Abstract
Observations of man-made structures in terms of digital images, laser scans or sketches are inherently uncertain due to the acquisition process. Thus reverse engineering has to be applied to obtain topologically consistent and geometrically correct model instances by feature aggregation. The corresponding spatial reasoning process usually implies the detection of adjacencies, the generation and testing of hypotheses, and finally the enforcement of the detected relations. We present a complete and general work-flow for geometric reasoning that takes the uncertainty of the observations and of the derived low-level features into account. Thereby we exploit algebraic projective geometry to ease the formulation of geometric constraints. As this comes at the expense of an over-parametrization, we introduce an adjustment model which stringently incorporates uncertainty and copes with singular covariance matrices. The size of the resulting normal equation system depends only on the number of established constraints which paves the way to efficient solutions. We demonstrate the usefulness and the feasibility of the approach with results for the automatic analysis of a sketch and for a building reconstruction based on an airborne laser scan.
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References
Benkő, P., Kós, G., Várady, T., Andor, L., Martin, R.: Constrained fitting in reverse engineering. Comput. Aided Geom. Des. 19(3), 173–205 (2002)
Bron, C., Kerbosch, J.: Algorithm 457: finding all cliques of an undirected graph. Commun. ACM 16(9), 575–577 (1973)
Cazals, F., Karande, C.: A note on the problem of reporting maximal cliques. Theor. Comput. Sci. 407(1–3), 564–568 (2008)
Förstner, W.: Mid-level vision processes for automatic building extraction. In: Gruen, A., Kuebler, O., Agouris, P. (eds.) Automatic Extraction of Man-Made Objects from Aerial and Space Images. Monte Verita, pp. 179–188. Birkhäuser, Basel (1995)
Förstner, W., Brunn, A., Heuel, S.: Statistically testing uncertain geometric relations. In: Sommer, G., Krüger, N., Perwass, C. (eds.) Mustererkennung 2000. Informatik aktuell, pp. 17–26. Springer, Heidelberg (2000)
Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2000)
Hebel, M., Arens, M., Stilla, U.: Change detection in urban areas by direct comparison of multi-view and multi-temporal ALS data. In: Stilla, U., Rottensteiner, F., Mayer, H., Jutzi, B., Butenuth, M. (eds.) PIA 2011. LNCS, vol. 6952, pp. 185–196. Springer, Heidelberg (2011)
Heuel, S.: Uncertain Projective Geometry. LNCS, vol. 3008. Springer, Heidelberg (2004)
Hoffmann, C.M., Joan-Arinyo, R.: A brief on constraint solving. Comput. Aided Des. Appl. 2(5), 655–663 (2005)
Kanatani, K.: Statistical analysis of geometric computation. CVGIP: Image Underst. 59(3), 286–306 (1994)
Kanatani, K.: Statistical Optimization for Geometric Computation: Theory and Practice, 2nd edn. Artificial Intelligence Laboratory, Department of Computer Science, Gumma University, Japan (1995)
Koch, K.R.: Parameter Estimation and Hypothesis Testing in Linear Models, 2nd edn. Springer, Berlin (1999)
Loch-Dehbi, S., Plümer, L.: Automatic reasoning for geometric constraints in 3D city models with uncertain observations. ISPRS J. Photogrammetry Remote Sens. 66, 177–187 (2011)
Mäntylä, M.: An Introduction to Solid Modeling. Computer Science Press, Inc., New York (1987)
McGlone, J.C., Mikhail, E.M., Bethel, J. (eds.): Manual of Photogrammetry, 5th edn. American Society of Photogrammetry and Remote Sensing, Bethesda (2004)
Meidow, J., Beder, C., Förstner, W.: Reasoning with uncertain points, straight lines, and straight line segments in 2D. ISPRS J. Photogrammetry Remote Sens. 64(2), 125–139 (2009)
Meidow, J., Förstner, W., Beder, C.: Optimal parameter estimation with homogeneous entities and arbitrary constraints. In: Denzler, J., Notni, G., Süße, H. (eds.) Pattern Recognition. LNCS, vol. 5748, pp. 292–301. Springer, Heidelberg (2009)
Pohl, M., Meidow, J., Bulatov, D.: Extraction and refinement of building faces in 3D point clouds. In: Image and Signal Processing for Remote Sensing XIX, p. 88920V. Society of Photo-Optical Instrumentation Engineers (2013)
Rabbani, T., van den Heuvel, F.A., Vosselmann, G.: Segmentation of point clouds using smoothness constraint. In: Proceedings of the ISPRS Commission V Symposium ‘Image Engineering and Vision Metrology’. ISPRS Archives, vol. XXXVI, Part 5, pp. 248–253 (2006)
Rusu, R.B., Cousins, S.: 3D is here: Point Cloud Library (PCL). In: IEEE International Conference on Robotics and Automation (ICRA), p. 14 (2011)
Triggs, B., McLauchlan, P.F., Hartley, R.I., Fitzgibbon, A.W.: Bundle adjustment – a modern synthesis. In: Triggs, B., Zisserman, A., Szeliski, R. (eds.) Vision Algorithms 1999. LNCS, vol. 1883, pp. 298–372. Springer, Heidelberg (2000)
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Meidow, J. (2014). Geometric Reasoning for Uncertain Observations of Man-Made Structures. In: Jiang, X., Hornegger, J., Koch, R. (eds) Pattern Recognition. GCPR 2014. Lecture Notes in Computer Science(), vol 8753. Springer, Cham. https://doi.org/10.1007/978-3-319-11752-2_46
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DOI: https://doi.org/10.1007/978-3-319-11752-2_46
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