The min-max multiple traveling salesman problem (min-max mTSP) is a significant variant of the min-max routing problem, focusing on minimizing the longest subtour cost among multiple salesmen working cooperatively. This problem is highly relevant in real-world scenarios but is notoriously challenging, especially as the scale increases with numerous salesmen covering thousands of cities. This paper presents a novel approach for solving large-scale min-max mTSP. Our method, based on deep reinforcement learning, introduces a novel two-stage process. In the first stage, we generate an initial solution using a constructive model incorporating global and local attention mechanisms through a gated network. Additionally, we employ multi-task training on a single constructive model across various mTSP problems with differing numbers of salesmen, using weighted task balancing to balance the multi-task learning process. In the second stage, the initial solution is iteratively refined using improvement policy, which re-optimizes the current subtours to form a new better one. To the best of our knowledge, our method is the first capable of handling problems with up to 10,000 nodes. The experimental results demonstrate that our approach achieves the best solution on 71% of the problems in randomly uniform datasets, outperforming all existing methods. Our code is available athttps://github.com/1hhix/CMIP

Currently, the development of the foundation model, metaverse, nonfungible token (NFT), and other emerging technologies has brought profound effects on the whole art field, including art creation, dissemination, transaction, etc. However, there is no research focusing on the framework, methodologies, and applications of the human–machine collaborative creation in the metaverse era. Based on parallel theory, this article proposes a novel human–machine collaborative creation paradigm called ArtVerse, in which machines take on the roles of humans to perform creation exploration and evolution and build decentralized art organizations. Besides, the operational processes involving several key technologies are designed to achieve the proposed ArtVerse. Then, a prototype system of ArtVerse, our long-term efforts toward the human–machine collaborative painting, is presented. Finally, a new ecology of artistic creation in the metaverse era is demonstrated through the applications of the ArtVerse.

In this paper, we present a novel appearance model using sparse representation and online dictionary learning techniques for visual tracking. In our approach, the visual appearance is represented by sparse representation, and the online dictionary learning strategy is used to adapt the appearance variations during tracking. We unify the sparse representation and online dictionary learning by defining a sparsity consistency constraint that facilitates the generative and discriminative capabilities of the appearance model. An elastic-net constraint is enforced during the dictionary learning stage to capture the characteristics of the local appearances that are insensitive to partial occlusions. Hence, the target appearance is effectively recovered from the corruptions using the sparse coefficients with respect to the learned sparse bases containing local appearances. In the proposed method, the dictionary is undercomplete and can thus be efficiently implemented for tracking. Moreover, we employ a median absolute deviation based robust similarity metric to eliminate the outliers and evaluate the likelihood between the observations and the model. Finally, we integrate the proposed appearance model with the particle filter framework to form a robust visual tracking algorithm. Experiments on benchmark video sequences show that the proposed appearance model outperforms the other state-of-the-art approaches in tracking performance.

In this paper, an online visual object tracking algorithm based on the discriminative sparse representation framework with supervised learning is proposed. Different from the generative sparse representation based tracking algorithms, the proposed method casts the tracking problem into a binary classification task. A linear classifier is embedded into the sparse representation model by incorporating the classification error into the objective function to achieve discriminative classification. The dictionary and the classifier are jointly trained using the online dictionary learning algorithm, thus allow the model can adapt the dynamic variations of target appearance and background environment. The target locations are updated based on the classification score and the greedy search motion model. The proposed method is evaluated using four benchmark datasets and is compared with three state-of-the-art tracking algorithms. The results show that the discriminative sparse representation facilitates the tracking performance.

In this work, we propose a robust and flexible appearance model based on the structured sparse representation framework. In our method, we model the complex nonlinear appearance manifold and the occlusion as a sparse linear combination of structured union of subspaces in a basis library, which consists of multiple incremental learned target subspaces and a partitioned occlusion template set. In order to enhance the discriminative power of the model, a number of clustered background subspaces are also added into the basis library and updated during tracking. With the Block Orthogonal Matching Pursuit (BOMP) algorithm, we show that the new flexible structured sparse representation based appearance model facilitates the tracking performance compared with the prototype structured sparse representation model and other state of the art tracking algorithms.

Tracking multiple moving targets in a video is a challenge because of several factors, including noisy video data, varying number of targets, and mutual occlusion problems. The Gaussian mixture probability hypothesis density (GM-PHD) filter, which aims to recursively propagate the intensity associated with the multi-target posterior density, can overcome the difficulty caused by the data association. This paper develops a multi-target visual tracking system that combines the GM-PHD filter with object detection. First, a new birth intensity estimation algorithm based on entropy distribution and coverage rate is proposed to automatically and accurately track the newborn targets in a noisy video. Then, a robust game-theoretical mutual occlusion handling algorithm with an improved spatial color appearance model is proposed to effectively track the targets in mutual occlusion. The spatial color appearance model is improved by incorporating interferences of other targets within the occlusion region. Finally, the experiments conducted on publicly available videos demonstrate the good performance of the proposed visual tracking system.

This paper presents a novel algorithm for robust visual object tracking based on the structured sparse representation framework. Conventional structured sparse representation based tracker models the nonlinear appearance manifold with a single subspace that is difficult to handle significant pose and illumination changes. Different from the afore-mentioned method, the proposed algorithm approximates the nonlinear appearance manifold by multiple low dimensional subspaces computed by an incremental learning scheme based on the merging and insert strategy. In order to enhance the discriminative power of the model, a number of clustered background subspaces are also added into the basis library and updated during tracking. With the Block Orthogonal Matching Pursuit (BOMP) algorithm, we show that the complex nonlinear appearance manifold can effectively represent by a sparse linear combination of structured union of subspaces. Experiments on benchmark video sequences show that the new structured sparse representation model improves the robustness of tracking.

Tracking multiple moving targets in video is still a challenge because of mutual occlusion problem. This paper presents a Gaussian mixture probability hypothesis density-based visual tracking system with game theory-based mutual occlusion handling. First, a two-step occlusion reasoning algorithm is proposed to determine the occlusion region. Then, the spatial constraint-based appearance model with other interacting targets¶ interferences is modeled. Finally, an n-person, non-zero-sum, non-cooperative game is constructed to handle the mutual occlusion problem. The individual measurements within the occlusion region are regarded as the players in the constructed game competing for the maximum utilities by using the certain strategies. The Nash Equilibrium of the game is the optimal estimation of the locations of the players within the occlusion region. Experiments conducted on publicly available videos demonstrate the good performance of the proposed occlusion handling algorithm.

We present a novel appearance model using sparse coding with online sparse dictionary learning techniques for robust visual tracking. In the proposed appearance model, the target appearance is modeled via online sparse dictionary learning technique with an “elastic-net constraint”. This scheme allows us to capture the characteristics of the target local appearance, and promotes the robustness against partial occlusions during tracking. Additionally, we unify the sparse coding and online dictionary learning by defining a “sparsity consistency constraint” that facilitates the generative and discriminative capabilities of the appearance model. Moreover, we propose a robust similarity metric that can eliminate the outliers from the corrupted observations. We then integrate the proposed appearance model with the particle filter framework to form a robust visual tracking algorithm. Experiments on publicly available benchmark video sequences demonstrate that the proposed appearance model improves the tracking performance compared with other state-of-the-art approaches.

Multi-target tracking in video is a challenge due to noisy video data, varying number of targets, and the data association problems. In this paper, a multi-target visual tracking system that incorporates object detection with the Gaussian mixture PHD filter is developed. The main contribution of this paper is to propose a new birth intensity online estimation method that based on the entropy distribution and the coverage rate. First, the birth intensity is initialized by using the previously obtained targets' states and measurements. The measurements are obtained by object detection and classified into the birth measurements and the survival measurements. Then it is updated according to the currently obtained birth measurements. In the update stage, the instability of the entropy distribution is applied to remove components like noises within the birth intensity which are irrelevant with the currently obtained birth measurements. And the coverage rate between each birth intensity component and corresponding birth measurement is computed to further eliminate the noises. Finally, experiments are implemented to show the performance of the proposed visual tracking system, especially to show the good performance for tracking the newborn targets.

We propose a robust visual tracker based on structured sparse representation appearance model. The appearance of tracking target is modeled as a sparse linear combination of Eigen templates plus a sparse error due to occlusions. We address the structured sparse representation that preferably matches the practical visual tracking problem by taking the contiguous spatial distribution of occlusion into account. The sparsity is achieved by Block Orthogonal Matching Pursuit (BOMP) for solving structured sparse representation problem more efficiently. The model update scheme, based on incremental Singular Value Decomposition (SVD), guarantees the Eigen templates that are able to capture the variations of target appearance online. Then the approximation error is adopted to build a probabilistic observation model that integrates with a stochastic affine motion model to form a particle filter framework for visual tracking. Thanks to the block structure of sparse representation and BOMP, our proposed tracker demonstrates superiority on both efficiency and robustness improvement in comparison experiments with publicly available benchmark video sequences.