Abstract
The problem of estimating a shape in a 3D point cloud data is important due to its general applicability in image analysis, computer vision, and graphics. It is challenging because the data is typically noisy, cluttered, partly missing and unordered. We address shape estimation using a template object under a fully statistical model, where the data is assumed to be modeled using a Poisson process on the object’s boundary (surfaces), corrupted by additive noise and a clutter process. Using analytical likelihood function dictated by the model, we optimize over pose and scale associated with hypothesized templates and estimate most likely shapes in observed point clouds under given shape hypotheses. We demonstrate this framework using examples of 2D and 3D shape estimation in simulated and real data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C.T.: Point set surfaces. In: Proc. Visualization 2001, pp. 21–28 (2001)
Besl, P., McKay, H.: A method for registration of 3-D shapes. IEEE Trans. on Pattern Analysis and Machine Intelligence 14(2), 239–256 (1992)
Blanz, V., Mehl, A., Vetter, T., Seidel, H.: A statistical method for robust 3D surface reconstruction from sparse data. In: Proc. the 2nd International Symposium on 3D Data Processing, Visualization, and Transmission, pp. 293–300 (2004)
Chui, H., Rangarajan, A.: A new point matching algorithm for non-rigid registration. Computer Vision and Image Understanding 89(2-3), 114 – 141 (2003)
Cohen-Seiner, D., Alliez, P., Desbrun, M.: Variational shape approximation. ACM Trans. on Graphics 23, 905–914 (2004)
Dey, T.K., Goswami, S.: Provable surface reconstruction from noisy samples. Journal of Computational Geometry: Theory and Applications 35, 124–141 (2006)
Dryden, I.L., Hirst, J.D., Melville, J.L.: Statistical analysis of unlabeled point sets: Comparing molecules in chemoinformatics. Biometrics 63(1), 237–251 (2007)
Halma, A., ter Haar, F., Bovenkamp, E., Eendebak, P., van Eekeren, A.: Single spin image-ICP matching for efficient 3D object recognition. In: Proc. ACM workshop on 3D object retrieval, pp. 21–26 (2010)
Hoppe, H., DeRose, T., Duchamp, T., Mcdonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: Proc. ACM SIGGRAPH, pp. 71–78 (1992)
Kent, J., Mardia, K., Taylor, C.: Matching problems for unlabeled configurations. In: Aykroyd, R.G., Barber, S., Mardia, K.V. (eds.) LASR 2004 Proc. Bioinformatics, Images, and Wavelets, pp. 33–40 (2004)
Kolluri, R., Shewchuk, J.R., O’Brien, J.F.: Spectral surface reconstruction from noisy point clouds. In: Proc. Geometry Processing (Eurographics/ ACM SIGGRAPH), pp. 11–21 (2004)
Lafarge, F., Mallet, C.: Building large urban environments from unstructured point data. In: ICCV, pp. 1068 –1075 (2011)
Mederos, B., Amenta, N., Velho, L., de Figueiredo, L.H.: Surface reconstruction from noisy point clouds. In: Proc. Geometry Processing (Eurographics/ ACM SIGGRAPH), pp. 53–62 (2005)
Schroeder, W.J.: A topology modifying progressive decimation algorithm. In: Proc. Visualization 1997, pp. 205–212 (1997)
de Souza, K.M.A., Kent, J.T., Mardia, K.V.: Stochastic templates for aquaculture images and a parallel pattern detector. Journal of the Royal Statistical Society Series C 48(2), 211–227 (1999)
Srivastava, A., Jermyn, I.H.: Looking for shapes in cluttered, two-dimensional point clouds. IEEE Trans. on Pattern Analysis and Machine Intelligence 31(9), 1616–1629 (September, 2009)
Su, J., Zhu, Z., Srivastava, A., Huffer, F.: Detection of shapes in 2d point clouds generated from images. In: ICPR, pp. 2640–2643 (2010)
Verma, V., Kumar, R., Hsu, S.: 3D building detection and modeling from aerial lidar data. In: CVPR, vol. 2, pp. 2213 – 2220 (2006)
Wu, J., Kobbelt, L.: Structure recovery via hybrid variational surface approximation. Computer Graphics Forum 24, 277–284 (2005)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Su, J., Tang, LL. (2014). Shape Estimation from 3D Point Clouds. In: Pan, JS., Snasel, V., Corchado, E., Abraham, A., Wang, SL. (eds) Intelligent Data analysis and its Applications, Volume I. Advances in Intelligent Systems and Computing, vol 297. Springer, Cham. https://doi.org/10.1007/978-3-319-07776-5_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-07776-5_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07775-8
Online ISBN: 978-3-319-07776-5
eBook Packages: EngineeringEngineering (R0)