[show abstract][hide abstract] ABSTRACT: We present a new approach to robustly solve photometric stereo problems. We cast the problem of recovering surface normals from multiple lighting conditions as a problem of recovering a low-rank matrix with both missing entries and corrupted entries, which model all types of non-Lambertian eects such as shadows and specularities. Unlike previ- ous approaches that use Least-Squares or heuristic robust techniques, our method uses advanced convex optimization techniques that are guaranteed to nd the correct low-rank matrix by simultaneously xing its missing and erroneous entries. Extensive experimental results demonstrate that our method achieves unprecedentedly accurate estimates of surface nor- mals in the presence of signicant amount of shadows and specularities. The new technique can be used to improve virtually any photometric stereo method including uncalibrated photometric stereo.
Computer Vision - ACCV 2010 - 10th Asian Conference on Computer Vision, Queenstown, New Zealand, November 8-12, 2010, Revised Selected Papers, Part III; 01/2010
[show abstract][hide abstract] ABSTRACT: l1-minimization refers to finding the minimum l1-norm solution to an
underdetermined linear system b=Ax. It has recently received much attention,
mainly motivated by the new compressive sensing theory that shows that under
quite general conditions the minimum l1-norm solution is also the sparsest
solution to the system of linear equations. Although the underlying problem is
a linear program, conventional algorithms such as interior-point methods suffer
from poor scalability for large-scale real world problems. A number of
accelerated algorithms have been recently proposed that take advantage of the
special structure of the l1-minimization problem. In this paper, we provide a
comprehensive review of five representative approaches, namely, Gradient
Projection, Homotopy, Iterative Shrinkage-Thresholding, Proximal Gradient, and
Augmented Lagrange Multiplier. The work is intended to fill in a gap in the
existing literature to systematically benchmark the performance of these
algorithms using a consistent experimental setting. In particular, the paper
will focus on a recently proposed face recognition algorithm, where a sparse
representation framework has been used to recover human identities from facial
images that may be affected by illumination, occlusion, and facial disguise.
MATLAB implementations of the algorithms described in this paper have been made
[show abstract][hide abstract] ABSTRACT: This paper studies algorithms for solving the prob- lem of recovering a low-rank matrix with a fraction of its entries arbitrarily corrupted. This problem can be viewed as a robust version of classical PCA, and arises in a number of application domains, including image processing, web data ranking, and bioinformatic data analysis. It was recently shown that under surprisingly broad conditions, it can be exactly solved via a convex programming surrogate that combines nuclear norm minimization and ' 1 -norm minimization. This paper develops and compares two complementary approaches for solving this convex program. The first is an accelerated proximal gradient algorithm directly applied to the primal; while the second is a gradient algorithm applied to the dual problem. Both are several orders of magnitude faster than the previous state- of-the-art algorithm for this problem, which was based on iterative thresholding. Simulations demonstrate the performance improvement that can be obtained via these two algorithms, and clarify their relative merits.