Non-sparse Linear Representations for Visual Tracking with Online Reservoir Metric Learning

Most sparse linear representation-based trackers need to solve a computationally expensive L1-regularized optimization problem. To address this problem, we propose a visual tracker based on non-sparse linear representations, which admit an efficient closed-form solution without sacrificing accuracy. Moreover, in order to capture the correlation information between different feature dimensions, we learn a Mahalanobis distance metric in an online fashion and incorporate the learned metric into the optimization problem for obtaining the linear representation. We show that online metric learning using proximity comparison significantly improves the robustness of the tracking, especially on those sequences exhibiting drastic appearance changes. Furthermore, in order to prevent the unbounded growth in the number of training samples for the metric learning, we design a time-weighted reservoir sampling method to maintain and update limited-sized foreground and background sample buffers for balancing sample diversity and adaptability. Experimental results on challenging videos demonstrate the effectiveness and robustness of the proposed tracker.Comment: Appearing in IEEE Conf. Computer Vision and Pattern Recognition, 201

LCOT: Linear circular optimal transport

The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e., probability measures supported on the unit circle, and introduce a new computationally efficient metric for these measures, denoted as Linear Circular Optimal Transport (LCOT). The proposed metric comes with an explicit linear embedding that allows one to apply Machine Learning (ML) algorithms to the embedded measures and seamlessly modify the underlying metric for the ML algorithm to LCOT. We show that the proposed metric is rooted in the Circular Optimal Transport (COT) and can be considered the linearization of the COT metric with respect to a fixed reference measure. We provide a theoretical analysis of the proposed metric and derive the computational complexities for pairwise comparison of circular probability measures. Lastly, through a set of numerical experiments, we demonstrate the benefits of LCOT in learning representations of circular measures

Learning Non-Metric Visual Similarity for Image Retrieval

Measuring visual similarity between two or more instances within a data distribution is a fundamental task in image retrieval. Theoretically, non-metric distances are able to generate a more complex and accurate similarity model than metric distances, provided that the non-linear data distribution is precisely captured by the system. In this work, we explore neural networks models for learning a non-metric similarity function for instance search. We argue that non-metric similarity functions based on neural networks can build a better model of human visual perception than standard metric distances. As our proposed similarity function is differentiable, we explore a real end-to-end trainable approach for image retrieval, i.e. we learn the weights from the input image pixels to the final similarity score. Experimental evaluation shows that non-metric similarity networks are able to learn visual similarities between images and improve performance on top of state-of-the-art image representations, boosting results in standard image retrieval datasets with respect standard metric distances