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22
Elastically deformable models
 Computer Graphics
, 1987
"... The goal of visual modeling research is to develop mathematical models and associated algorithms for the analysis and synthesis of visual information. Image analysis and synthesis characterize the domains of computer vision and computer graphics, respectively. For nearly three decades, the vision an ..."
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Cited by 764 (19 self)
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The goal of visual modeling research is to develop mathematical models and associated algorithms for the analysis and synthesis of visual information. Image analysis and synthesis characterize the domains of computer vision and computer graphics, respectively. For nearly three decades, the vision and graphics fields have been developing almost entirely independently—this despite the fact that, at least conceptually, the two disciplines are bound in a mutually converse relationship. Graphics, the direct problem, involves the synthesis of images from object models, whereas vision, the inverse problem, involves the analysis of images to infer object models. Visual modeling takes a unified approach to vision and graphics via modeling that exploits computational physics. In addition to geometry, physicsbased modeling employs forces, torques, internal strain energies, and other physical quantities to control the creation and evolution of models. Mathematically, the approach prescribes systems of dynamic (ordinary and partial) differential equations to govern model behavior. These equations of motion may be
Learning to Track the Visual Motion of Contours
 Artificial Intelligence
, 1995
"... A development of a method for tracking visual contours is described. Given an "untrained" tracker, a trainingmotion of an object can be observed over some extended time and stored as an image sequence. The image sequence is used to learn parameters in a stochastic differential equation m ..."
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Cited by 100 (17 self)
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A development of a method for tracking visual contours is described. Given an "untrained" tracker, a trainingmotion of an object can be observed over some extended time and stored as an image sequence. The image sequence is used to learn parameters in a stochastic differential equation model. These are used, in turn, to build a tracker whose predictor imitates the motion in the training set. Tests show that the resulting trackers can be markedly tuned to desired curve shapes and classes of motions. Contents 1 Introduction 2 2 Tracking framework 2 2.1 Curve representation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2.2 Tracking as estimation over time : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2.3 Rigid body transformations : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2.4 Curves in motion : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 2.5 Discretetime model : : : : : : : : : :...
Articulated and Elastic Nonrigid Motion: A Review
 In Proc. IEEE Workshop on Motion of NonRigid and Articulated Objects
, 1994
"... Motion of physical objects is nonrigid, in general. Most researchers have focused on the study of the motion and structure of rigid objects because of its simplicity and elegance. Recently, investigation of nonrigid structure and motion transformation has drawn the attention of researchers from a w ..."
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Cited by 50 (2 self)
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Motion of physical objects is nonrigid, in general. Most researchers have focused on the study of the motion and structure of rigid objects because of its simplicity and elegance. Recently, investigation of nonrigid structure and motion transformation has drawn the attention of researchers from a wide spectrum of disciplines. Since the nonrigid motion class encompasses a huge domain, we restrict our overview to the motion analysis of articulated and elastic nonrigid objects. Numerous approaches that have been proposed to recover the 3D structure and motion of objects are studied. The discussion includes both: 1) motion recovery without shape models, and 2) modelbased analysis, and covers a number of examples of real world objects. 1 Introduction In computer vision research, motion analysis has been largely restricted to rigid objects. However, in the real world, nonrigid motion of objects is the rule. In the past few years, there has been a growing interest in the study of nonri...
Learning Dynamics of Complex Motions from Image Sequences
, 1996
"... The performance of Active Contours in tracking is highly dependent on the availability of an appropriate model of shape and motion, to use as a predictor. Models can be handbuilt, but it is far more effective and less timeconsuming to learn them from a training set. Techniques to do this exist bot ..."
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Cited by 47 (7 self)
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The performance of Active Contours in tracking is highly dependent on the availability of an appropriate model of shape and motion, to use as a predictor. Models can be handbuilt, but it is far more effective and less timeconsuming to learn them from a training set. Techniques to do this exist both for shape, and for shape and motion jointly. This paper extends the range of shape and motion models in two significant ways. The first is to model jointly the random variations in shape arising within an objectclass and those occuring during object motion. The resulting algorithm is applied to tracking of plants captured by a video camera mounted on an agricultural robot. The second addresses the tracking of coupled objects such as head and lips. In both cases, new algorithms are shown to make important contributions to tracking performance.
Visual analysis of high DOF articulated objects with application to hand tracking
, 1995
"... Measurement ofhuman hand and body motion is an important task for applications ranging from athletic performance analysis to advanced userinterfaces. Commercial human motion sensors are invasive, requiring the user to wear gloves or targets. This thesis addresses noninvasive realtime 3D tracking of ..."
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Cited by 36 (4 self)
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Measurement ofhuman hand and body motion is an important task for applications ranging from athletic performance analysis to advanced userinterfaces. Commercial human motion sensors are invasive, requiring the user to wear gloves or targets. This thesis addresses noninvasive realtime 3D tracking of human motion using sequences of ordinary video images. In contrast to other sensors, video cameras are passive and inobtrusive, and can easily be added to existing work environments. Other computer vision systems have demonstrated realtime tracking of a single rigid object in six degreesoffreedom (DOFs). Articulated objects like the hand present three challenges to existing rigidbody tracking algorithms: a large number of DOFs (27 for the hand), nonlinear kinematic constraints, and complex selfocclusion e ects. This thesis presentsanovel tracking framework for articulated objects that uses explicit kinematic models to overcome these obstacles. Kinematic models play twomain roles in this work: they provide geometric
Uncertainty Assessment for Reconstructions Based on Deformable Geometry
, 1997
"... Deformable geometric models can be used in the context of Bayesian analysis to solve illposed tomographic reconstruction problems. The uncertainties associated with a Bayesian analysis may be assessed by generating a set of random samples from the posterior, which may be accomplished using a Markov ..."
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Cited by 17 (8 self)
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Deformable geometric models can be used in the context of Bayesian analysis to solve illposed tomographic reconstruction problems. The uncertainties associated with a Bayesian analysis may be assessed by generating a set of random samples from the posterior, which may be accomplished using a MarkovChain MonteCarlo (MCMC) technique. We demonstrate the combination of these techniques for a reconstruction of a twodimensional object from two orthogonal noisy projections. The reconstructed object is modeled in terms of a deformable geometricallydefined boundary with a uniform interior density yielding a nonlinear reconstruction problem. We show how an MCMC sequence can be used to estimate uncertainties in the location of the edge of the reconstructed object.
Exploring the reliability of Bayesian reconstructions
 in Image Processing
, 1995
"... The Bayesian approach allows one to combine measurement data with prior knowledge about models of reality to draw inferences about the validity of those models. The posterior probability quantifies the degree of certainty one has about those models. We propose a method to explore the reliability, or ..."
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Cited by 14 (11 self)
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The Bayesian approach allows one to combine measurement data with prior knowledge about models of reality to draw inferences about the validity of those models. The posterior probability quantifies the degree of certainty one has about those models. We propose a method to explore the reliability, or uncertainty, of specific features of a Bayesian solution. If one draws an analogy between the negative logarithm of the posterior and a physical potential, the gradient of this potential can be interpreted as a force that acts on the model. As model parameters are perturbed from their maximum a posteriori (MAP) values, the strength of the restoring force that drives them back to the MAP solution is directly related to the uncertainty in those parameter estimates. The correlations between the uncertainties of parameter estimates can be elucidated.
The Hard Truth
 in Maximum Entropy and Bayesian Methods
, 1996
"... Bayesian methodology provides the means to combine prior knowledge about competing models of reality and available data to draw inferences about the validity of those models. The posterior quantifies the degree of certainty one has about those models. We propose a method to determine the uncertainty ..."
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Cited by 11 (10 self)
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Bayesian methodology provides the means to combine prior knowledge about competing models of reality and available data to draw inferences about the validity of those models. The posterior quantifies the degree of certainty one has about those models. We propose a method to determine the uncertainty in a specific feature of a Bayesian solution. Our approach is based on an analogy between the negative logarithm of the posterior and a physical potential. This analogy leads to the interpretation of gradient of this potential as a force that acts on the model. As model parameters are perturbed from their maximum a posterJori (MAP) values, the strength of the restoring force that drives them back to the MAP solution is directly related to the uncertainty in those parameter estimates. The correlations between the uncertainties of parameter estimates can be elucidated.