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A graph-spectral method for surface height recovery (2004)
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| Venue: | PATTERN RECOGNITION |
| Citations: | 9 - 4 self |
BibTeX
@MISC{Robles-kelly04agraph-spectral,
author = {Antonio Robles-kelly and Edwin R. Hancock},
title = { A graph-spectral method for surface height recovery},
year = {2004}
}
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Abstract
This paper describes a graph-spectral method for 3D surface integration. The algorithm takes as its input a 2D field of surface normal estimates,delivered,for instance,by a shape-from-shading or shape-from-texture procedure. We commence by using the surface normals to obtain an affinity weight matrix whose elements are related to the surface curvature. The weight matrix is used to compute a row-normalized transition probability matrix,and we pose the recovery of the integration path as that of finding the steady-state random walk for the Markov chain defined by this matrix. The steady-state random walk is given by the leading eigenvector of the original affinity weight matrix. By threading the surface normals together along the path specified by the magnitude order of the components of the leading eigenvector we perform surface integration. The height increments along the path are simply related to the traversed path length and the slope of the local tangent plane. The method is evaluated on needle-maps delivered by a shape-from-shading algorithm applied to real-world data and also on synthetic data. The method is compared with the local geometric height reconstruction method of Bors,Hancock and Wilson, and the global methods of Horn and Brooks and Frankot and Chellappa.
Keyphrases
graph-spectral method surface height recovery surface integration surface normal steady-state random walk traversed path length shape-from-texture procedure row-normalized transition probability matrix shape-from-shading algorithm markov chain surface normal estimate magnitude order local tangent plane original affinity weight matrix height increment affinity weight matrix global method synthetic data surface curvature weight matrix local geometric height reconstruction method integration path
