Joint Transformation Learning via the L2,1-Norm Metric for Robust Graph Matching

Enhanced robust spatial feature selection and correlation filter learning for UAV tracking

Spatial boundary effect can significantly reduce the performance of a learned discriminative correlation filter (DCF) model. A commonly used method to relieve this effect is to extract appearance features from a wider region of a target. However, this way would introduce unexpected features from background pixels and noises, which will lead to a decrease of the filter's discrimination power. To address this shortcoming, this paper proposes an innovative method called enhanced robust spatial feature selection and correlation filter Learning (EFSCF), which performs jointly sparse feature learning to handle boundary effects effectively while suppressing the influence of background pixels and noises. Unlike the ℓ₂-norm-based tracking approaches that are prone to non-Gaussian noises, the proposed method imposes the ℓ_2,1-norm on the loss term to enhance the robustness against the training outliers. To enhance the discrimination further, a jointly sparse feature selection scheme based on the ℓ_2,1 -norm is designed to regularize the filter in rows and columns simultaneously. To the best of the authors' knowledge, this has been the first work exploring the structural sparsity in rows and columns of a learned filter simultaneously. The proposed model can be efficiently solved by an alternating direction multiplier method. The proposed EFSCF is verified by experiments on four challenging unmanned aerial vehicle datasets under severe noise and appearance changes, and the results show that the proposed method can achieve better tracking performance than the state-of-the-art trackers.

Elastic Net Constraint-Based Tensor Model for High-Order Graph Matching

The procedure of establishing the correspondence between two sets of feature points is important in computer vision applications. In this article, an elastic net constraint-based tensor model is proposed for high-order graph matching. To control the tradeoff between the sparsity and the accuracy of the matching results, an elastic net constraint is introduced into the tensor-based graph matching model. Then, a nonmonotone spectral projected gradient (NSPG) method is derived to solve the proposed matching model. During the optimization of using NSPG, we propose an algorithm to calculate the projection on the feasible convex sets of elastic net constraint. Further, the global convergence of solving the proposed model using the NSPG method was proved. The superiority of the proposed method is verified through experiments on the synthetic data and natural images.

Revisiting L2,1-Norm Robustness With Vector Outlier Regularization

In many real-world applications, data usually contain outliers. One popular approach is to use the L_2,1 -norm function as a robust loss/error function. However, the robustness of the L_2,1 -norm function is not well understood so far. In this brief, we propose a new vector outlier regularization (VOR) framework to understand and analyze the robustness of the L_2,1 -norm function. Our VOR function defines a data point to be the outlier if it is outside a threshold with respect to a theoretical prediction, and regularizes it, i.e., pull it back to the threshold line. Thus, in the VOR function, how far an outlier lies away from its theoretical predicted value does not affect the final regularization and analysis results. One important aspect of the VOR function is that it has an equivalent continuous formulation, based on which we can prove that the L_2,1 -norm function is the limiting case of the proposed VOR function. Based on this theoretical result, we thus provide a new and intuitive explanation for the robustness property of the L_2,1 -norm function. As an example, we use the VOR function to matrix factorization and propose a VOR principal component analysis (PCA) (VORPCA). We show some benefits of VORPCA on data reconstruction and clustering tasks.