  Robust fitting is a fundamental problem in low-level vision, which is
typically achieved by maximum consensus (MC) estimators to identify inliers
first or by M-estimators directly. While these two methods are discriminately
preferred in different applications, truncated loss based M-estimators are
similar to MC as they can also identify inliers. This work revisits a
formulation that achieves simultaneous inlier identification and model
estimation (SIME) using truncated loss. It has a generalized form adapts to
both linear and nonlinear residual models. We show that as SIME takes fitting
residual into account in finding inliers, its lowest achievable residual in
model fitting is lower than that of MC robust fitting. Then, an alternating
minimization (AM) algorithm is employed to solve the SIME formulation.
Meanwhile, a semidefinite relaxation (SDR) embedded AM algorithm is developed
in order to ease the high nonconvexity of the SIME formulation. Furthermore,
the new algorithms are applied to various 2D/3D registration problems.
Experimental results show that the new algorithms significantly outperform
RANSAC and deterministic approximate MC methods at high outlier ratios.
Besides, in rotation and Euclidean registration problems, the new algorithms
also compare favorably with state-of-the-art registration methods, especially
in high noise and outliers. Code is available at
\textit{https://github.com/FWen/mcme.git}.
