Noise on Meshes

1
Noise on Meshes
Meshes obtained from real world objects are often
noisy.
From range image of Stanford Bunny
Angel modelfrom shadow scanning
2
Mesh Smoothing is Required
MeshSmoothing
3
General smoothing procedure
Shape evolution
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Laplacian Smoothing Flow
Average of the vectors to neighboring vertices
Move each vertex
Median direction
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Umbrella operator

• Umbrella operator
• Weighted umbrella operator

Laplacian smoothing
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Difficulties of smoothing
How to find appropriate l and number of iterations
Over-smoothing
Best
Noisy
Iterations
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Properties of Laplacian flow

• increases mesh regularity.
• develops unnatural deformations.

High density sampling
Low density sampling
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Discrete mean curvature flow
Speed discrete mean curvature
Direction normal
Move each vertex
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Properties of mean curvature flow

• increases mesh irregularity.
• doesnt develop unnatural deformations.

High density sampling
Low density sampling
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Discrete Mean Curvature
aj
P
Qj
bj
11
Explicit and Implicit Mesh Evolutions
Shape evolution
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An Image Processing Approach
Smooth the field of mesh normals
2D Image
Triangle mesh
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An Image Processing Approach

• Smooth mesh normals
• Reconstruct smoothed mesh from new normals

Smoothing normals
Reconstruction from mesh normals
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An Image Processing Approach
Distance error
Derivative error
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An Image Processing Approach
Reconstruction from smoothed normals
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Many Problems Remain
Mesh smoothing remains to be an active research
area
Scanned mesh
Photo
Smoothed mesh