Generalized projection based M-estimator: Theory and applications

Abstract

We introduce a robust estimator called generalized projection based M-estimator (gpbM) which does not require the user to specify any scale parameters. For multiple inlier structures, with different noise covariances, the estimator iteratively determines one inlier structure at a time. Unlike pbM, where the scale of the inlier noise is estimated simultaneously with the model parameters, gpbM has three distinct stages -scale estimation, robust model estimation and inlier/outlier dichotomy. We evaluate our performance on challenging synthetic data, face image clustering upto ten different faces from Yale Face Database B and multi-body projective motion segmentation problem on Hopkins155 dataset. Results of state-of-the-art methods are presented for comparison.

Conjugate gradient on Grassmann manifolds for robust subspace estimation

“…The generalized projection based M-estimator (gpbM), introduced recently in [22], is a robust subspace estimation algorithm. Both the number of inlier structures and the scale of inlier noise are estimated automatically without any user intervention.…”

“…See [27] for a brief description of these methods. Recently, the projection based M-estimator (pbM) of [34] was extended to the generalized pbM (gpbM) [22]. The main advantage of pbM and gpbM over RAN-SAC and RANSAC-like regression algorithms is that both pbM and gpbM do not require from the user an estimate of the scale of the noise corrupting inlier points.…”

“…In this paper, we extend the work of [22] to robustly estimate subspaces by using concepts of Riemannian geometry. While the main idea of work follows that of [34], it is different from [34] in a number of ways.…”

“…In the recent past, the problem of subspace estimation has been formulated in many different ways. Important methods include robust regression based approaches [34,22], spectral clustering based approaches [6,41] and clustering random hypothesis on Grassmann manifolds [35,2].…”

Robust shape from depth images with GR2T

“…the Hough transform [30,29,31,32], M-estimators [33] and Generalized Projection Based M-Estimators [34,35]. When the densities function p is chosen differentiable, then the average likelihood can be optimised with standard stochastic exploration techniques and in particular with gradient ascent algorithms [28].…”