Statistically Testing Uncertain Geometrie Relations

Förstner, Wolfgang; Brunn, Ansgar; Heuel, Stephan

doi:10.1007/978-3-642-59802-9_3

Cited by 20 publications

(10 citation statements)

References 3 publications

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“…Formulations for constraints as multivariate polynomials can be found in (Brenner, 2005). Constraints and statistical tests for geometric entities in homogeneous representation are provided by (Heuel, 2004, Förstner et al, 2000. In (Pohl et al, 2013), a greedy algorithm is used to select a set of independent and consistent constraints automatically.…”

Section: Related Workmentioning

confidence: 99%

Enhancement of Generic Building Models by Recognition and Enforcement of Geometric Constraints

Meidow

Hammer

Pohl

et al. 2016

ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:Many buildings in 3D city models can be represented by generic models, e.g. boundary representations or polyhedrons, without expressing building-specific knowledge explicitly. Without additional constraints, the bounding faces of these building reconstructions do not feature expected structures such as orthogonality or parallelism. The recognition and enforcement of man-made structures within model instances is one way to enhance 3D city models. Since the reconstructions are derived from uncertain and imprecise data, crisp relations such as orthogonality or parallelism are rarely satisfied exactly. Furthermore, the uncertainty of geometric entities is usually not specified in 3D city models. Therefore, we propose a point sampling which simulates the initial point cloud acquisition by airborne laser scanning and provides estimates for the uncertainties. We present a complete workflow for recognition and enforcement of man-made structures in a given boundary representation. The recognition is performed by hypothesis testing and the enforcement of the detected constraints by a global adjustment of all bounding faces. Since the adjustment changes not only the geometry but also the topology of faces, we obtain improved building models which feature regular structures and a potentially reduced complexity. The feasibility and the usability of the approach are demonstrated with a real data set.

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Section: Related Workmentioning

confidence: 99%

Enhancement of Generic Building Models by Recognition and Enforcement of Geometric Constraints

Meidow

Hammer

Pohl

et al. 2016

ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci.

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“…Therefore, we estimated the 3D points using the iterative linear estimation model Gauss-Helmert with constraints. The details of the Gauss-Helmert model can be found in Förstner (2005) andMcGlone et. al.…”

Section: The Generation Of Uncertain Artificial 3d Point Entitiesmentioning

confidence: 99%

Accurate Matching and Reconstruction of Line Features From Ultra High Resolution Stereo Aerial Images

Wegner

Heipke

et al. 2012

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:In this study, a new reconstruction approach is proposed for the line segments that are nearly-aligned (≤ 10º) with the epipolar line. The method manipulates the redundancy inherent in line pair-relations to generate artificial 3D point entities and utilize those entities during the estimation process to improve the height values of the reconstructed line segments. The best point entities for the reconstruction are selected based on a newly proposed weight function. To test the performance of the proposed approach, we selected three test patches over a built up area of the city of Vaihingen-Germany. Based on the results, the proposed approach produced highly promising reconstruction results for the line segments that are nearly-aligned with the epipolar line.

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“…Thus rigorous uncertainty propagation can be achieved and a statistical test can determine whether the grouping hypothesis is to be rejected or not, based on a user defined significance value. In [4] a compact framework for testing uncertain geometric relations is presented, on which our method is based. If we assume Gaussian noise and if Σ xx and Σ yy the covariance matrices of the direction vectors x and y respectively, the variance of their dot product is given by the expression:…”

Section: Boundary Groupingmentioning

confidence: 99%

Robust Extraction of Vertices in Range Images by Constraining the Hough Transform

Katsoulas

2003

Pattern Recognition and Image Analysis

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Abstract. We describe a technique for extracting vertices from range images of cluttered box-like objects. Edge detection is performed and an edge map is acquired. Extraction of vertices is carried out using the edge map and comprises two steps: Linear boundary detection in 3D and boundary grouping. In order to recover the four parameters of a 3D linear segment, we decompose the problem in two 2D subproblems, each recovering two line parameters. These subproblems are solved by means of the Hough Transform, constrained in this way so that accurate and efficient propagation of the edge points localization error is achieved. Pairs of orthogonal boundaries are grouped to form a vertex. The orthogonality of a boundary pair is determined by a simple statistical test. Our strategy comprises many advantages, the most important of which robustness, computational efficiency and accuracy, the combination of which is not to be found in existing approaches.

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Statistically Testing Uncertain Geometrie Relations

Cited by 20 publications

References 3 publications

Enhancement of Generic Building Models by Recognition and Enforcement of Geometric Constraints

Enhancement of Generic Building Models by Recognition and Enforcement of Geometric Constraints

Accurate Matching and Reconstruction of Line Features From Ultra High Resolution Stereo Aerial Images

Robust Extraction of Vertices in Range Images by Constraining the Hough Transform

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