Post on 25-Jul-2020
12014.09.08 FU Berlin – AG Geom
Sunil YadavABV Seminar17.08.2017
Geometry Processing Pipeline3D Scanning, Smoothing…., 3D Printing and Medical Imaging
Applications
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Outline
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Outline
Data Acquisition
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Outline
Data AcquisitionSurface
Reconstruction
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Outline
Data AcquisitionSurface
Reconstruction
Surface Smoothing
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Outline
Data AcquisitionSurface
Reconstruction
Surface Smoothing
Feature Analysis
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Outline
Data AcquisitionSurface
Reconstruction
Surface Smoothing
Feature Analysis
Parametrization, Application,
Printing
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GPP - Stairs
Data AcquisitionSurface
Reconstruction
Surface Smoothing
Feature Analysis
Parametrization, Application,
Printing
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Consist of two basic elements:
Data Acquisition – 3D Laser Scanner
• Laser Light as the light emitting source.
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Consist of two basic elements:
Data Acquisition – 3D Laser Scanner
• Laser Light as the light emitting source.
• CCD (charge coupled device) sensors as the
detector of the laser light
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Consist of two basic elements:
Data Acquisition – 3D Laser Scanner
• Laser Light as the light emitting source.
• CCD (charge coupled device) sensors as the
detector of the laser light
Laser source is connected to rotor.
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CCD sensors are uniformly arranged in a
rectangular grid (640x480).
Consist of two basic elements:
Data Acquisition – 3D Laser Scanner
• Laser Light as the light emitting source.
• CCD (charge coupled device) sensors as the
detector of the laser light
Laser source is connected to rotor.
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Data Acquisition – 3D Laser Scanner
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Data Acquisition – 3D Laser Scanner
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Data Acquisition – 3D Laser Scanner
Height value is calculated as:
tantan
tan
Fbaselinez
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Data Acquisition – 3D Laser Scanner
Height value is calculated as:
tantan
tan
Fbaselinez
F, focal length of the camera (8,14
and 25 mm).
Measurement accuracy depends on β.
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CCD Sensors and Laser
β is measured by detecting the position of
the imaged diffusion spot.
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CCD Sensors and Laser
β is measured by detecting the position of
the imaged diffusion spot.
2
5.0
x
xx
d AeI
Laser light follows the Gaussian intensity
distribution.
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CCD Sensors and Laser
β is measured by detecting the position of
the imaged diffusion spot.
2
5.0
x
xx
d AeI
Laser light follows the Gaussian intensity
distribution.
If surface has non-uniform reflectance characteristics?
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Reflectance Error
Due to different reflectance, position of the center of the gravity may not give the proper result.
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Other Errors
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Data Acquisition – Points only
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Data Acquisition – Points only
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GPP - Stairs
Data Acquisition
Surface Reconstruction
Surface Smoothing
Feature Analysis
Parametrization, Application,
Printing
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Surface Reconstruction
No connectivity, no surface
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Surface Reconstruction
No connectivity, no surface
Simplest way
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Surface
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Data Acquisition – Regular Points
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Triangulated Surface
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Data Acquisition – Irregular Points
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Surface Reconstruction
Irregular vertices.
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Surface Reconstruction
Irregular vertices
Apply K-nn algorithm.
ip
jp
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Surface Reconstruction
Irregular vertices
Apply K-nn algorithm.
ip
jp
Apply PCA.
ij
n
j
T
ij ppppn
C
1
0
1
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Surface Reconstruction
Irregular vertices
Apply K-nn algorithm.
Apply PCA.
ij
n
j
T
ij ppppn
C
1
0
1
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Surface Reconstruction
Irregular vertices
Apply K-nn algorithm.
Apply PCA.
ij
n
j
T
ij ppppn
C
1
0
1
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Triangulated Surface
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Feature Analysis
Data AcquisitionSurface
Reconstruction
Surface Smoothing
Feature Analysis
Parametrization
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Feature Analysis – Shape operator and Curvature
• Shape operator is a linear operator to compute the surface bending.
NDvS vp
Definition: Let M subset R3 be a regular surface and let N be a surface normal to
M defined in a neighborhood of a point p in M. For a tangent vector vp to M at p
we put .
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Feature Analysis – Shape operator and Curvature
Principle curvatures are eigenvalues of the Shape operator:
• Shape operator is a linear operator to compute the surface bending.
NDvS vp
Definition: Let M subset R3 be a regular surface and let N be a surface normal to
M defined in a neighborhood of a point p in M. For a tangent vector vp to M at p
we put .
- Maximum Principle curvature1
2 - Minimum Principle curvature
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Curvature
Cylinder
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Curvature
1
Maximum
Principle
curvature
Cylinder
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Curvature
1 2
Maximum
Principle
curvature
Minimum
Principle
curvature
Cylinder
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Curvature
1 22
21 H
Maximum
Principle
curvature
Minimum
Principle
curvature
Cylinder
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Curvature
1 22
21 H
Maximum
Principle
curvature
Minimum
Principle
curvature
Mean
curvature
Cylinder
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Curvature
1 22
21 H 21 K
Maximum
Principle
curvature
Minimum
Principle
curvature
Mean
curvature
Cylinder
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Curvature
1 22
21 H 21 K
Maximum
Principle
curvature
Minimum
Principle
curvature
Mean
curvature
Gauss
curvature
Cylinder
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Mean Curvature – More example
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Mean Curvature – More example
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GPP - Stairs
Data AcquisitionSurface
Reconstruction
Surface Smoothing
Feature Analysis
Parametrization, Application,
Printing
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Smoothing/Denoising
Bending energy on a surface:
• Willmore Energy:
s
dAH 2
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Smoothing/Denoising
Bending energy on a surface:
• Willmore Energy:
s
dAH 2
• Thin plate/Anisotropic energy:
s
dA2
2
2
1
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Smoothing/Denoising
Bending energy on a surface:
• Willmore Energy:
s
dAH 2
• Thin plate/Anisotropic energy:
s
dA2
2
2
1
To remove the noise components, minimize the anisotropic energies
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Smoothing/Denoising – Isotropic (Laplacian)
Laplace Beltrami Operator:
Hnfs 2
Uniform discretization of Laplace Beltrami operator:
i
Nj
j
v
vvN
Lv
1
iv
jv
Weighted discretization of Laplace Beltrami operator: Cotangent Operator
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Smoothing/Denoising – Isotropic (Laplacian)
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Smoothing/Denoising – Isotropic (Laplacian)
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Isotropic (Laplacian) - Drawbacks
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Isotropic (Laplacian) - Drawbacks
50 iterations
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Isotropic (Laplacian) - Drawbacks
50 iterations
200 iterations
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Isotropic (Laplacian) - Drawbacks
50 iterations
200 iterations
1000 iterations
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Smoothing/Denoising – Anisotropic
otherwisear
a
awNHHwxH r
xxe
eeeiA
ji 22
2
,
,
1
)(2
1
Feature Preserving smoothing:
Based on anisotropic diffusion equation.
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Smoothing/Denoising – Anisotropic
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Smoothing/Denoising – Anisotropic
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Anisotropic Smoothing – more examples
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With Multiple scans and processing
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Results
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GPP - Stairs
Data AcquisitionSurface
Reconstruction
Surface Smoothing
Feature Analysis
Parametrization, Application,
Printing
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Medical Application – 3D shape
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• Resample volume scan to the radial scan using the polar coordinate transformation.
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Radial Scans on Volume
• Using Bilinear interpolation.
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Radial Scans
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Cubic Bezier Fitting
• Split whole scan in to 4 parts.
• Splitting points: rim points and foveal pit
eiQ
icQcsQ
seQ
• Each segement can be approximated by using the Bezier cubics.
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Fitted Radial Scans
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Fitted Radial Scans
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Optical Nerve Head Morphometry
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Surface reconstruction
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Outlier removal and Smoothing
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Interior Region based on Landmarks
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Interior Region based on Landmarks
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Annular shape ONH – User defined radius (2mm)
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Annular shape ONH – User defined radius (2mm) - ROI
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ROI - Landmarks
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ROI –Ellipse Fitted Landmarks
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Interior region - Landmarks
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Annular Region ONH
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Annular Region ONH - Volume
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Interior Region ONH
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Interior Region ONH
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Mean Shape of Healthy Right Eye
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Thank You for your Attention