Surface reconstruction from gradient fields is an important
final step in several applications involving gradient manipulations
and estimation. Typically, the resulting gradient
field is non-integrable due to linear/non-linear gradient manipulations,
or due to presence of noise/outliers in gradient
estimation. In this paper, we analyze integrability as error
correction, inspired from recent work in compressed sensing,
particulary L0-L1 equivalence. We propose to obtain
the surface by finding the gradient field which best fits the
corrupted gradient field in L1 sense. We present an exhaustive
analysis of the properties of L1 solution for gradient
field integration using linear algebra and graph analogy.
We consider three cases: (a) noise, but no outliers (b)
no-noise but outliers and (c) presence of both noise and outliers
in the given gradient field. We show that L1 solution
performs as well as least squares in the absence of outliers.
While previous L0-L1 equivalence w...
Dikpal Reddy, Amit K. Agrawal, Rama Chellappa