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997
Tracking People with Twists and Exponential Maps
, 1998
"... This paper demonstrates a new visual motion estimation technique that is able to recover high degreeoffreedom articulated human body configurations in complex video sequences. We introduce the use of a novel mathematical technique, the product of exponential maps and twist motions, and its integra ..."
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Cited by 443 (5 self)
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This paper demonstrates a new visual motion estimation technique that is able to recover high degreeoffreedom articulated human body configurations in complex video sequences. We introduce the use of a novel mathematical technique, the product of exponential maps and twist motions, and its integration into a differential motion estimation. This results in solving simple linear systems, and enables us to recover robustly the kinematic degreesoffreedom in noise and complex self occluded configurations. We demonstrate this on several image sequences of people doing articulated full body movements, and visualize the results in reanimating an artificial 3D human model. We are also able to recover and reanimate the famous movements of Eadweard Muybridge's motion studies from the last century. To the best of our knowledge, this is the first computer vision based system that is able to process such challenging footage and recover complex motions with such high accuracy.
MAPRM: A probabilistic roadmap planner with sampling on the medial axis of the free space
 In Proc. IEEE Int. Conf. Robot. Autom. (ICRA
, 1999
"... Probabilistic roadmap planning methods have been shown to perform well in a number of practical situations, but their performance degrades when paths are required to pass through narrow passages in the free space. We propose a new method of sampling the configuration space in which randomly generate ..."
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Cited by 181 (47 self)
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Probabilistic roadmap planning methods have been shown to perform well in a number of practical situations, but their performance degrades when paths are required to pass through narrow passages in the free space. We propose a new method of sampling the configuration space in which randomly generated configurations, free or not, are retracted onto the medial axis of the free space. We give algorithms that perform this retraction while avoiding explicit computation of the medial axis, and we show that sampling and retracting in this manner increases the number of nodes found in small volume corridors in a way that is independent of the volume of the corridor and depends only on the characteristics of the obstacles bounding it. Theoretical and experimental results are given to show that this improves performance on problems requiring traversal of narrow passages. 1
Tracking multiple humans in complex situations
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2004
"... Abstract—Tracking multiple humans in complex situations is challenging. The difficulties are tackled with appropriate knowledge in the form of various models in our approach. Human motion is decomposed into its global motion and limb motion. In the first part, we show how multiple human objects are ..."
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Cited by 134 (3 self)
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Abstract—Tracking multiple humans in complex situations is challenging. The difficulties are tackled with appropriate knowledge in the form of various models in our approach. Human motion is decomposed into its global motion and limb motion. In the first part, we show how multiple human objects are segmented and their global motions are tracked in 3D using ellipsoid human shape models. Experiments show that it successfully applies to the cases where a small number of people move together, have occlusion, and cast shadow or reflection. In the second part, we estimate the modes (e.g., walking, running, standing) of the locomotion and 3D body postures by making inference in a prior locomotion model. Camera model and ground plane assumptions provide geometric constraints in both parts. Robust results are shown on some difficult sequences. Index Terms—Multiplehuman segmentation, multiplehuman tracking, visual surveillance, human shape model, human locomotion model. 1
Robust Hybrid Control for Autonomous Vehicle Motion Planning
, 2000
"... The operation of an autonomous vehicle in an unknown, dynamic environment is a very complex problem, especially when the vehicle is required to use its full maneuvering capabilities, and to react in real time to changes in the operational environment. A possible approach to reduce the computationa ..."
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Cited by 128 (10 self)
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The operation of an autonomous vehicle in an unknown, dynamic environment is a very complex problem, especially when the vehicle is required to use its full maneuvering capabilities, and to react in real time to changes in the operational environment. A possible approach to reduce the computational complexity of the motion planning problem for a nonlinear, high dimensional system, is based on a quantization of the system dynamics, leading to a control architecture based on a hybrid automaton, the states of which represent feasible trajectory primitives for the vehicle. This paper focuses on the feasibility of this approach: the structure of a Robust Hybrid Automaton is defined and its properties are analyzed. Algorithms are presented for timeoptimal motion planning in a free workspace, and in the presence of fixed or moving obstacles. A case study involving a small autonomous helicopter is presented: a nonlinear control law for maneuver execution is provided, and a robust hyb...
Means and Averaging in the Group of Rotations
, 2002
"... In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius inner product gives rise to a mean rotation that is given by the closest special orthogonal matrix to ..."
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Cited by 114 (3 self)
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In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius inner product gives rise to a mean rotation that is given by the closest special orthogonal matrix to the usual arithmetic mean of the given rotation matrices. The mean rotation associated with the intrinsic metric on SO(3) is the Riemannian center of mass of the given rotation matrices. We show that the Riemannian mean rotation shares many common features with the geometric mean of positive numbers and the geometric mean of positive Hermitian operators. We give some examples with closedform solutions of both notions of mean.
Hybrid zero dynamics of planar biped walkers
 IEEE Trans. Automat. Control
"... endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution m ..."
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Cited by 112 (30 self)
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endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubspermissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. NOTE: At the time of publication, author Daniel Koditschek was affiliated with the University of Michigan. Currently (August 2005), he is a faculty
Human Body Model Acquisition and Tracking Using Voxel Data
, 2003
"... We present an integrated system for automatic acquisition of the human body model and motion tracking using input from multiple synchronized video streams. The video frames are segmented and the 3D voxel reconstructions of the human body shape in each frame are computed from the foreground silhouett ..."
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Cited by 108 (7 self)
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We present an integrated system for automatic acquisition of the human body model and motion tracking using input from multiple synchronized video streams. The video frames are segmented and the 3D voxel reconstructions of the human body shape in each frame are computed from the foreground silhouettes. These reconstructions are then used as input to the model acquisition and tracking algorithms.
ShapefromSilhouette Across Time  Part I: Theory and Algorithms
 International Journal of Computer Vision
, 2005
"... ShapeFromSilhouette (SFS) is a shape reconstruction method which constructs a 3D shape estimate of an object using silhouette images of the object. The output of a SFS algorithm is known as the Visual Hull (VH). Traditionally SFS is either performed on static objects, or separately at each time in ..."
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Cited by 105 (3 self)
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ShapeFromSilhouette (SFS) is a shape reconstruction method which constructs a 3D shape estimate of an object using silhouette images of the object. The output of a SFS algorithm is known as the Visual Hull (VH). Traditionally SFS is either performed on static objects, or separately at each time instant in the case of videos of moving objects. In this paper we develop a theory of performing SFS across time: estimating the shape of a dynamic object (with unknown motion) by combining all of the silhouette images of the object over time. We first introduce a one dimensional element called a Bounding Edge to represent the Visual Hull. We then show that aligning two Visual Hulls using just their silhouettes is in general ambiguous and derive the geometric constraints (in terms of Bounding Edges) that govern the alignment. To break the alignment ambiguity, we combine stereo information with silhouette information and derive a Temporal SFS algorithm which consists of two steps: (1) estimate the motion of the objects over time (Visual Hull Alignment) and (2) combine the silhouette information using the estimated motion (Visual Hull Refinement). The algorithm is first developed for rigid objects and then extended to articulated objects. In the Part II of this paper we apply our temporal SFS algorithm to two humanrelated applications: (1) the acquisition of detailed human kinematic models and (2) markerless motion tracking.
Meshbased inverse kinematics
 ACM Trans. Graph
, 2005
"... The ability to position a small subset of mesh vertices and produce a meaningful overall deformation of the entire mesh is a fundamental task in mesh editing and animation. However, the class of meaningful deformations varies from mesh to mesh and depends on mesh kinematics, which prescribes valid m ..."
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Cited by 98 (8 self)
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The ability to position a small subset of mesh vertices and produce a meaningful overall deformation of the entire mesh is a fundamental task in mesh editing and animation. However, the class of meaningful deformations varies from mesh to mesh and depends on mesh kinematics, which prescribes valid mesh configurations, and a selection mechanism for choosing among them. Drawing an analogy to the traditional use of skeletonbased inverse kinematics for posing skeletons, we define meshbased inverse kinematics as the problem of finding meaningful mesh deformations that meet specified vertex constraints. Our solution relies on example meshes to indicate the class of meaningful deformations. Each example is represented with a feature vector of deformation gradients that capture the affine transformations which individual triangles undergo relative to a reference pose. To pose a mesh, our algorithm efficiently searches among all meshes with specified vertex positions to find the one that is closest to some pose in a nonlinear span of the example feature vectors. Since the search is not restricted to the span of example shapes, this produces compelling deformations even when the constraints require poses that are different from those observed in the examples. Furthermore, because the span is formed by a nonlinear blend of the example feature vectors, the blending component of our system may also be used independently to pose meshes by specifying blending weights or to compute multiway morph sequences.