A Simple Method for Subspace Estimation with Corrupted Columns

• This paper presents a simple and effective way of solving the robust subspace estimation problem where the corruptions are column-wise. The method we present can handle a large class of robust loss functions and is simple to implement. It is based on Iteratively Reweighted Least Squares (IRLS) and works in an iterative manner by solving a weighted least-squares rank-constrained problem in every iteration. By considering the special case of column-wise loss functions, we show that each such surrogate problem admits a closed form solution. Unlike many other approaches to subspace estimation, we make no relaxation of the low-rank constraint and our method is guaranteed to produce a subspace estimate with the correct dimension. Subspace estimation is a core problem for several applications in computer vision. We empirically demonstrate the performance of our method and compare it to several other techniques for subspace estimation. Experimental results are given for both synthetic and real image data including the following applications: linear shape basis estimation, plane fitting and non-rigid structure from motion.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Medicinteknik -- Medicinsk bildbehandling (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Medical Engineering -- Medical Image Processing (hsv//eng)

NATURVETENSKAP  -- Data- och informationsvetenskap -- Datorseende och robotik (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Computer Vision and Robotics (hsv//eng)

Keyword

Optimization

Estimation

Closed-form solutions

Robustness

Computer vision

Convergence

Shape

Closed-form solutions

Computer vision

Convergence

Estimation

Optimization

Robustness

Shape

Publication and Content Type

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