  Feature-based object matching is a fundamental problem for many applications
in computer vision, such as object recognition, 3D reconstruction, tracking,
and motion segmentation. In this work, we consider simultaneously matching
object instances in a set of images, where both inlier and outlier features are
extracted. The task is to identify the inlier features and establish their
consistent correspondences across the image set. This is a challenging
combinatorial problem, and the problem complexity grows exponentially with the
image number. To this end, we propose a novel framework, termed ROML, to
address this problem. ROML optimizes simultaneously a partial permutation
matrix (PPM) for each image, and feature correspondences are established by the
obtained PPMs. Two of our key contributions are summarized as follows. (1) We
formulate the problem as rank and sparsity minimization for PPM optimization,
and treat simultaneous optimization of multiple PPMs as a regularized consensus
problem in the context of distributed optimization. (2) We use the ADMM method
to solve the thus formulated ROML problem, in which a subproblem associated
with a single PPM optimization appears to be a difficult integer quadratic
program (IQP). We prove that under wildly applicable conditions, this IQP is
equivalent to a linear sum assignment problem (LSAP), which can be efficiently
solved to an exact solution. Extensive experiments on rigid/non-rigid object
matching, matching instances of a common object category, and common object
localization show the efficacy of our proposed method.
