Shape Modeling International 2007 – University of Utah, School of Computing Robust Smooth Feature Extraction from Point Clouds Joel Daniels ¹ Linh Ha ¹ Tilo Ochotta ² Claudio Silva ¹ ² University of Konstanz, Germany ¹ University of Utah, USA

Shape Modeling International 2007 – University of Utah, School of Computing Point-based Models Digital scanner technology – Collection of 3D point samples Discrete data of utmost simplicity – Reduced storage requirements – Improved visualization performance Geometric Processing – Conventional algorithms inoperable – Requirements of a new set of algorithms Handle noisy data and sample artifacts **Avoid rebuilding connectivity**

Shape Modeling International 2007 – University of Utah, School of Computing Sharp Features G 1 discontinuities – Multiple intersecting surfaces – Creases, boundaries, edges and corners Applications – Visualization highlight important characteristics Texturing and line drawings – Geometric processing Projections, filtering, resampling, simplification, etc. Compression, reconstruction (to come)

Shape Modeling International 2007 – University of Utah, School of Computing Sharp Features G 1 discontinuities – Multiple intersecting surfaces – Creases, boundaries, edges and corners Applications – Visualization highlight important characteristics Texturing and line drawings – Geometric processing Projections, filtering, resampling, simplification, etc. Compression, reconstruction (to come)

Shape Modeling International 2007 – University of Utah, School of Computing Point Set Surfaces Moving Least Squares (MLS) – Approximate surface fit over local neighborhood – Project point to the surface approximation – Relaxes noise and features arbitrarily Robust Moving Least Squares (RMLS) – Intelligent selection of local neighborhoods Measured residual of an MLS fit Threshold test determines appropriateness Define multiple neighborhoods (surfaces) Iteratively insert and remove points based on statistics of the residual error – Smooth noise while reconstructing sharp features

Shape Modeling International 2007 – University of Utah, School of Computing Point Set Surfaces Moving Least Squares (MLS) – Approximate surface fit over local neighborhood – Project point to the surface approximation – Relaxes noise and features arbitrarily Robust Moving Least Squares (RMLS) – Intelligent selection of local neighborhoods Measured residual of an MLS fit Threshold test determines appropriateness Define multiple neighborhoods (surfaces) Iteratively insert and remove points based on statistics of the residual error – Smooth noise while reconstructing sharp features

Shape Modeling International 2007 – University of Utah, School of Computing Point Set Surfaces RMLS Edge Conflicts – Independent neighborhood segmentation for each point – Does not guarantee consistency between neighbors – Differing surfaces  noisy normals and feature edge

Shape Modeling International 2007 – University of Utah, School of Computing The Ins and Outs Input: Point-Based Model without normal vectors Output: Set of feature curves with normal vectors for defining surfaces Goals: – Produce a smooth set of feature curves that highlight sharp edges – Handle noisy data and poor sampling quality using robust statistics to compute projections – Remove the jittering effects of RMLS

Shape Modeling International 2007 – University of Utah, School of Computing Algorithm Overview 1. Extract points near features 2. Project to edges using RMLS fit surfaces 3. PCA smoothing procedure 4. Grow feature curves through points Input Cloud (Stage 1) (Stage 2) (Stage 3) (Stage 4) Output Features

Shape Modeling International 2007 – University of Utah, School of Computing (Stage 1) Tolerance Tuning Residual: max distance of neighborhood pts to the MLS surface fit Threshold test: Automatic (mean residual) vs. user tuned value τ = 0.082τ = 0.014τ = (automatic)

Shape Modeling International 2007 – University of Utah, School of Computing (Stage 2) Feature Projections RMLS defined surfaces – Newton method to find intersections – Project to the intersection of closest two surfaces (edge point) – Project to the intersection of three surfaces (corner point) Associate weight as the inverse distance to original point

Shape Modeling International 2007 – University of Utah, School of Computing (Stage 2) Corner Computation Cluster corner points within a user defined radius Weighted average computed for each cluster Save closest corner point to average

Shape Modeling International 2007 – University of Utah, School of Computing (Stage 3) PCA Smoothing PCA based smoothing removes RMLS noise – Neighborhood size determined by correlation to principle component BeforeAfter

Shape Modeling International 2007 – University of Utah, School of Computing (Stage 3) PCA Smoothing PCA based smoothing removes RMLS noise – Neighborhood size determined by correlation to principle component – Neighborhood size bounded by distance to nearest corner

Shape Modeling International 2007 – University of Utah, School of Computing (Stage 4) Feature Growth Priority Queue – Order points by distance to nearest corner point (furthest to closest) Feature Construction

Shape Modeling International 2007 – University of Utah, School of Computing (Stage 4) Feature Completion Ignoring the dissipated edge Extending features towards each other Forming new corners

Shape Modeling International 2007 – University of Utah, School of Computing Constructed Features Surface normals associated with curves during growth Relaxation iteration removes perturbations

Shape Modeling International 2007 – University of Utah, School of Computing Performance Results Large Models – Culls many points to focus on the feature regions Expensive RMLS computation times – Pre-process algorithm to improve other applications

Shape Modeling International 2007 – University of Utah, School of Computing Sampling Noise Uniform noise perturb points – Percentages of the bounding volume diagonal – Expected noise from scanners within 1% Extreme noise and poor sampling quality – Handles sample artifacts and noisy data – Error is reduced in comparison to noise levels Ground Truth

Shape Modeling International 2007 – University of Utah, School of Computing Applications – Segmentation Closed loop region segmentation – Seed with a random point – Grow outwards adding neighbors until feature points found – Add neighbors using RMLS neighborhood statistics

Shape Modeling International 2007 – University of Utah, School of Computing Applications – Feature Meshing Remesh segmented regions – Propagating wavefront algorithm [Schreiner:CGF:2006] – Triangle sizes based on guidance field (curvature based) – Seed algorithm with feature polylines Achieve sharp features without modification of algorithm Reduced triangle count – Triangle sizes are determined by the curvature along the feature edge rather than across it!

Shape Modeling International 2007 – University of Utah, School of Computing Applications – Compression Wavelet Compression Multi-height Fields [Ochotta:PBG:2004] – Seeds segmentation process – Aligned segmentation along features – Achieves better compression results Original segmentation Revised segmentation

Shape Modeling International 2007 – University of Utah, School of Computing Final Summary Projects points to feature edges – Addresses RMLS jittering artifacts – Able to compensate for poor sample quality and noise levels Produce a set of feature curves as a pre- process – Useful data as input for geometric processing algorithms Limitations – Expensive RMLS projection procedure – Incomplete or erroneous features due to high noise or poor sampling Future Works – Additional applications: projection and resampling methods

Shape Modeling International 2007 – University of Utah, School of Computing Thanks. [Schreiner:CGF:2006] J. Schreiner, C. Scheidegger, S. Fleishman, and C. Silva Direct (Re)Meshing for Efficient Surface Processing Computer Graphics Forum 25(3), 527 – 536, [Ochotta:PBG:2004] T. Ochotta and D. Saupe Compression of Point-Based 3D Models by Shape-Adaptive Wavelet Coding of Multi-Height Fields Eurographics Symposium on Point- Based Graphics, 2004.

Shape Modeling International 2007 – University of Utah, School of Computing

Existing versus New Data Using current data to define edges – Edges accuracy determined by sampling quality Project onto approximated features – Compensates for poor sampling

Shape Modeling International 2007 – University of Utah, School of Computing Point Cloud Compression Compress segmented regions – Seeds segmentation process [Ochotta:2004] – Aligned segmentation along features – Achieves better compression results Original 0.26 bpp 10.1 RMS 0.48 bpp 2.45 RMS

Shape Modeling International 2007 – University of Utah, School of Computing Remeshing with Features Remesh segmented regions – The feature polylines seed the Afront triangulation algorithm [Schreiner:2006] – Achieve sharp features without modification of algorithm Reduced triangle count – Triangle sizes are determined by the curvature along the feature edge rather than across it!