, coplanar and touching faces are merged and inner faces or parts are removed.
The size of object parts which can be reconstructed is of course limited by the available density of DSM points,i.e. details smaller than approximately 1 m can not be captured. For virtual reality applications this problem can be avoided by texture mapping of real imagery as a substitute for geometric modeling, since the use of photo realistic texture enhances the perceived detail even in the absence of a detailed geometric model.


4 GENERATION OF VIRTUAL REALITY MODELS
The creation of a 3D city model for virtual reality applications usually consists of a geometric building reconstruction followed by texture mapping to obtain a photo realistic model representation. In principle, terrestrial imagery is sufficient to provide the required information for both tasks.Nevertheless, especially the terrestrial acquisition of the building geometry by architectural photogrammetry proves to be a time-consuming process that has to be carried out interactively for each building. The basic idea of our approach is to speed up the time consuming process of virtual city model creation by using DSM and ground plans for geometric processing and terrestrial images only for texture mapping. Since the vertices of the 3D building models which are generated from ground plans and laser data provide sufficient control point information, the texture mapping from the terrestrial images is simplified considerably.Therefore the generation of virtual reality models is more efficient compared to standard architectural photogrammetry, where a number of tie points has to be measured inmultiple images.
The goal of texture processing is to provide a rectified image for each visible building face. Hence for each image the corresponding facade polygon has to be selected from the 3D city model generated in the previous processing step.For this purpose the wire frame of the reconstructed buildings as well as the indices of the faces are projected to the aerial image (see figure 13). If the viewpoints were sketched into a map or an ortho image during the terrestrial image acquisition, this representation allows a simple interactive definition of the corresponding face index for each
terrestrial image.
For texture mapping the image has to be correctly positioned, oriented and scaled to represent its associated sur face. In our approach an image section representing a planar surface is rectified by applying a projective transformation. The 7 parameters of the projective transformation are determined by a minimum number of 4 points in 3D world coordinates on a plane (in 3D space) and their corresponding image coordinates. Of course, this approach can only be used with sufficiently planar structures. After the selection of the corresponding 3D building face based on the visualization presented in figure 13, at least four tie points between the face polygon and the terrestrial image have to be determined. For this purpose the nodes of the face polygon have to be identified and measured in the terrestrial image.Since the points have to be positioned very precisely, the displayed texture can be scaled to any desired resolution.
Figure 14 shows an example for terrestrial imagery which was taken for texture mapping. The images were acquired with a Kodak DCS 120 digital camera. The points measured for the rectification are marked by white dots. If a node of the face is hidden by an obstacle, the corner point can be alternatively calculated from points measured at the edges of the facade. The rectified image sections then can be assigned to their corresponding faces in the 3D model.
In order to control the correct assignment of the texture, the 3D buildings are displayed in a viewer which allows all basic transformations to the model (translation, rotation, scaling) immediately after the texture mapping (see figure 15).
For the final visualizations (see figures 16 and 17) the ortho image as well as artificial trees are added to the virtual model.

5 CONCLUSION

Recent advances in three-dimensional displays, real-time texturing and computer graphics h

結果 (中文) 1:

分割被支持通过引入地面计划信息。当然给定的地面计划限制扩建电力需求侧管理范围，也要进行研究。更重要的是建筑物的，每个地面规划面积可以基于 DSM 的表面法线以来可能的平面要提取方向的方向实现的 segmentationwithin 是建筑物的 predefined 的轮廓。这被出于摆脱地面计划元素可能屋顶平面的单位法向量的方向必须垂直于此段的观察。因此，不同阶层的平面图多边形用于触发与预计的法向量垂直于此元素的平面曲面分割。为方便起见，这一步讨论使用的建筑，这可以由一个单一的南玻基元表示。在理解 6 提供的数字地籍图地面计划预计正射影像图的相应章节。相应的 DSM 理解 7 所示。实施的分割基于电力需求侧管理，它由中割裂那 6 个人的小的白线表面的法线方向。由于直接数值微分往往放大噪声和模糊信号内容，局部最小二乘通常被计算在周围的电力需求侧管理的每个元素的一个小窗口内。然后兴国函数的导数可以解析确定相应的离散 DSM 点计算表面法线。表面的法线方向的分布对应于地面上的计划的四个主要轴线。即使这些方向也可以通过分析表面的法线方向的直方图计算，他们得到了解析给定的地面上的计划，这是更为可靠。与表面正常对应检查的地面计划方向的所有点都结合到一个区域。这个结果在由中割裂那 6 个人的阴影区域的分割。分割过程的结果可以习惯移位所谓兼容性区域，估计每个屋顶的即只有 DSM 段地面计划部分相容的法向量的方向利用时相应的屋顶平面的参数估计。分割的理解 6 触发髋屋顶建筑的重建因为这个模型 (屋顶组成的 4 面) 是唯一一个哪到分割过程的结果相符。为理解 5 中显示的更复杂建筑物割裂那 8 个人提出了分割。图 9 显示了建筑基元改建基于地面计划分解和上面讨论的分割。图 10 给出了结果的自动三维建筑重建完整的测试区域。为可视化重建的建筑物被装上地图的比例为 1: 5000，用于数字化地面计划。3.4 互动 refinement 的初步重建在我们的方法重建受到假设，所有墙壁愈合所导致的可变斜率的 planarroof 脸的地面多边形和屋檐下的所有行都具有相同的高度。这些假设都相当一般。然而，一个人必须牢记，基于这种方法任何屋顶建设提供不正确的结果，如果地面多边形内的屋顶结构不遵循从地面多边形可以获得的线索。如果多个平面出现从单一的多边形元素或建筑物的部分所载像一个海湾的屋顶表面不由地面上的计划，这可能是例如可以这样做的。图 11 显示经改造后大楼与原始的 DSM 表面涂覆一层。DSM 表面和在屋顶平面的对应点之间的区别的重建质量提供了可靠的测试。为此 RMS 值计算每个建筑和其分部位。其余的地区，都不符合单项重建给额外的提示，如果人工交互需要进一步 refinement。因为这些地区由以前的分割，它们可以被可视化一起与计算在单项运算符有效值根据评估步骤。到目前为止所有建筑物都重建完全满意。到目前为止使用地面计划被数字化只是从地图。不小心数字化地面计划与尊重的重建算法。即使重建是 sufficient 很多级别的明细数据，由于算法的问题 mentionedabove 重建进一步改进可能需要非常复杂的建筑。由此可以得出，如果我们为了 refine 的地面计划捕获分析初步重建。图 8 显示了原始地面计划和 DSM 分割成平面区域。对于这个示例的黑色的矩形包含这两个分段的区域不兼容于他们周围的屋顶平面和因此不被用来重建的相应建设原始参数。基于此信息生成黑色多边形除-积极的运算符。然后，此矩形自动触发重建原始，进一步建设占屋顶的海湾。单项重建的结果如割裂那个人 12 所示。这个可视化 CSG 表示形式转换为建筑边界表示。如果线框有充分提出，此步骤是必需的所有建筑物。因此南玻基元集的联盟已将被计算。在此过程中基元相交，共面和感人的面孔将合并和删除内曲面或零件。对象部件，可以被重建的大小，当然受到可用密度的电力需求侧管理方面进行辨析细节小于不能捕获约 1 米。对于虚拟现实应用程序可以通过纹理映射的真实意象作为几何建模的代替品避免这个问题，自从使用照片真实感纹理增强了感知的细节，即使在没有一个详细的几何模型。4 代的虚拟现实模型The creation of a 3D city model for virtual reality applications usually consists of a geometric building reconstruction followed by texture mapping to obtain a photo realistic model representation. In principle, terrestrial imagery is sufficient to provide the required information for both tasks.Nevertheless, especially the terrestrial acquisition of the building geometry by architectural photogrammetry proves to be a time-consuming process that has to be carried out interactively for each building. The basic idea of our approach is to speed up the time consuming process of virtual city model creation by using DSM and ground plans for geometric processing and terrestrial images only for texture mapping. Since the vertices of the 3D building models which are generated from ground plans and laser data provide sufficient control point information, the texture mapping from the terrestrial images is simplified considerably.Therefore the generation of virtual reality models is more efficient compared to standard architectural photogrammetry, where a number of tie points has to be measured inmultiple images.The goal of texture processing is to provide a rectified image for each visible building face. Hence for each image the corresponding facade polygon has to be selected from the 3D city model generated in the previous processing step.For this purpose the wire frame of the reconstructed buildings as well as the indices of the faces are projected to the aerial image (see figure 13). If the viewpoints were sketched into a map or an ortho image during the terrestrial image acquisition, this representation allows a simple interactive definition of the corresponding face index for eachterrestrial image.For texture mapping the image has to be correctly positioned, oriented and scaled to represent its associated sur face. In our approach an image section representing a planar surface is rectified by applying a projective transformation. The 7 parameters of the projective transformation are determined by a minimum number of 4 points in 3D world coordinates on a plane (in 3D space) and their corresponding image coordinates. Of course, this approach can only be used with sufficiently planar structures. After the selection of the corresponding 3D building face based on the visualization presented in figure 13, at least four tie points between the face polygon and the terrestrial image have to be determined. For this purpose the nodes of the face polygon have to be identified and measured in the terrestrial image.Since the points have to be positioned very precisely, the displayed texture can be scaled to any desired resolution.Figure 14 shows an example for terrestrial imagery which was taken for texture mapping. The images were acquired with a Kodak DCS 120 digital camera. The points measured for the rectification are marked by white dots. If a node of the face is hidden by an obstacle, the corner point can be alternatively calculated from points measured at the edges of the facade. The rectified image sections then can be assigned to their corresponding faces in the 3D model.In order to control the correct assignment of the texture, the 3D buildings are displayed in a viewer which allows all basic transformations to the model (translation, rotation, scaling) immediately after the texture mapping (see figure 15).For the final visualizations (see figures 16 and 17) the ortho image as well as artificial trees are added to the virtual model.5 CONCLUSIONRecent advances in three-dimensional displays, real-time texturing and computer graphics h

結果 (中文) 3:

分割的支持，通过引入地面计划信息。当然，鉴于土地规划制约要检查的DSM地区延伸。更重要的是，实现segmentationwithin每个土地规划面积可以基于DSM的表面的法线方向，由于平面可能的方向的表面被提取预定fi内德的建筑物的轮廓。这是出于观察，一个可能的屋顶平面的一个可能的屋顶平面的方向，从一个元素的地面计划的单位的方向垂直于这段。因此，地面计划的多边形的不同的段被用来触发一个平面的表面与投影的垂直于该元素的法线向量。为了简单起见，这一步是用建筑的讨论，这可以由一个单一的原始
CSG表示。在fi图6由数字地籍图提供地面计划预计的正射影像对应的部分。DSM是fi如图7所示。实现的分割是基于DSM的表面法线的方向，这是由fi图6小白色线表示。因为直接数值分化倾向于放大噪声和模糊的信号内容，局部最小二乘fi不计算在DSM的每个元素的小窗口内。连续函数的导数就可以分析确定在相应的离散DSM分为了计算表面法线。
的表面法线方向的分布对应于地面计划的四个主要轴线。即使这些方向也可以计算通过分析的直方图的表面法线方向，他们是通过解析给定的地面计划，这是更可靠。所有点的表面法线对应的检查地面计划方向相结合的区域。这样的结果如图6所示的fi阴影区表示的分割。分割过程的结果可以用来去fiNE所谓兼容性地区每个屋顶的估计，即只有用与地面规划段的法线矢量方向的法线方向的侧边段被利用，同时估计相应的屋顶平面的参数。如图6所示的fi分割触发与髋屋顶建筑物的重建，因为这个模型（屋顶由4面）是唯一一个fiTS的分割过程的结果。
图5中显示fi的分割是fi图8给出了更复杂的建筑。图9显示了基于地面计划分解和上面讨论的分割的建筑基元。图10给出了完整的试验区的自动三维重建的结果。