Paper Info
Title
Integrating surface normal vectors using fast marching method
Abstract
Integration of surface normal vectors is a vital component in many shape reconstruction algorithms that require integrating surface normals to produce their final outputs, the depth values. In this paper, we introduce a fast and efficient method for computing the depth values from surface normal vectors. The method is based on solving the Eikonal equation using Fast Marching Method. We introduce two ideas. First, while it is not possible to solve for the depths Z directly using Fast Marching Method, we solve the Eikonal equation for a function W of the form W = Z + λf. With appropriately chosen values for λ, we can ensure that the Eikonal equation for W can be solved using Fast Marching Method. Second, we solve for W in two stages with two different λ values, first in a small neighborhood of the given initial point with large λ, and then for the rest of the domain with a smaller λ. This step is needed because of the finite machine precision and rounding-off errors. The proposed method is very easy to implement, and we demonstrate experimentally that, with insignificant loss in precision, our method is considerably faster than the usual optimization method that uses conjugate gradient to minimize an error function.
Year
DOI
Venue
2006
10.1007/11744078_19
ECCV (3)
Keywords
Field
DocType
surface normal,depth value,surface normal vector,form w,efficient method,fast marching method,eikonal equation,function w,usual optimization method,integrating surface,fast marching
Conjugate gradient method,Error function,Applied mathematics,Round-off error,Machine epsilon,Artificial intelligence,Geometry,Computer vision,Fast marching method,Eikonal equation,Eikonal approximation,Normal,Mathematics
Conference
Volume
ISSN
ISBN
3953
0302-9743
3-540-33836-5
Citations 
PageRank 
References 
10
0.72
8
Authors
4
Name
Order
Citations
PageRank
Jeffrey Ho12190101.78
Jongwoo Lim24105144.58
Yang Ming-Hsuan315303620.69
David Kriegman47693451.96