Feature Preserving Sketchingof Volume Data

Jens Kerber, Michael Wand, Martin Bokeloh,Jens Krüger, Hans-Peter Seidel

Saarland University and MPI Informatik

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Goals

• Task• Reduce visual complexity• Extract crease lines• Faithfully reproduce/illustrate geometry• Robust to noise• Preserving connectivity/topology

• Point based features in volumes• Too many• Not expressive enough• Abstraction to line features necessary

Jens Kerber, Saarland University and MPI Informatik

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Overview

• Key ingredient:• Iteratively reweighted least squares approximation

Jens Kerber, Saarland University and MPI Informatik

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Local Fitting 2D Example

• Approximate local neighborhood• Fit quadratic curve• Weight influence of pixels bilaterally• Refine iteratively

Jens Kerber, Saarland University and MPI Informatik

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Local Fitting 3D Example

• Approximate local neighborhood• Fit quadratic function 3D -> 3D• Iso surface• Weight influence of voxels bilaterally• Refine iteratively

Jens Kerber, Saarland University and MPI Informatik

Behavior at an edge

Behavior at a corner

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Mathematical Description

• Resulting function• best describes local conditions• least square sense

Jens Kerber, Saarland University and MPI Informatik

2 2 2

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(1, , , , , , , , , )

( , , , , , , , , , )

T

yz zzx y z xx xy xz yy

f a c

a x y z x xy xz y yz z

c c c c c c c c c c c

Normal Hessian Matrix

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Descriptor

• For all voxels• Orthonormal basis (vectors)

• normal, first and second principal curvature direction• Local coordinates (values)

• gradient and bendings

Jens Kerber, Saarland University and MPI Informatik

G

Kmax

Kminnkmin

kmax

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Areas of Interest

• Selecting voxels by thresholding• High gradient

• Iso-surface transitions• High tangent

• Edges and corners• Colorcoded by kmin

Jens Kerber, Saarland University and MPI Informatik

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Projection

• Shrink the spatial extension• Similar to Mean-Shift-Filtering

• Continuous shift• Gradient decent

• Restricted to move in one plane• slice perpendicular to the tangential direction• Preserves connectivity

• Bilateral weights for all neighbors• depending of deviations in orientation

Jens Kerber, Saarland University and MPI Informatik

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Projection

Jens Kerber, Saarland University and MPI Informatik

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Projection

Jens Kerber, Saarland University and MPI Informatik

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Projection

Jens Kerber, Saarland University and MPI Informatik

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Projection

Jens Kerber, Saarland University and MPI Informatik

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Projection

Jens Kerber, Saarland University and MPI Informatik

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Projection

Jens Kerber, Saarland University and MPI Informatik

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Projection

Jens Kerber, Saarland University and MPI Informatik

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Projection

Jens Kerber, Saarland University and MPI Informatik

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Projection

Jens Kerber, Saarland University and MPI Informatik

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Without restriction

Jens Kerber, Saarland University and MPI Informatik

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Projection

Jens Kerber, Saarland University and MPI Informatik

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Clustering

• Region growing• collect all neighbors with similar orientation

Jens Kerber, Saarland University and MPI Informatik

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Visualization

• Inflate for rendering• Thin tubes around each line• Implicit distance function• Marching cubes based meshing

• Ambient occlusion• Environment map• Impression of depth order and overlaps

• Highlight intersections and corners• Locations where clusters of differing orientations meet

Jens Kerber, Saarland University and MPI Informatik

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Visualization

Jens Kerber, Saarland University and MPI Informatik

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With and Without Restriction

Jens Kerber, Saarland University and MPI Informatik

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Video

Jens Kerber, Saarland University and MPI Informatik

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Visualization

Jens Kerber, Saarland University and MPI Informatik

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Video

Jens Kerber, Saarland University and MPI Informatik

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Outlook: Symmetries

Jens Kerber, Saarland University and MPI Informatik

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• Thank you for your attention!

• Questions?

Jens Kerber, Saarland University and MPI Informatik