Shape Reconstruction from Samples with Cocone
-
Upload
william-burns -
Category
Documents
-
view
31 -
download
1
description
Transcript of Shape Reconstruction from Samples with Cocone
Shape Reconstruction from Shape Reconstruction from Samples with CoconeSamples with Cocone
Tamal K. Dey
Dept. of CIS
Ohio State University
A point cloud and reconstruction
Surface meshing from sample
A point set from satelite imaging
A reconstruction with and A reconstruction with and without noisewithout noise
Why Sample Based Modeling?
• Sampling is easy and convenient with advanced technology
• Automatization (no manual intervention for meshing)
• Uniform approach for variety of inputs (laser scanner, probe digitizer, MRI,scientific simulations)
• Robust algorithms are available
Challenges
• Nonuniform data
• Boundaries
• Undersampling
• Large data
• Noise
Nonuniform data
Boundaries
Undersampling
Large data
3.4 million points3.4 million points
Cocone
• Cocone meets the challenges
• It guarantees geometrically close surface with same topological type
• Detects boundaries
• Detects undersampling
• Handles large data (Supercocone)
• Watertight surface (Tight Cocone)
Sampling (ABE98)
Each x has a sample within f(x)
f(x) is the distance to medial axis
Voronoi/Delaunay
Surface and Voronoi Diagram
• Restricted Voronoi
• Restricted Delaunay
• skinny Voronoi cell
• poles
Cocone algorithm
• Cocone
Space spanned by vectors making angle /8 with horizontal
Radius, height and neighbors• p is the farthest point from p in the cocone.
•radius r(p): p radius of cocone
• height h(p): min distance to the poles
• cocone neighbors Np
Flatness condition
• Vertex p is flat if
1. Ratio condition: r(p) h(p)
2. Normal condition: v(p),v(q) q with pNq
Boundary detection
Boundary(P,,) Compute the set R of flat vertices;
while pR and pNq with qR and r(p)h(p) and v(p),v(q) R:=Rp; endwhile return P\Rend
Detected Boundary Samples
Detected Boundary Samples
Undersampling repaired
Holes are created
Tight Cocone
Guarantee: A water tight surface no Guarantee: A water tight surface no matter how the input is.matter how the input is.
Tight Cocone output
Holes are created
Hole filling
Time
Time
Large Data• Delaunay takes space and time
• Exact computation is necessary. Doubles the time.
Floating point Exact arithmetic
Large Data (Supercocone)
•Octree subdivision
Cracks• Cracks appear in surface computed from octree boxes
Surface matching
David’s Head
2 mil points, 93 minutes
Lucy25
3.5 million points, 198 mints
Shape of arbitrary dimension
Tangent and Normal Polytopes
• T(p) = V(p)T(p)
• N(p) = V(p)N(p)
Experiments
Sample Decimation
Original
40K points
= 0.4
8K points
= 0.33
12K points
Rocker
0.33
11K points
Original
35K points
Bunny
0.4
7K points
0.33
11K points
Original
35K points
Bunny
0.4
7K points
0.33
11K points
Original
35K points
Triangle Aspect Ratio
Medial axis
Medial axis
Noise
Outliers Cleaned
Noise (Local)
This is a challenge unsolved. Perturbation by very tiny amount is tolerated by Cocone.
Boundaries
Engineering Medical
Geometric Models
Sports Drug design
Undersampling for Nonsmoothness
Modeling by Parts
Simplification
• Sample decimation vs. model decimation
Guarantees• Topology preserved, no self intersection, feature dependent
13751 tri 3100 tri
Multiresolution
15766 tri 10202 tri 7102 tri
Model Analysis
• Feature line detection
• Detection of dimensionality
Mixed Dimensions
Model Reconstruction after Data Segmentation
Conclusions• SBGM with Del/Vor diagrams has great potential
• Challenges are
• Boundaries
• Nonsmoothness
• Noise
• Large data
• Robust simplification
• Robust feature detection