Navigating robots safely and efficiently in crowded and complex environments remains a significant challenge. However, due to the dynamic and intricate nature of these settings, planning efficient and collision-free paths for robots to track is particularly difficult. In this paper, we uniquely bridge the robot’s perception, decision-making and control processes by utilizing the convex obstacle-free region computed from 2D LiDAR data. The overall pipeline is threefold: (1) We proposes a robot navigation framework that utilizes deep reinforcement learning (DRL), conceptualizing the observation as the convex obstacle-free region, a departure from general reliance on raw sensor inputs. (2) We design the action space, derived from the intersection of the robot’s kinematic limits and the convex region, to enable efficient sampling of inherently collision-free reference points. These actions assists in guiding the robot to move towards the goal and interact with other obstacles during navigation. (3) We employ model predictive control (MPC) to track the trajectory formed by the reference points while satisfying constraints imposed by the convex obstacle-free region and the robot’s kinodynamic limits. The effectiveness of proposed improvements has been validated through two sets of ablation studies and a comparative experiment against the Timed Elastic Band (TEB), demonstrating improved navigation performance in crowded and complex environments.

Convolutional neural networks (CNNs) usually come with numerous parameters and thus are not convenient for some situations, such as when the storage space is limited. Low-rank decomposition is one effective way for network compression or compaction. However, the current methods are far from theoretical optimal compression performance because the low-rankness of the commonly trained convolution filter sets is limited because of the versatility of convolution filters. We propose a novel compact design for convolutional layers with spatial transformation for achieving a much lower-rank form. The convolution filters in our design are generated using a predefined Tucker product form, followed by learnable individual spatial transformations on each filter. The low-rank (Tucker) part lowers the parameter capacity while the transformation part enhances the feature representation capacity. We validate our proposed approach on an image classification task. Our approach focuses on compressing parameters while also improving accuracy. We perform experiments on the MNIST, CIFAR10, CIFAR100, and ImageNet datasets. On the ImageNet dataset, our approach outperforms low-rank based state-of-the-arts by 2% to 6% in top-1 validation accuracy. Furthermore, our approach outperforms a series of low-rank-based state-of-the-arts on various datasets. The experiments validate the efficacy of our proposed method. Our code is available at https://github.com/liubc17/low_rank_compact_transformed.

Tensor completion methods based on the tensor train (TT) have the issues of inaccurate weight assignment and ineffective tensor augmentation pre-processing. In this work, we propose a novel tensor completion approach via the element-wise weighted technique. Accordingly, a novel formulation for tensor completion and an effective optimization algorithm, called tensor completion by parallel weighted matrix factorization via tensor train (TWMac-TT), is proposed. In addition, we specifically consider the recovery quality of edge elements from adjacent blocks. Different from traditional reshaping and ket augmentation, we utilize a new tensor augmentation technique called overlapping ket augmentation, which can further avoid blocking artifacts. We then conduct extensive performance evaluations on synthetic data and several real image data sets. Our experimental results demonstrate that the proposed algorithm TWMac-TT outperforms several other competing tensor completion methods. The code is available athttps://github.com/yzcv/TWMac-TT-OKA

Falling snow not only blocks human vision, but also significantly degrades the effectiveness of computer vision systems in outdoor environment. In this paper, we aim to remove snowflakes in videos by using the global and local low-rank property of snowflake-removed scenes. The stationary background and the mixture of moving foreground as well as falling snowflake are extracted via the global low-rank matrix decomposition. Some snowflake features, such as its color and size, are used to separate out the snowflakes from other moving objects. Then, the mean absolute difference based patch matching is applied to align every same moving object over frames to grab its low-rank structure. As such, the falling snowflake in front of moving objects can be removed via the local low-rank decomposition. Finally, the snowflake removed videos are generated by pasting moving foreground to stationary backgrounds. Experiments show that our method can remove snowflakes effectively and outperforms the comparison methods.

The low-rank tensor factorization (LRTF) technique has received increasing attention in many computer vision applications. Compared with the traditional matrix factorization technique, it can better preserve the intrinsic structure information and thus has a better low-dimensional subspace recovery performance. Basically, the desired low-rank tensor is recovered by minimizing the least square loss between the input data and its factorized representation. Since the least square loss is most optimal when the noise follows a Gaussian distribution, -norm-based methods are designed to deal with outliers. Unfortunately, they may lose their effectiveness when dealing with real data, which are often contaminated by complex noise. In this paper, we consider integrating the noise modeling technique into a generalized weighted LRTF (GWLRTF) procedure. This procedure treats the original issue as an LRTF problem and models the noise using a mixture of Gaussians (MoG), a procedure called MoG GWLRTF. To extend the applicability of the model, two typical tensor factorization operations, i.e., CANDECOMP/PARAFAC factorization and Tucker factorization, are incorporated into the LRTF procedure. Its parameters are updated under the expectation-maximization framework. Extensive experiments indicate the respective advantages of these two versions of MoG GWLRTF in various applications and also demonstrate their effectiveness compared with other competing methods.

The RPCA model has achieved good performances in various applications. However, two defects limit its effectiveness. Firstly, it is designed for dealing with data in matrix form, which fails to exploit the structure information of higher order tensor data in some pratical situations. Secondly, it adopts L1-norm to tackle noise part which makes it only valid for sparse noise. In this paper, we propose a tensor RPCA model based on CP decomposition and model data noise by Mixture of Gaussians (MoG). The use of tensor structure to raw data allows us to make full use of the inherent structure priors, and MoG is a general approximator to any blends of consecutive distributions, which makes our approach capable of regaining the low dimensional linear subspace from a wide range of noises or their mixture. The model is solved by a new proposed algorithm inferred under a variational Bayesian framework. The superiority of our approach over the existing state-of-the-art approaches is demonstrated by extensive experiments on both of synthetic and real data.

Because of the limitations of matrix factorization, such as losing spatial structure information, the concept of tensor factorization has been applied for the recovery of a low dimensional subspace from high dimensional visual data. Generally, the recovery is achieved by minimizing the loss function between the observed data and the factorization representation. Under different assumptions of the noise distribution, the loss functions are in various forms, like L1 and L2 norms. However, real data are often corrupted by noise with an unknown distribution. Then any specific form of loss function for one specific kind of noise often fails to tackle such real data with unknown noise. In this paper, we propose a tensor factorization algorithm to model the noise as a Mixture of Gaussians (MoG). As MoG has the ability of universally approximating any hybrids of continuous distributions, our algorithm can effectively recover the low dimensional subspace from various forms of noisy observations. The parameters of MoG are estimated under the EM framework and through a new developed algorithm of weighted low-rank tensor factorization (WLRTF). The effectiveness of our algorithm are substantiated by extensive experiments on both of synthetic data and real image data.