@conference {12517,
	title = {Enforcing integrability by error correction using l1-minimization},
	booktitle = {Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on},
	year = {2009},
	month = {2009/06//},
	pages = {2350 - 2357},
	abstract = {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 lscr<sub>0</sub> - lscr<sub>1</sub> equivalence. We propose to obtain the surface by finding the gradient field which best fits the corrupted gradient field in lscr<sub>1</sub> sense. We present an exhaustive analysis of the properties of lscr<sub>1</sub> 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 lscr<sub>1</sub> solution performs as well as least squares in the absence of outliers. While previous lscr<sub>0</sub> - lscr<sub>1</sub> equivalence work has focused on the number of errors (outliers), we show that the location of errors is equally important for gradient field integration. We characterize the lscr<sub>1</sub> solution both in terms of location and number of outliers, and outline scenarios where lscr<sub>1</sub> solution is equivalent to lscr<sub>0</sub> solution. We also show that when lscr<sub>1</sub> solution is not able to remove outliers, the property of local error confinement holds: i.e., the errors do not propagate to the entire surface as in least squares. We compare with previous techniques and show that lscr<sub>1</sub> solution performs well across all scenarios without the need for any tunable parameter adjustments.},
	keywords = {-, algebra;lscr<sub>0</sub>, algebra;minimisation;, analogy;integrability;least, compressed, correction;gradient, equivalence;lscr<sub>1</sub>-minimization;noise-outlier;surface, estimation;gradient, field, integration;gradient, lscr<sub>1</sub>, manipulation;graph, methods;graph, reconstruction;error, reconstruction;linear, sensing;error, squares;linear, theory;image},
	doi = {10.1109/CVPR.2009.5206603},
	author = {Reddy, D. and Agrawal,A. and Chellapa, Rama}
}
