geometry processing pipeline 3d scanning, …...3d scanning, smoothing…., 3d printing and medical...

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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