1 / 46

460 likes | 593 Vues

Uncertainty and Variability in Point Cloud Surface Data. Mark Pauly 1,2 , Niloy J. Mitra 1 , Leonidas J. Guibas 1. 1 Stanford University. 2 ETH, Zurich. Point Cloud Data (PCD). To model some underlying curve/surface. Sources of Uncertainty. Discrete sampling of a manifold

Télécharger la présentation
## Uncertainty and Variability in Point Cloud Surface Data

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Uncertainty and Variability in Point Cloud Surface Data**Mark Pauly1,2, Niloy J. Mitra1, Leonidas J. Guibas1 1 Stanford University 2 ETH, Zurich**Point Cloud Data (PCD)**To model some underlying curve/surface**Sources of Uncertainty**• Discrete sampling of a manifold • Sampling density • Features of the underlying curve/surface • Noise • Noise characteristics**Uncertainty in PCD**Reconstruction algorithm PCD curve/ surface But is this unique?**A possible reconstruction**Motivation**or this one,**Motivation**or this …..**Motivation**So look for probabilistic answers.**Motivation priors !**What are our Goals?**• Try to evaluate properties of the set of (interpolating) curves/surfaces. • Answers in probabilistic sense. • Capture the uncertainty introduced by point representation.**Related Work**• Surface reconstruction • reconstruct the connectivity • get a possible mesh representation • PCD for geometric modeling • MLS based algorithms • Kalaiah and Varshney • PCA based statistical model • Tensor voting**Likelihood that a surface interpolating P passes though a**point x in space Set of all interpolating surfaces for PCD P Prior for a surface S in MP Notations**Expected Value**Conceptually we can define likelihood as Surface prior ? Set of all interpolating surfaces ? Characteristic function**How to get FP(x) ?**• input : set of points P • implicitly assume some priors (geometric) • General idea: • Each point piP gives a local vote of likelihood • 1.Local likelihood depends on how well neighborhood of piagrees with x. • 2. Weight of vote depends on distance of pi from x.**x**x Estimates for x Interpolating curve more likely to pass through x Prior : preference to linear interpolation**x**qi(x) qi(x) x pi pj pi pj Estimates for x**Likelihood Estimate by pi**Distance weighing High if x agrees with neighbors of pi**Likelihood Estimates**Normalization constant**Finally…**O(N) O(1) Covariance matrix (independent of x !)**Likelihood Map: Fi(x)**likelihood Estimates by point pi**Likelihood Map: Fi(x)**Pinch point is pi High likelihood Estimates by point pi**Likelihood Map: Fi(x)**Distance weighting**Likelihood Map: FP(x)**likelihood O(N)**Confidence Map**• How much do we trust the local estimates? • Eigenvalue based approach • Likelihood estimates based on covariance matrices Ci • Tangency information implicitly coded in Ci**Confidence Map**denote the eigenvalues of Ci. Low value denotes high confidence (similar to sampling criteria proposed by Alexa et al. )**Confidence Map**confidence Red indicates regions with bad normal estimates**Maps in 2d**Likelihood Map Confidence Map**Confidence Map**Likelihood Map Maps in 3d**Noise Model**• Each point pi corrupted with additive noise i • zero mean • noise distribution gi • noise covariance matrix i • Noise distributions gi-s are assumed to be independent**Noise**Expected likelihood map simplifies to a convolution. Modified covariance matrix convolution**Likelihood Map for Noisy PCD**gi No noise With noise**Scale Space**Proportional to local sampling density**Scale Space**Good separation Bad estimates in noisy section**Scale Space**Cannot detect separation Better estimates in noisy section**Application 1: Most Likely Surface**Noisy PCD Likelihood Map**Application 1: Most Likely Surface**Active Contour Sharp features missed?**Application 2: Re-sampling**Given the shape !! Confidence map Add points in low confidence areas**Application 2: Re-sampling**Add points in low confidence areas**Application 3: Weighted PCD**PCD 1 PCD 2**Application 3: Weighted PCD**Merged PCD**Application 3: Weighted PCD**Merged PCD Too noisy Too smooth**Application 3: Weighted PCD**Confidence Map Likelihood Map**Application 3: Weighted PCD**Weighted PCD**Application 3: Weighted PCD**Weighted PCD Merged PCD**Future Work**• Soft classification of medical data • Analyze variability in family of shapes • Incorporate context information to get better priors • Statistical modeling of surface topology

More Related