Conference Paper

Robust Photometric Stereo via Low-Rank Matrix Completion and Recovery

DOI: 10.1007/978-3-642-19318-7_55 Conference: Computer Vision - ACCV 2010 - 10th Asian Conference on Computer Vision, Queenstown, New Zealand, November 8-12, 2010, Revised Selected Papers, Part III
Source: DBLP


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.

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    • "Several theoretical results quantify technical conditions whereby the solutions of (1) and (3) are actually equivalent using a suitable choice for α [6], [8]. Unfortunately, these conditions are highly restrictive and do not provably hold in practical situations of interest such as photometric stereo [41], face clustering [14], motion segmentation [14], or background subtraction [6]. Moreover, both the nuclear and 1 norms are highly sensitive to data variances, often over-shrinking large singular values of Z or coefficients in E [15]. "
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    ABSTRACT: Commonly used in computer vision and other applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into low rank and sparse components, the latter representing unwanted outliers. Although the resulting optimization problem is typically NP-hard, convex relaxations provide a computationally-expedient alternative with theoretical support. However, in practical regimes performance guarantees break down and a variety of non-convex alternatives, including Bayesian-inspired models, have been proposed to boost estimation quality. Unfortunately though, without additional a priori knowledge none of these methods can significantly expand the critical operational range such that exact principal subspace recovery is possible. Into this mix we propose a novel pseudo-Bayesian algorithm that explicitly compensates for design weaknesses in many existing non-convex approaches leading to state-of-the-art performance with a sound analytical foundation.
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    • "Several researchers have also sought to relax the Lambertian reflectance assumption and incorporate effects such as specular highlights and shadows. New techniques have been introduced based on non-Lambertian reflectance models [14], [15], [16], or sophisticated statistic methods to automatically filter nonlambertian effects [17], [18], [19]. However, less attention has been paid to relaxing assumptions on the lighting model. "
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    ABSTRACT: In this paper, we propose a near-light illuminationmodel for image relighting and 3D shape recovery. Classicmethods such as used by the popular RTI software from CulturalHeritage Imaging assume that lighting is infinitely far away fromthe scene. However, this constraint is impossible to achieve inpractice: light sources cannot be too far away from the scenedue to space and power constraints. This causes non uniform illumination artifacts due to variations in the distance betweenthe light source and points in the scene. We correct this effectto provide much more uniformly lit images that yield moreappealing image for relighting applications. Furthermore, weuse our near-light model for more accurate photometric stereocalculations of surface normals, eliminating the “potato-chip”shaped surface reconstruction error that results from violating thefar-light assumption. We verify our model with both free-formcapture using hand-held flash as the illumination source, andcapture using LED lights mounted on a dome shaped surface
    Full-text · Conference Paper · Sep 2015
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    • "Many recent works such as [37] [38] have shown that it is indeed possible to recover a low-rank matrix efficiently and exactly by convex optimization methods when a small number of samples or incomplete samples are available. Here, the SISR problem is recast as that of recovering and completing a low-rank augmented matrix (MCR) in the presence of random perturbations and noise (see [45]). This problem can be expressed as a rank minimization problem, which can be solved by the augmented Lagrange multiplier method (ALM) [46]. "
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    ABSTRACT: Methods of achieving image super-resolution (SR) have been the object of research for some time. These approaches suggest that when a low-resolution (LR) image is directly downsampled from its corresponding high-resolution (HR) image without blurring, i.e., the blurring kernel is the Dirac delta function, the reconstruction becomes an image-interpolation problem. Hence, this is a pervasive way to explore the linear relationship among neighboring pixels to reconstruct a HR image from a LR input image. This paper seeks an efficient method to determine the local order of the linear model implicitly. According to the theory of low-rank matrix completion and recovery, a method for performing single-image SR is proposed by formulating the reconstruction as the recovery of a low-rank matrix, which can be solved by the augmented Lagrange multiplier method. In addition, the proposed method can be used to handle noisy data and random perturbations robustly. The experimental results show that the proposed method is effective and competitive compared with other methods.
    Full-text · Article · Aug 2015 · IEEE Transactions on Circuits and Systems for Video Technology
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