Event camera is an emerging bio-inspired vision sensors that report per-pixel brightness changes asynchronously. It holds noticeable advantage of high dynamic range, high speed response, and low power budget that enable it to best capture local motions in uncontrolled environments. This motivates us to unlock the potential of event cameras for human pose estimation, as the human pose estimation with event cameras is rarely explored. Due to the novel paradigm shift from conventional frame-based cameras, however, event signals in a time interval contain very limited information, as event cameras can only capture the moving body parts and ignores those static body parts, resulting in some parts to be incomplete or even disappeared in the time interval. This paper proposes a novel densely connected recurrent architecture to address the problem of incomplete information. By this recurrent architecture, we can explicitly model not only the sequential but also non-sequential geometric consistency across time steps to accumulate information from previous frames to recover the entire human bodies, achieving a stable and accurate human pose estimation from event data. Moreover, to better evaluate our model, we collect a large scale multimodal event-based dataset that comes with human pose annotations, which is by far the most challenging one to the best of our knowledge. The experimental results on two public datasets and our own dataset demonstrate the effectiveness and strength of our approach. Code can be available online for facilitating the future research.
Washington University School of Medicine（华盛顿大学医学院）
Deep Learning networks have established themselves as providing state of art performance for semantic segmentation. These techniques are widely applied specifically to medical detection, segmentation and classification. The advent of the U-Net based architecture has become particularly popular for this application. In this paper we present the Dense Recurrent Residual Convolutional Neural Network(Dense R2U CNN) which is a synthesis of Recurrent CNN, Residual Network and Dense Convolutional Network based on the U-Net model architecture. The residual unit helps training deeper network, while the…
Rutgers University（罗格斯大学）；Binghamton University（宾厄姆顿大学）；IBM T. J. Watson（IBM T. J. 沃森研究中心）；SenseTime（商汤科技）
In this paper, we propose quantized densely connected U-Nets for efficient visual landmark localization. The idea is that features of the same semantic meanings are globally reused across the stacked U-Nets. This dense connectivity largely improves the information flow, yielding improved localization accuracy. However, a vanilla dense design would suffer from critical efficiency issue in both training and testing. To solve this problem, we first propose order-K dense connectivity to trim off long-distance shortcuts; then, we use a memory-efficient implementation to significantly boost the trai…
Conventional methods for human pose estimation either require a high degree of instrumentation, by relying on many inertial measurement units (IMUs), or constraint the recording space, by relying on extrinsic cameras. These deficits are tackled through the approach of human pose estimation from sparse IMU data. We define attention-oriented adjacency adaptive graph convolutional long-short term memory networks (A3GC-LSTM), to tackle human pose estimation based on six IMUs, through incorporating the human body graph structure directly into the network. The A3GC-LSTM combines both spatial and tem…
Visual Geometry Group（视觉几何组）；Department of Engineering Science（工程科学系）；University of Oxford（牛津大学）
We propose a novel ConvNet model for predicting 2D human body poses in an image. The model regresses a heatmap representation for each body keypoint, and is able to learn and represent both the part appearances and the context of the part configuration. We make the following three contributions: (i) an architecture combining a feed forward module with a recurrent module, where the recurrent module can be run iteratively to improve the performance, (ii) the model can be trained end-to-end and from scratch, with auxiliary losses incorporated to improve performance, (iii) we investigate whether k…
Although many approaches for multi-human pose estimation in videos have shown profound results, they require densely annotated data which entails excessive man labor. Furthermore, there exists occlusion and motion blur that inevitably lead to poor estimation performance. To address these problems, we propose a method that leverages an attention mask for occluded joints and encodes temporal dependency between frames using transformers. First, our framework composes different combinations of sparsely annotated frames that denote the track of the overall joint movement. We propose an occlusion at…
Shanghai Jiao Tong University（上海交通大学）；Zhejiang University（浙江大学）；Massachusetts Institute of Technology（麻省理工学院）
Deep convolutional neural networks (CNNs) have made impressive progress in many video recognition tasks such as video pose estimation and video object detection. However, CNN inference on video is computationally expensive due to processing dense frames individually. In this work, we propose a framework called Recurrent Residual Module (RRM) to accelerate the CNN inference for video recognition tasks. This framework has a novel design of using the similarity of the intermediate feature maps of two consecutive frames, to largely reduce the redundant computation. One unique property of the propo…
We observed that recent state-of-the-art results on single image human pose estimation were achieved by multi-stage Convolution Neural Networks (CNN). Notwithstanding the superior performance on static images, the application of these models on videos is not only computationally intensive, it also suffers from performance degeneration and flicking. Such suboptimal results are mainly attributed to the inability of imposing sequential geometric consistency, handling severe image quality degradation (e.g. motion blur and occlusion) as well as the inability of capturing the temporal correlation am…
The Johns Hopkins University Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）；The Johns Hopkins University（约翰斯·霍普金斯大学）
An object's geocentric pose, defined as the height above ground and orientation with respect to gravity, is a powerful representation of real-world structure for object detection, segmentation, and localization tasks using RGBD images. For close-range vision tasks, height and orientation have been derived directly from stereo-computed depth and more recently from monocular depth predicted by deep networks. For long-range vision tasks such as Earth observation, depth cannot be reliably estimated with monocular images. Inspired by recent work in monocular height above ground prediction and optic…
Heidelberg University（海德堡大学）；Facebook AI Research（Facebook人工智能研究院）；MPI for Evolutionary Anthropology（马克斯·普朗克进化人类学研究所）
Recent contributions have demonstrated that it is possible to recognize the pose of humans densely and accurately given a large dataset of poses annotated in detail. In principle, the same approach could be extended to any animal class, but the effort required for collecting new annotations for each case makes this strategy impractical, despite important applications in natural conservation, science and business. We show that, at least for proximal animal classes such as chimpanzees, it is possible to transfer the knowledge existing in dense pose recognition for humans, as well as in more gene…
We propose a viewpoint invariant model for 3D human pose estimation from a single depth image. To achieve this, our discriminative model embeds local regions into a learned viewpoint invariant feature space. Formulated as a multi-task learning problem, our model is able to selectively predict partial poses in the presence of noise and occlusion. Our approach leverages a convolutional and recurrent network architecture with a top-down error feedback mechanism to self-correct previous pose estimates in an end-to-end manner. We evaluate our model on a previously published depth dataset and a newl…
Learning semantical dynamics and spatiotemporal collaboration for human pose estimation in video
School of Artificial Intelligence, Jilin University（吉林大学人工智能学院）；School of Computer Science and Technology, East China Normal University（华东师范大学计算机科学与技术学院）
Multi-frame human pose estimation in complicated situations is challenging. Although state-of-the-art human joints detectors have demonstrated remarkable results for static images, their performances come short when we apply these models to video sequences. Prevalent shortcomings include the failure to handle motion blur, video defocus, or pose occlusions, arising from the inability in capturing the temporal dependency among video frames. On the other hand, directly employing conventional recurrent neural networks incurs empirical difficulties in modeling spatial contexts, especially for deali…
Although the performance of 3D human pose and shape estimation methods has improved significantly in recent years, existing approaches typically generate 3D poses defined in camera or human-centered coordinate system. This makes it difficult to estimate a person's pure pose and motion in world coordinate system for a video captured using a moving camera. To address this issue, this paper presents a camera motion agnostic approach for predicting 3D human pose and mesh defined in the world coordinate system. The core idea of the proposed approach is to estimate the difference between two adjacen…
Estimating 3D human poses from video is a challenging problem. The lack of 3D human pose annotations is a major obstacle for supervised training and for generalization to unseen datasets. In this work, we address this problem by proposing a weakly-supervised training scheme that does not require 3D annotations or calibrated cameras. The proposed method relies on temporal information and triangulation. Using 2D poses from multiple views as the input, we first estimate the relative camera orientations and then generate 3D poses via triangulation. The triangulation is only applied to the views wi…
Google（谷歌）；Bar-Ilan University（巴伊兰大学）；University of Zurich（苏黎世大学）
We propose a lightweight real-time sign language detection model, as we identify the need for such a case in videoconferencing. We extract optical flow features based on human pose estimation and, using a linear classifier, show these features are meaningful with an accuracy of 80%, evaluated on the DGS Corpus. Using a recurrent model directly on the input, we see improvements of up to 91% accuracy, while still working under 4ms. We describe a demo application to sign language detection in the browser in order to demonstrate its usage possibility in videoconferencing applications.
We introduce a simple yet effective algorithm that uses convolutional neural networks to directly estimate object poses from videos. Our approach leverages the temporal information from a video sequence, and is computationally efficient and robust to support robotic and AR domains. Our proposed network takes a pre-trained 2D object detector as input, and aggregates visual features through a recurrent neural network to make predictions at each frame. Experimental evaluation on the YCB-Video dataset show that our approach is on par with the state-of-the-art algorithms. Further, with a speed of 3…
This paper introduces key machine learning operations that allow the realization of robust, joint 6D pose estimation of multiple instances of objects either densely packed or in unstructured piles from RGB-D data. The first objective is to learn semantic and instance-boundary detectors without manual labeling. An adversarial training framework in conjunction with physics-based simulation is used to achieve detectors that behave similarly in synthetic and real data. Given the stochastic output of such detectors, candidates for object poses are sampled. The second objective is to automatically l…
3D human articulated pose recovery from monocular image sequences is very challenging due to the diverse appearances, viewpoints, occlusions, and also the human 3D pose is inherently ambiguous from the monocular imagery. It is thus critical to exploit rich spatial and temporal long-range dependencies among body joints for accurate 3D pose sequence prediction. Existing approaches usually manually design some elaborate prior terms and human body kinematic constraints for capturing structures, which are often insufficient to exploit all intrinsic structures and not scalable for all scenarios. In …
Object grasping is critical for many applications, which is also a challenging computer vision problem. However, for the clustered scene, current researches suffer from the problems of insufficient training data and the lacking of evaluation benchmarks. In this work, we contribute a large-scale grasp pose detection dataset with a unified evaluation system. Our dataset contains 87,040 RGBD images with over 370 million grasp poses. Meanwhile, our evaluation system directly reports whether a grasping is successful or not by analytic computation, which is able to evaluate any kind of grasp poses w…
To address the sequential changes of images including poses, in this paper we propose a recurrent regression neural network(RRNN) framework to unify two classic tasks of cross-pose face recognition on still images and video-based face recognition. To imitate the changes of images, we explicitly construct the potential dependencies of sequential images so as to regularize the final learning model. By performing progressive transforms for sequentially adjacent images, RRNN can adaptively memorize and forget the information that benefits for the final classification. For face recognition of still…
Qihoo 360（奇虎360）；Beijing Academy of Artificial Intelligence（北京智源人工智能研究院）；National University of Singapore（新加坡国立大学）
Human motion prediction, which aims to predict future human poses given past poses, has recently seen increased interest. Many recent approaches are based on Recurrent Neural Networks (RNN) which model human poses with exponential maps. These approaches neglect the pose velocity as well as temporal relation of different poses, and tend to converge to the mean pose or fail to generate natural-looking poses. We therefore propose a novel Position-Velocity Recurrent Encoder-Decoder (PVRED) for human motion prediction, which makes full use of pose velocities and temporal positional information. A t…
We present a robust method for estimating the facial pose and shape information from a densely annotated facial image. The method relies on Convolutional Point-set Representation (CPR), a carefully designed matrix representation to summarize different layers of information encoded in the set of detected points in the annotated image. The CPR disentangles the dependencies of shape and different pose parameters and enables updating different parameters in a sequential manner via convolutional neural networks and recurrent layers. When updating the pose parameters, we sample reprojection errors a…
We propose the Encoder-Recurrent-Decoder (ERD) model for recognition and prediction of human body pose in videos and motion capture. The ERD model is a recurrent neural network that incorporates nonlinear encoder and decoder networks before and after recurrent layers. We test instantiations of ERD architectures in the tasks of motion capture (mocap) generation, body pose labeling and body pose forecasting in videos. Our model handles mocap training data across multiple subjects and activity domains, and synthesizes novel motions while avoid drifting for long periods of time. For human pose lab…
We present an online approach to efficiently and simultaneously detect and track the 2D pose of multiple people in a video sequence. We build upon Part Affinity Field (PAF) representation designed for static images, and propose an architecture that can encode and predict Spatio-Temporal Affinity Fields (STAF) across a video sequence. In particular, we propose a novel temporal topology cross-linked across limbs which can consistently handle body motions of a wide range of magnitudes. Additionally, we make the overall approach recurrent in nature, where the network ingests STAF heatmaps from pre…
The Chinese University of Hong Kong（香港中文大学）；T Stone Robotics Institute, The Chinese University of Hong Kong（香港中文大学T Stone机器人研究所）
Category-level 6D pose estimation, aiming to predict the location and orientation of unseen object instances, is fundamental to many scenarios such as robotic manipulation and augmented reality, yet still remains unsolved. Precisely recovering instance 3D model in the canonical space and accurately matching it with the observation is an essential point when estimating 6D pose for unseen objects. In this paper, we achieve accurate category-level 6D pose estimation via cascaded relation and recurrent reconstruction networks. Specifically, a novel cascaded relation network is dedicated for advanc…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We propose a flexible person generation framework called Dressing in Order (DiOr), which supports 2D pose transfer, virtual try-on, and several fashion editing tasks. The key to DiOr is a novel recurrent generation pipeline to sequentially put garments on a person, so that trying on the same garments in different orders will result in different looks. Our system can produce dressing effects not achievable by existing work, including different interactions of garments (e.g., wearing a top tucked into the bottom or over it), as well as layering of multiple garments of the same type (e.g., jacket…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；UCLA Vision Lab（加州大学洛杉矶分校视觉实验室）；Robotics and Mechanisms Laboratory（机器人与机械实验室）；Laboratory for Embedded Machines and Ubiquitous Robots（嵌入式机器与普适机器人实验室）
In this paper, we propose an online path planning architecture that extends the model predictive control (MPC) formulation to consider future location uncertainties for safer navigation through cluttered environments. Our algorithm combines an object detection pipeline with a recurrent neural network (RNN) which infers the covariance of state estimates through each step of our MPC's finite time horizon. The RNN model is trained on a dataset that comprises of robot and landmark poses generated from camera images and inertial measurement unit (IMU) readings via a state-of-the-art visual-inertial…
School of Big Data & Software Engineering, Chongqing University（重庆大学大数据与软件工程学院）；Chongqing University（重庆大学）
The primary goal of skeletal motion prediction is to generate future motion by observing a sequence of 3D skeletons. A key challenge in motion prediction is the fact that a motion can often be performed in several different ways, with each consisting of its own configuration of poses and their spatio-temporal dependencies, and as a result, the predicted poses often converge to the motionless poses or non-human like motions in long-term prediction. This leads us to define a hierarchical recurrent network model that explicitly characterizes these internal configurations of poses and their local …
Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））；Chongqing Normal University（重庆师范大学）；National Center for Applied Mathematics in Chongqing（重庆国家应用数学中心）；Northeast Forestry University（东北林业大学）；Inner Mongolia University（内蒙古大学）；Southern University of Science and Technology（南方科技大学）
Existing methods for video-based person re-identification (ReID) mainly learn the appearance feature of a given pedestrian via a feature extractor and a feature aggregator. However, the appearance models would fail when different pedestrians have similar appearances. Considering that different pedestrians have different walking postures and body proportions, we propose to learn the discriminative pose feature beyond the appearance feature for video retrieval. Specifically, we implement a two-branch architecture to separately learn the appearance feature and pose feature, and then concatenate t…
This paper proposes a robust localization system that employs deep learning for better scene representation, and enhances the accuracy of 6-DOF camera pose estimation. Inspired by the fact that global scene structure can be revealed by wide field-of-view, we leverage the large overlap of a fisheye camera between adjacent frames, and the powerful high-level feature representations of deep learning. Our main contribution is the novel network architecture that extracts both temporal and spatial information using a Recurrent Neural Network. Specifically, we propose a novel pose regularization term…
We propose a joint model of human joint detection and association for 2D multi-person pose estimation (MPPE). The approach unifies training of joint detection and association without a need for further processing or sophisticated heuristics in order to associate the joints with people individually. The approach consists of two stages, where in the first stage joint detection heatmaps and association features are extracted, and in the second stage, whose input are the extracted features of the first stage, we introduce a recurrent neural network (RNN) which predicts the heatmaps of a single per…
Technische Universität München（慕尼黑工业大学）；Ludwig-Maximilians-University of Munich（慕尼黑大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
One-shot pose estimation for tasks such as body joint localization, camera pose estimation, and object tracking are generally noisy, and temporal filters have been extensively used for regularization. One of the most widely-used methods is the Kalman filter, which is both extremely simple and general. However, Kalman filters require a motion model and measurement model to be specified a priori, which burdens the modeler and simultaneously demands that we use explicit models that are often only crude approximations of reality. For example, in the pose-estimation tasks mentioned above, it is com…
The Chinese University of Hong Kong（香港中文大学）；Zhejiang University（浙江大学）
6-DoF object pose estimation from a monocular image is challenging, and a post-refinement procedure is generally needed for high-precision estimation. In this paper, we propose a framework based on a recurrent neural network (RNN) for object pose refinement, which is robust to erroneous initial poses and occlusions. During the recurrent iterations, object pose refinement is formulated as a non-linear least squares problem based on the estimated correspondence field (between a rendered image and the observed image). The problem is then solved by a differentiable Levenberg-Marquardt (LM) algorit…
The high incidence rate of prostate disease poses a requirement in early detection for diagnosis. As one of the main imaging methods used for prostate cancer detection, Magnetic Resonance Imaging (MRI) has wide range of appearance and imbalance problems, making automated prostate segmentation fundamental but challenging. Here we propose a novel Densely Dilated Spatial Pooling Convolutional Network (DDSP ConNet) in encoder-decoder structure. It employs dense structure to combine dilated convolution and global pooling, thus supplies coarse segmentation results from encoder and decoder subnet and…
There are increasing interests of studying the video-to-depth (V2D) problem with machine learning techniques. While earlier methods directly learn a mapping from images to depth maps and camera poses, more recent works enforce multi-view geometry constraints through optimization embedded in the learning framework. This paper presents a novel optimization method based on recurrent neural networks to further exploit the potential of neural networks in V2D. Specifically, our neural optimizer alternately updates the depth and camera poses through iterations to minimize a feature-metric cost, and t…
Universitat de Barcelona（巴塞罗那大学）；Computer Vision Center（计算机视觉中心）；University of Calgary（卡尔加里大学）；University of Larestan（拉雷斯坦大学）
Gaze behavior is an important non-verbal cue in social signal processing and human-computer interaction. In this paper, we tackle the problem of person- and head pose-independent 3D gaze estimation from remote cameras, using a multi-modal recurrent convolutional neural network (CNN). We propose to combine face, eyes region, and face landmarks as individual streams in a CNN to estimate gaze in still images. Then, we exploit the dynamic nature of gaze by feeding the learned features of all the frames in a sequence to a many-to-one recurrent module that predicts the 3D gaze vector of the last fra…
Object pose estimation is a key perceptual capability in robotics. We propose a fully-convolutional extension of the PoseCNN method, which densely predicts object translations and orientations. This has several advantages such as improving the spatial resolution of the orientation predictions -- useful in highly-cluttered arrangements, significant reduction in parameters by avoiding full connectivity, and fast inference. We propose and discuss several aggregation methods for dense orientation predictions that can be applied as a post-processing step, such as averaging and clustering techniques…
Beijing University of Posts and Telecommunications（北京邮电大学）
This paper proposes a new framework to solve the problem of monocular visual odometry, called MagicVO . Based on Convolutional Neural Network (CNN) and Bi-directional LSTM (Bi-LSTM), MagicVO outputs a 6-DoF absolute-scale pose at each position of the camera with a sequence of continuous monocular images as input. It not only utilizes the outstanding performance of CNN in image feature processing to extract the rich features of image frames fully but also learns the geometric relationship from image sequences pre and post through Bi-LSTM to get a more accurate prediction. A pipeline of the Magi…
Apple Inc.（苹果公司）；Carnegie Mellon University（卡内基梅隆大学）
The ability for an agent to localize itself within an environment is crucial for many real-world applications. For unknown environments, Simultaneous Localization and Mapping (SLAM) enables incremental and concurrent building of and localizing within a map. We present a new, differentiable architecture, Neural Graph Optimizer, progressing towards a complete neural network solution for SLAM by designing a system composed of a local pose estimation model, a novel pose selection module, and a novel graph optimization process. The entire architecture is trained in an end-to-end fashion, enabling t…
Seoul National University（首尔大学）；University of Birmingham（伯明翰大学）
3D hand pose estimation based on RGB images has been studied for a long time. Most of the studies, however, have performed frame-by-frame estimation based on independent static images. In this paper, we attempt to not only consider the appearance of a hand but incorporate the temporal movement information of a hand in motion into the learning framework for better 3D hand pose estimation performance, which leads to the necessity of a large scale dataset with sequential RGB hand images. We propose a novel method that generates a synthetic dataset that mimics natural human hand movements by re-en…
German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）；TU Kaiserslautern（凯泽斯劳滕工业大学）；Technische Universität München（慕尼黑工业大学）；Google（谷歌）
Establishing correspondences from image to 3D has been a key task of 6DoF object pose estimation for a long time. To predict pose more accurately, deeply learned dense maps replaced sparse templates. Dense methods also improved pose estimation in the presence of occlusion. More recently researchers have shown improvements by learning object fragments as segmentation. In this work, we present a discrete descriptor, which can represent the object surface densely. By incorporating a hierarchical binary grouping, we can encode the object surface very efficiently. Moreover, we propose a coarse to f…
In applications such as autonomous driving, it is important to understand, infer, and anticipate the intention and future behavior of pedestrians. This ability allows vehicles to avoid collisions and improve ride safety and quality. This paper proposes a biomechanically inspired recurrent neural network (Bio-LSTM) that can predict the location and 3D articulated body pose of pedestrians in a global coordinate frame, given 3D poses and locations estimated in prior frames with inaccuracy. The proposed network is able to predict poses and global locations for multiple pedestrians simultaneously, …
We address the task of 6D pose estimation of known rigid objects from single input images in scenarios where the objects are partly occluded. Recent RGB-D-based methods are robust to moderate degrees of occlusion. For RGB inputs, no previous method works well for partly occluded objects. Our main contribution is to present the first deep learning-based system that estimates accurate poses for partly occluded objects from RGB-D and RGB input. We achieve this with a new instance-aware pipeline that decomposes 6D object pose estimation into a sequence of simpler steps, where each step removes spe…
Shandong University（山东大学）；University of Wollongong（伍伦贡大学）
Recurrent neural networks (RNNs) are known to be difficult to train due to the gradient vanishing and exploding problems and thus difficult to learn long-term patterns and construct deep networks. To address these problems, this paper proposes a new type of RNNs with the recurrent connection formulated as Hadamard product, referred to as independently recurrent neural network (IndRNN), where neurons in the same layer are independent of each other and connected across layers. Due to the better behaved gradient backpropagation, IndRNN with regulated recurrent weights effectively addresses the gr…
Deep learning for predicting or generating 3D human pose sequences is an active research area. Previous work regresses either joint rotations or joint positions. The former strategy is prone to error accumulation along the kinematic chain, as well as discontinuities when using Euler angle or exponential map parameterizations. The latter requires re-projection onto skeleton constraints to avoid bone stretching and invalid configurations. This work addresses both limitations. Our recurrent network, QuaterNet, represents rotations with quaternions and our loss function performs forward kinematics…
Rutgers University（罗格斯大学）；IBM T. J. Watson（IBM T.J.沃森研究中心）；Snapchat Research（Snapchat研究院）
We propose a novel recurrent encoder-decoder network model for real-time video-based face alignment. Our proposed model predicts 2D facial point maps regularized by a regression loss, while uniquely exploiting recurrent learning at both spatial and temporal dimensions. At the spatial level, we add a feedback loop connection between the combined output response map and the input, in order to enable iterative coarse-to-fine face alignment using a single network model. At the temporal level, we first decouple the features in the bottleneck of the network into temporal-variant factors, such as pos…
3D hand pose estimation from a single depth image plays an important role in computer vision and human-computer interaction. Although recent hand pose estimation methods using convolution neural network (CNN) have shown notable improvements in accuracy, most of them have a limitation that they rely on a complex network structure without fully exploiting the articulated structure of the hand. A hand, which is an articulated object, is composed of six local parts: the palm and five independent fingers. Each finger consists of sequential-joints that provide constrained motion, referred to as a ki…
