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- W2554489623 abstract "In this paper, we present a new technique for solving the difficult problem of estimating the axis of symmetry for axially symmetric surfaces. Accurate solutions to this problem are important in archaeology for systems that seek to reconstruct pottery vessels from measurements of their fragment s. Our approach estimates quadratic surfaces at each measured surface point and uses a Markov Random Field superimposed on measured mesh surface to combine surface estimates into surface patches, each of which lies close to a single 3D quadratic surface. For each surface patch, we estimate a quadratic implicit polynomial whose coefficient s directly provide an estimate of the unknown axis location and orientation. Using the bootstrap method, distribution s for the axis parameters associated with each surface patch are computed. These competing estimates of the global axis are combined using Maximum Likelihood Estimation (MLE) to provide the final estimate. Our approach differs from past approaches by combining estimates derived from large surface regions that include many measurements instead of combining many local (often pointwise) estimates of the surface to determine the global estimate. Estimates from these large regions are more robust to noise and have sufficient data to provide statistical estimates of the uncertainty in the computed estimates. Major benefits of this technique include: (i) a pre-segmentation of the surface to identify noisy, i.e., a-symmetric, regions and (ii) a Bayes ian method for merging estimates that makes the axis estimate robust to outliers and highly-variable estimates." @default.
- W2554489623 created "2016-11-30" @default.
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- W2554489623 date "2008-01-01" @default.
- W2554489623 modified "2023-09-27" @default.
- W2554489623 title "Using Markov Random Fields and Algebraic Geometry to Extract 3D Symmetry Properties" @default.
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