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Robust Moving Least-squares Fitting with Sharp Features Shachar Fleishman* Daniel Cohen-Or § Claudio T. Silva* * University of Utah § Tel-Aviv university
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Surface reconstruction Noise Smooth surface Smooth sharp features Method for identifying and reconstructing sharp features
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Point set surfaces (Levin ’98) Defines a smooth surface using a projection operator
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Point set surfaces Defines a smooth surface using a projection operator Noisy point set The surface S is defined:
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The MLS projection: overview Find a point q on the surfaces whose normal goes through the projected point x q is the projection of x
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The MLS projection: overview Find a point q on the surfaces whose normal goes through the projected point x q is the projection of x Improve approximation order using polynomial fit
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Sharp features Smoothed out Ambiguous
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Sharp features Smoothed out Ambiguous – Classify
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Projection near sharp feature
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Classification Using outlier identification algorithm That fits a polynomial patch to a neighborhood
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Classification Using outlier identification algorithm That fits a polynomial patch to a neighborhood
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Statistics 101 Find the center of a set of points mean
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Statistics 101 Find the center of a set of points Robustly using median mean median
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Regression with backward search Loop – Fit a model – Remove point with maximal residual Until no more outliers
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Regression with backward search Outliers can have a significant influence of the fitted model
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Regression with forward search (Atkinson and Riani) Start with an initial good but crude surface – LMS (least median of squares) Incrementally improve the fit Monitor the search
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Monitoring the forward search Residual plot
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Monitoring the forward search Residual plot
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Results Polynomial fit allows reconstruction of curved edges Input with missing data Reconstructed and corners Smooth MLS MLS w. edges
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Results Noisy input Reconstructed input smooth sharp
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Results Outliers are ignoredMisaligned regions are determined to be two regions Local decision may cause inconsistencies
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Summary Classification of noisy point sets to smooth regions Application to PSS – Reconstruct surfaces with sharp features from noisy data – Improve the stability of the projection Local decisions may result different neighborhoods for adjacent points Can be applied to other surface reconstruction methods such as the MPU
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Acknowledgements Department of Energy under the VIEWS program and the MICS office The National Science Foundation under grants CCF-0401498, EIA-0323604, and OISE-0405402 A University of Utah Seed Grant The Israel Science Foundation (founded by the Israel Academy of Sciences and Humanities), and the Israeli Ministry of Science
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