Research Papers

Wavelet SDF-Reps: Solid Modeling With Volumetric Scans

[+] Author and Article Information
Duane Storti, Mark A. Ganter, William R. Ledoux, Randal P. Ching

Department of Mechanical Engineering, University of Washington, Seattle, WA 98195

Yangqiu Patrick Hu, David Haynor

Department of Radiology, University of Washington, Seattle, WA 98195

J. Comput. Inf. Sci. Eng 9(3), 031006 (Aug 21, 2009) (10 pages) doi:10.1115/1.3184604 History: Received January 03, 2008; Revised October 17, 2008; Published August 21, 2009

This paper describes a new formulation of solid modeling for treating parts derived from volumetric scans (computed tomography, magnetic resonance, etc.) along with parts from traditional computer-aided design operations. Recent advances in segmentation via level set methods produce voxel grids of signed distance values, and we interpolate the signed distance values using wavelets to produce an implicit or function-based representation called wavelet signed distance function representation that provides inherent support for data compression, multiscale modeling, and skeletal-based operations.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Analysis of 1D SDF data. (a) Original sampled data. (b) Coarser sampling provided by low resolution coefficients. (c) High resolution coefficients. Note that the vertical scale differs from the previous plots by a factor of 20. High resolution coefficients vanish except near the slope discontinuities. (d) SDF values reconstructed after ∼40% data compression.

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Figure 2

Wavelet derivative of sample 1D SDF data.

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Figure 3

SDF for a rectangle in 2D: contour plot of the level sets superposed on carpet plot of SDF values.

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Figure 4

Wavelet analysis of one slice of a 2D SDF. (a) SDF data points corresponding to Y=50 in Fig. 3. (b) Low resolution coefficients provide coarser sampling. (c) High resolution coefficients have, with few exceptions, small magnitudes. Note that vertical scale differs by a factor of 24 from (a) and (b).

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Figure 5

Tensor product wavelet analysis of 2D SDF data. (a) Result of 1D analysis in x-direction. (b) Result of 1D analysis in y-direction of wavelet coefficients from (a). Large coefficients provide coarser version of the SDF (front left). Remaining coefficients are small, with visible ripples associated with the skeleton points.

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Figure 6

3D wavelet SDF-rep for a human talus. (a) Image of the SDF-rep based on 1283 data grid. (b) Image of coarser model based on 643 grid of low resolution wavelet coefficients. (c) Wavelet data compression of 3D SDF-rep. 99.5% of the wavelet data is suppressed corresponding to 200:1 compression.

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Figure 7

Talus and calcaneus SDF-reps derived from 3D scan data unioned with SDF-rep obtained by virtual scan of cylindrical pin.

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Figure 8

Skeletal model derived from wavelet SDF-rep. (a) Skeletal grid points of the talus identified using wavelet derivatives to evaluate the gradient. (b) Skeletal data (skeleton points with radii specified by SDF) as alternative geometric representation. (c) Offset talus obtained by uniformly increasing radii. (d) Semitransparent rendering of offset talus and original talus.

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Figure 9

Skeletal modeling examples: skeletal design of a talar/calcaneal pad. (a) The pad fits between the talus (top) and calcaneus (bottom). (b) The calcaneus is removed to provide a better view of the pad.



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