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:**Subspace recovery from noisy or even corrupted data is crit-ical for various applications in machine learning and data analysis. To detect outliers, Robust PCA (R-PCA) via Out-lier Pursuit was proposed and had found many successful ap-plications. However, the current theoretical analysis on Out-lier Pursuit only shows that it succeeds when the sparsity of the corruption matrix is of O(n/r), where n is the number of the samples and r is the rank of the intrinsic matrix which may be comparable to n. Moreover, the regularization param-eter is suggested as 3/(7 √ γn), where γ is a parameter that is not known a priori. In this paper, with incoherence condi-tion and proposed ambiguity condition we prove that Outlier Pursuit succeeds when the rank of the intrinsic matrix is of O(n/ log n) and the sparsity of the corruption matrix is of O(n). We further show that the orders of both bounds are tight. Thus R-PCA via Outlier Pursuit is able to recover in-trinsic matrix of higher rank and identify much denser cor-ruptions than what the existing results could predict. More-over, we suggest that the regularization parameter be chosen as 1/ √ log n, which is definite. Our analysis waives the ne-cessity of tuning the regularization parameter and also sig-nificantly extends the working range of the Outlier Pursuit. Experiments on synthetic and real data verify our theories.AAAI Conference on Artificial Intelligence 2015; 01/2015 -
##### Conference Paper: Color Photometric Stereo Using a Rainbow Light for Non-Lambertian Multicolored Surfaces

Asian Conference on Computer Vision; 11/2014 -
##### 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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