Total Variation Regularization Term-Based Low-Rank and Sparse Matrix Representation Model for Infrared Moving Target Tracking

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the general affine rank minimization problem is NP-hard. In this paper, we show that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds with overwhelming probability. The techniques used in our analysis have strong parallels in the compressed sensing framework. We discuss how affine rank minimization generalizes this pre-existing concept and outline a dictionary relating concepts from cardinality minimization to those of rank minimization.

Object tracking has been one of the most important and active research areas in the field of computer vision. A large number of tracking algorithms have been proposed in recent years with demonstrated success. However, the set of sequences used for evaluation is often not sufficient or is sometimes biased for certain types of algorithms. Many datasets do not have common ground-truth object positions or extents, and this makes comparisons among the reported quantitative results difficult. In addition, the initial conditions or parameters of the evaluated tracking algorithms are not the same, and thus, the quantitative results reported in literature are incomparable or sometimes contradictory. To address these issues, we carry out an extensive evaluation of the state-of-the-art online object-tracking algorithms with various evaluation criteria to understand how these methods perform within the same framework. In this work, we first construct a large dataset with ground-truth object positions and extents for tracking and introduce the sequence attributes for the performance analysis. Second, we integrate most of the publicly available trackers into one code library with uniform input and output formats to facilitate large-scale performance evaluation. Third, we extensively evaluate the performance of 31 algorithms on 100 sequences with different initialization settings. By analyzing the quantitative results, we identify effective approaches for robust tracking and provide potential future research directions in this field.