Surface Nets

8/14/2019 Surface Nets

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MERL - A Mitsubishi Electric Research Lab

Constrained Elastic

SurfaceNets:

generating smooth surfaces from

binary segmented data

Sarah F. F. Gibson


Binary Databinary segmentation produces rough,

unrealistic models

need models with smooth surfaces for high

quality rendering and for modeling physical

interactions


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Artifacts from Binary Data

polygon rendered medial meniscus

from MRI @ 0.27x0.27x0.25 mm resolution

volume rendered knee bones

from MRI @ 0.27x0.27x1.4 mm resolution


Surface Smoothing

existing techniques:

1) local smoothing (e.g. low pass filtering of the

binary data) and then surface construction using

an algorithm such as Marching Cubes

2) global smoothingby warping a

parameterized surface to fit the binary surface


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Low-pass Filtering

low pass filtering smoothes local features

but does not remove terraces unless the

filter size is quite large


Problems with Local Smoothing

low pass filtering removes fine detail

indiscriminately

local filtering does not remove terracing

artifacts unless the filter size is large

additional smoothing and decimation of the

Marching Cubes surface is done without

reference to the original data


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Global Smoothing

global smoothing by warping a

parameterized surface to find a

minimum energy surface

example from I. Takanahi et al, SUNY-SB


Problems with Global Smoothing

choosing the number of grid points in the

parameterized model depends on the

amount of detail in the surface

tradeoffs between smoothness and surfacedetail is made by setting global parameters


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Constrained Elastic SurfaceNets


Constrained Elastic SurfaceNets

initialize an elastic net of surface nodes at the

resolution of the data to fit the binary surface

relax the net to smooth the surface while

constraining the nodes using the binary data

attain a globally smooth surface that is locally

faithful to the original segmentation


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Algorithm in 2Dcell

sample point

interior data sample


Algorithm in 2D

1) locate surface cells

surface cell



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Algorithm in 2D

2) place a SurfaceNet node at the center of

each surface cell

X X X

X X

X X

Xinterior data sample

X SurfaceNet node


Algorithm in 2D


3) establish links between 4-connected

surface nodes

X X X

X X

X X

X

X SurfaceNet nodeSurfaceNet link


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Algorithm in 2D


4) adjust node positions to relax the SurfaceNet

while remaining within the original surface cell

X X X

X

X

X

X

X

X SurfaceNet node

SurfaceNet link


2D Examples

initial

initial


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2D Examples

initial 1 iteration

initial 1 iteration


2D Examples

initial 1 iteration 30 iterations

initial 1 iteration 20 iterations


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Topological Considerations

For ambiguous surface topologies:


Topological ConsiderationsMarching Cubes makes arbitrary decisions

about surface topology


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Topological Considerations

Marching Cubes makes arbitrary decisions

about surface topology


Topological ConsiderationsSurface Nets maintain surface ambiguity for

later high level processing

X

X

X

X

X XXX


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3D Algorithm

1) locate surface cells

2) place a SurfaceNet node at the center of

each surface cell

3) establish links between 6-connected

surface nodes

4) adjust node positions to relax the

SurfaceNet while remaining within the

original surface cell


3D Examples

original surface 1 relaxation 2 relaxations 3 relaxations 4 relaxations

5 relaxations 6 relaxations 7 relaxations 8 relaxations 9 relaxations

10 relaxations 15 relaxations

Binary sphere:

radius 30 voxels


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3D Examples

original surface 1 relaxation 12 relaxations

Femur, 0.27 x 0.27 x 1.0 mm resolution


Building a Surface Triangle Model

Nice Properties of SurfaceNets:

1) surface triangles can be generated automatically

from the structure of the SurfaceNet

2) the triangle model only needs to be constructed

once

as the surface relaxes, the topology is maintained and

only the triangle vertex positions and normals change


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Surface Triangulation

each SurfaceNet node has 6 possible links

and hence 12 possible triangles

rightleft

top

bottom

front

back

x



front-back face

rightleft

top

bottom

front

back

x


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1



left-right face

rightleft

top

bottom

front

back

x



top-bottom face

rightleft

top

bottom

front

back

x


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construct the triangles for each node based

on the presence or absence of links to the

nodes 6 possible neighbors

orient triangles to point out of the

segmented object by referencing the binary

segmentation



Examples

brain atlas, segmented data courtesy of SPL, Brigham and Womens Hospital


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Examples

volume rendered brain from smoothed SurfaceNet


Examples

surface model of the femur

from SurfaceNets,

rendered with OpenGL

surface model of the femur

after low-pass filtering,

Marching Cubes, and

rendering with Vtk


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Examples

abdominal arteries, segmented data courtesy of SPL, Brigham and Womens Hospital


SurfaceNets:

removes terracing

artifacts

preserves fine detail

remains faithful to theoriginal segmentation

Binary Segmentation

Smooth Surface

Model

Polygon

Rendering

Volume

Rendering

SurfaceNets


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Thanks

data and binary segementations from the

Surgical Planning Lab, Brigham and

Womens Hospital

Mike Leventon for Vtk and Marching Cubes

example



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Why Use Binary Segmented Data?

Documents

Surface Nets