计算机图形学Lecture04-poissonrecon

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Poisson Surface

Reconstruction

Michael Kazhdan, Matthew Bolitho

Johns Hopkins University

Hugues Hoppe

Microsoft Research

Motivation

In many domains, scanners are used to

obtain virtual representations of 3D shapes

http://www.jhu.edu/digitalhammurabi/ http://graphics.stanford.edu/projects/mich/

Motivation

Scanning often gives only local connectivity

Motivation

Scanning often gives only local connectivity

We want a 3D Mesh for:

Parameterization

Computational Analysis

Rapid Prototyping

Rendering

Collision Detection

Surface Reconstruction

Generate a mesh from a set of surface samples

Surface Reconstruction

Generate a mesh from a set of surface samples

◼Three general approaches:

1. Computational Geometry

Boissonnat, 1984 Edelsbrunner, 1984

Amenta et al., 1998 Dey et al., 2003

2. Surface Fitting

Terzopoulos et al., 1991 Chen et al., 1995

3. Implicit Function Fitting

Hoppe et al., 1992 Curless et al., 1996

Whitaker, 1998 Carr et al., 2001

Davis et al., 2002 Ohtake et al., 2004

Turk et al., 2004 Shen et al., 2004

Kazhdan, 2005

Implicit Function Approach

< 0 > 0

◼Define a function with

value less than zero

outside the model and

greater than zero inside

Implicit Function Approach

◼Define a function with

value less than zero

outside the model and

greater than zero inside

◼Extract the zero-set

< 0 > 0

Accurate Reconstructions

◼To extract fine surface detail,

represent the implicit function

at a high resolution.

Limitation:

◼Regular voxel grids have

complexity proportional to

the volume not the surface.

Kazhdan 2005, FFT Reconstruction

Accurate Reconstructions

An accurate representation is only required

near the surface.

Limitations:

◼Solve large, dense linear systems

◼Hard to control away from samples

Carr et al. 2001, FastRBF

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PoissonSurfaceReconstructionMichaelKazhdan,MatthewBolithoJohnsHopkinsUniversityHuguesHoppeMicrosoftResearchMotivationInmanydomains,scannersareusedtoobtainvirtualrepresentationsof3Dshapeshttp://www.jhu.edu/digitalhammurabi/http://graphics.stanford.edu/projects/mich/MotivationScanningoftengivesonlyloc...

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