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

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**ABSTRACT:**In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate penalty term for matrix rank. The problem is that in many practical scenarios there is no longer any guarantee that we can correctly estimate generative low-rank matrices of interest, theoretical special cases notwithstanding. Consequently, this paper proposes an alternative empirical Bayesian procedure build upon a variational approximation that, unlike the nuclear norm, retains the same globally minimizing point estimate as the rank function under many useful constraints. However, locally minimizing solutions are largely smoothed away via marginalization, allowing the algorithm to succeed when standard convex relaxations completely fail. While the proposed methodology is generally applicable to a wide range of low-rank applications, we focus our attention on the robust principal component analysis problem (RPCA), which involves estimating an unknown low-rank matrix with unknown sparse corruptions. Theoretical and empirical evidence are presented to show that our method is potentially superior to related MAP-based approaches, for which the convex principle component pursuit (PCP) algorithm (Candes et al., 2011) can be viewed as a special case.07/2012; -
##### Conference Paper: Elevation angle from reflectance monotonicity: photometric stereo for general isotropic reflectances

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**ABSTRACT:**This paper exploits the monotonicity of general isotropic reflectances for estimating elevation angles of surface normal given the azimuth angles. With an assumption that the reflectance includes at least one lobe that is a monotonic function of the angle between the surface normal and half-vector (bisector of lighting and viewing directions), we prove that elevation angles can be uniquely determined when the surface is observed under varying directional lights densely and uniformly distributed over the hemisphere. We evaluate our method by experiments using synthetic and real data to show its wide applicability, even when the assumption does not strictly hold. By combining an existing method for azimuth angle estimation, our method derives complete surface normal estimates for general isotropic reflectances.Proceedings of the 12th European conference on Computer Vision - Volume Part III; 10/2012 -
##### Conference Paper: Heliometric stereo: shape from sun position

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**ABSTRACT:**In this work, we present a method to uncover shape from webcams "in the wild." We present a variant of photometric stereo which uses the sun as a distant light source, so that lighting direction can be computed from known GPS and timestamps. We propose an iterative, non-linear optimization process that optimizes the error in reproducing all images from an extended time-lapse with an image formation model that accounts for ambient lighting, shadows, changing light color, dense surface normal maps, radiometric calibration, and exposure. Unlike many approaches to uncalibrated outdoor image analysis, this procedure is automatic, and we report quantitative results by comparing extracted surface normals to Google Earth 3D models. We evaluate this procedure on data from a varied set of scenes and emphasize the advantages of including imagery from many months.Proceedings of the 12th European conference on Computer Vision - Volume Part II; 10/2012

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