Image-Consistent Surface Triangulation
Daniel D. MorrisTakeo Kanade
Robotics Institute
Carnegie Mellon University
Pittsburgh, PA 15213
Paper to appear in CVPR 2000: Image-Consistent Surface Triangulation (4.8 MBytes .ps.gz file)
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Abstract

Given a set of 3D points that we know lie on the surface of an object, we can define many possible surfaces that pass through all of these points. Even when we consider only surface triangulations, there are still an exponential number of valid triangulations that all fit the data. Each triangulation will produce a different faceted surface connecting the points.

OR ?
We want to overcome this ambiguity and find the particular surface that is closest to the true object surface. While we do not know the true surface, we have a set of images of the object. We propose selecting a triangulation based on its consistency with this set of images of the object. Our algorithm starts with an initial rough triangulation and refines the triangulation until it obtains a surface that best accounts for the images of the object.

An image sequence:

Features that are tracked by hand are shown in red:

3D point cloud:

Using our Structure from Motion algorithm, we recover the 3D feature positions shown in this point cloud:

Triangulations:

A typical naive triangulation is obtained by performing a 2D Delaunay triangulation in one of the images and projecting onto 3D. This can then be refined using our image-consistency algorithm to obtain a better triangulation:

Initial triangulation
Image consistent triangulation

Reconstructions

The reconstructions obtained from these triangulations are shown below.
Reconstruction from initial triangulation
Reconstruction from refined triangulation
Daniel D. Morris
Last modified: Fri Mar 24 15:52:24 EST 2000