Robust estimation for computer vision using Grassmann manifolds.
Saket Anand(1), Sushil Mittal(2), and Peter Meer(3)
(1) IIIT-Delhi, New Delhi, India
(2) Scibler Technologies, Santa Clara, USA
(3) Department of ECE, Rutgers University, Piscataway, NJ, USA
Real-world visual data is often corrupted and requires the use of
estimation techniques that are robust to noise and outliers. Robust
methods are well studied for Euclidean spaces and their use has
also been extended to Riemannian spaces. In this chapter, we present
the necessary mathematical
constructs for Grassmann manifolds, followed by two dirent algorithms
that can perform robust estimation on them. In the first one, we
describe a nonlinear mean shift algorithm for finding modes of the
underlying kernel density estimate (KDE). In the second one, a
user-independent robust regression algorithm, the generalized
projection based M-estimator (gpbM)
is detailed. We show that the gpbM estimates are significantly improved
if KDE optimization over the Grassmann manifold is also included.
The results for a few real-world computer vision problems are shown
to demonstrate the
importance of performing robust estimation using Grassmann manifolds.
Riemannian Computing in Computer Vision,
Co-editors: P.K. Turaga and A. Srivastava. Springer. Chapter 6.
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