Wenlong Zhang

Zhiming Chen, Rui Tuo, Wenlong Zhang

The thin plate spline smoother is a classical model for fnding a smooth function from the knowledge of its observation at scattered locations which may have random noises. We consider a nonconforming Morley finite element method to approximate the model. We prove the stochastic convergence of the finite element method which characterizes the tail property of the probability distribution function of the finite element error. We also propose a self-consistent iterative algorithm to determine the smoothing parameter based on our theoretical analysis. Numerical examples are included to confirm the theoretical analysis and to show the competitive performance of the self- consistent algorithm for finding the smoothing parameter.

Xiangtao Kong, Jinjin Gu, Yihao Liu et al.

Despite the tremendous success of deep models in various individual image restoration tasks, there are at least two major technical challenges preventing these works from being applied to real-world usages: (1) the lack of generalization ability and (2) the complex and unknown degradations in real-world scenarios. Existing deep models, tailored for specific individual image restoration tasks, often fall short in effectively addressing these challenges. In this paper, we present a new problem called general image restoration (GIR) which aims to address these challenges within a unified model. GIR covers most individual image restoration tasks (\eg, image denoising, deblurring, deraining and super-resolution) and their combinations for general purposes. This paper proceeds to delineate the essential aspects of GIR, including problem definition and the overarching significance of generalization performance. Moreover, the establishment of new datasets and a thorough evaluation framework for GIR models is discussed. We conduct a comprehensive evaluation of existing approaches for tackling the GIR challenge, illuminating their strengths and pragmatic challenges. By analyzing these approaches, we not only underscore the effectiveness of GIR but also highlight the difficulties in its practical implementation. At last, we also try to understand and interpret these models' behaviors to inspire the future direction. Our work can open up new valuable research directions and contribute to the research of general vision.

Zhiming Chen, Rui Tuo, Wenlong Zhang

In this paper we propose a finite element method for solving elliptic equations with the observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier. We show the convergence of the random finite element error in expectation and, when the noise is sub-Gaussian, in the Orlicz 2- norm which implies the probability that the finite element error estimates are violated decays exponentially. Numerical examples are included.

Xiaoyu Yue, Zidong Wang, Yuqing Wang et al.

Recent studies have demonstrated the importance of high-quality visual representations in image generation and have highlighted the limitations of generative models in image understanding. As a generative paradigm originally designed for natural language, autoregressive models face similar challenges. In this work, we present the first systematic investigation into the mechanisms of applying the next-token prediction paradigm to the visual domain. We identify three key properties that hinder the learning of high-level visual semantics: local and conditional dependence, inter-step semantic inconsistency, and spatial invariance deficiency. We show that these issues can be effectively addressed by introducing self-supervised objectives during training, leading to a novel training framework, Self-guided Training for AutoRegressive models (ST-AR). Without relying on pre-trained representation models, ST-AR significantly enhances the image understanding ability of autoregressive models and leads to improved generation quality. Specifically, ST-AR brings approximately 42% FID improvement for LlamaGen-L and 49% FID improvement for LlamaGen-XL, while maintaining the same sampling strategy.

Aniket Shirsat, Shatadal Mishra, Wenlong Zhang et al.

In this paper, we present a consensus-based decentralized multi-robot approach to reconstruct a discrete distribution of features, modeled as an occupancy grid map, that represent information contained in a bounded planar 2D environment, such as visual cues used for navigation or semantic labels associated with object detection. The robots explore the environment according to a random walk modeled by a discrete-time discrete-state (DTDS) Markov chain and estimate the feature distribution from their own measurements and the estimates communicated by neighboring robots, using a distributed Chernoff fusion protocol. We prove that under this decentralized fusion protocol, each robot's feature distribution converges to the ground truth distribution in an almost sure sense. We verify this result in numerical simulations that show that the Hellinger distance between the estimated and ground truth feature distributions converges to zero over time for each robot. We also validate our strategy through Software-In-The-Loop (SITL) simulations of quadrotors that search a bounded square grid for a set of visual features distributed on a discretized circle.

Karishma Patnaik, Shatadal Mishra, Zachary Chase et al.

Autonomous missions of small unmanned aerial vehicles (UAVs) are prone to collisions owing to environmental disturbances and localization errors. Consequently, a UAV that can endure collisions and perform recovery control in critical aerial missions is desirable to prevent loss of the vehicle and/or payload. We address this problem by proposing a novel foldable quadrotor system which can sustain collisions and recover safely. The quadrotor is designed with integrated mechanical compliance using a torsional spring such that the impact time is increased and the net impact force on the main body is decreased. The post-collision dynamics is analysed and a recovery controller is proposed which stabilizes the system to a hovering location without additional collisions. Flight test results on the proposed and a conventional quadrotor demonstrate that for the former, integrated spring-damper characteristics reduce the rebound velocity and lead to simple recovery control algorithms in the event of unintended collisions as compared to a rigid quadrotor of the same dimension.

Geoffrey Clark, Joseph Campbell, Seyed Mostafa Rezayat Sorkhabadi et al.

We propose in this paper Periodic Interaction Primitives - a probabilistic framework that can be used to learn compact models of periodic behavior. Our approach extends existing formulations of Interaction Primitives to periodic movement regimes, i.e., walking. We show that this model is particularly well-suited for learning data-driven, customized models of human walking, which can then be used for generating predictions over future states or for inferring latent, biomechanical variables. We also demonstrate how the same framework can be used to learn controllers for a robotic prosthesis using an imitation learning approach. Results in experiments with human participants indicate that Periodic Interaction Primitives efficiently generate predictions and ankle angle control signals for a robotic prosthetic ankle, with MAE of 2.21 degrees in 0.0008s per inference. Performance degrades gracefully in the presence of noise or sensor fall outs. Compared to alternatives, this algorithm functions 20 times faster and performed 4.5 times more accurately on test subjects.

Yi Ren, Steven Elliott, Yiwei Wang et al.

While intelligence of autonomous vehicles (AVs) has significantly advanced in recent years, accidents involving AVs suggest that these autonomous systems lack gracefulness in driving when interacting with human drivers. In the setting of a two-player game, we propose model predictive control based on social gracefulness, which is measured by the discrepancy between the actions taken by the AV and those that could have been taken in favor of the human driver. We define social awareness as the ability of an agent to infer such favorable actions based on knowledge about the other agent's intent, and further show that empathy, i.e., the ability to understand others' intent by simultaneously inferring others' understanding of the agent's self intent, is critical to successful intent inference. Lastly, through an intersection case, we show that the proposed gracefulness objective allows an AV to learn more sophisticated behavior, such as passive-aggressive motions that gently force the other agent to yield.

Mohammad Sharifzadeh, Roozbeh Khodambashi, Wenlong Zhang et al.

Many different robots have been designed and built to work under water. In many cases, researchers have chosen to use bio-inspired platforms. In most cases, the main goal of the fish inspired robots has been set to autonomously swim and maneuver in an environment spacious compared to the fish's size. In this paper, the identification control of a low-cost fish-inspired robot is studied with the goal of building a mechanism to not only swim in water but able to interact with its narrow environment. The robotic fish under study uses tail propulsion as main locomotion. Moreover, proper propulsion regimes are identified and used to model and control thrust generated by propulsion.

Ioannis Papavasileiou, Wenlong Zhang, Xin Wang et al.

As our population ages, neurological impairments and degeneration of the musculoskeletal system yield gait abnormalities, which can significantly reduce quality of life. Gait rehabilitative therapy has been widely adopted to help patients maximize community participation and living independence. To further improve the precision and efficiency of rehabilitative therapy, more objective methods need to be developed based on sensory data. In this paper, an algorithmic framework is proposed to provide classification of gait disorders caused by two common neurological diseases, stroke and Parkinson's Disease (PD), from ground contact force (GCF) data. An advanced machine learning method, multi-task feature learning (MTFL), is used to jointly train classification models of a subject's gait in three classes, post-stroke, PD and healthy gait. Gait parameters related to mobility, balance, strength and rhythm are used as features for the classification. Out of all the features used, the MTFL models capture the more important ones per disease, which will help provide better objective assessment and therapy progress tracking. To evaluate the proposed methodology we use data from a human participant study, which includes five PD patients, three post-stroke patients, and three healthy subjects. Despite the diversity of abnormalities, the evaluation shows that the proposed approach can successfully distinguish post-stroke and PD gait from healthy gait, as well as post-stroke from PD gait, with Area Under the Curve (AUC) score of at least 0.96. Moreover, the methodology helps select important gait features to better understand the key characteristics that distinguish abnormal gaits and design personalized treatment.