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Detection, classification and estimation of individual shapes in 2D and 3D point clouds

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  • Su, J.
  • Srivastava, A.
  • Huffer, F.W.

Abstract

The problems of detecting, classifying, and estimating shapes in point cloud data are important due to their general applicability in image analysis, computer vision, and graphics. They are challenging because the data is typically noisy, cluttered, and unordered. We study these problems using a fully statistical model where the data is modeled using a Poisson process on the object’s boundary (curves or surfaces), corrupted by additive noise and a clutter process. Using likelihood functions dictated by the model, we develop a generalized likelihood ratio test for detecting a shape in a point cloud. This ratio test is based on optimizing over some unknown parameters, including the pose and scale associated with hypothesized objects, and an empirical evaluation of the log-likelihood ratio distribution. Additionally, we develop a procedure for estimating most likely shapes in observed point clouds under given shape hypotheses. We demonstrate this framework using examples of 2D and 3D shape detection and estimation in both real and simulated data, and a usage of this framework in shape retrieval from a 3D shape database.

Suggested Citation

  • Su, J. & Srivastava, A. & Huffer, F.W., 2013. "Detection, classification and estimation of individual shapes in 2D and 3D point clouds," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 227-241.
    • Handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:227-241
    DOI: 10.1016/j.csda.2012.09.008
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    References listed on IDEAS

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    1. Peter J. Green & Kanti V. Mardia, 2006. "Bayesian alignment using hierarchical models, with applications in protein bioinformatics," Biometrika, Biometrika Trust, vol. 93(2), pages 235-254, June.
    2. K. M. A. De Souza & J. T. Kent & K. V. Mardia, 1999. "Stochastic Templates for Aquaculture Images and a Parallel Pattern Detector," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(2), pages 211-227.
    3. Ian L. Dryden & Jonathan D. Hirst & James L. Melville, 2007. "Statistical Analysis of Unlabeled Point Sets: Comparing Molecules in Chemoinformatics," Biometrics, The International Biometric Society, vol. 63(1), pages 237-251, March.
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    Cited by:

    1. Pulkkinen, Seppo, 2015. "Ridge-based method for finding curvilinear structures from noisy data," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 89-109.
    2. Bryner, Darshan & Huffer, Fred & Rosenthal, Michael & Tucker, J. Derek & Srivastava, Anuj, 2016. "Estimation of linear target-layer trajectories using cluttered point cloud data," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 1-22.
    3. Allassonnière, Stéphanie & Kuhn, Estelle, 2015. "Convergent stochastic Expectation Maximization algorithm with efficient sampling in high dimension. Application to deformable template model estimation," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 4-19.

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