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## CONDENSATION -- conditional density propagation for visual tracking (1998)

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### Other Repositories/Bibliography

Venue: | INTERNATIONAL JOURNAL OF COMPUTER VISION |

Citations: | 1492 - 12 self |

### Citations

5036 |
Stochastic relaxation, gibbs distribution, and the bayesian restoration of images
- Geman, Geman
- 1984
(Show Context)
Citation Context ...k is a normalisation constant that is independent of x. In cases where p(zjx) is sufficiently complex that p(xjz) cannot be evaluated simply in closed form, iterative sampling techniques can be used (=-=Geman and Geman, 1984-=-; Ripley and Sutherland, 1990; Grenander et al., 1991; Storvik, 1994). The factored sampling algorithm (Grenander et al., 1991) generates a random variate x from a distribution ~ p(x) that approximate... |

3872 | Snakes: Active contour models
- Kass, Witkin, et al.
- 1988
(Show Context)
Citation Context ...hape (Gennery, 1992; Harris, 1992). One important facility is the modelling of curve segments which interact with images (Fischler and Elschlager, 1973; Yuille and Hallinan, 1992) or image sequences (=-=Kass et al., 1987-=-; Dickmanns and Graefe, 1988). This is more general than modelling entire objects but more clutter-resistant than applying signalprocessing to low-level corners or edges. The methods to be discussed h... |

3847 | Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography - Fischler, Bolles - 1981 |

1971 |
Fundamentals of speech recognition
- Rabiner, Juang
- 1993
(Show Context)
Citation Context ...agation equation (4) in the Condensationsalgorithm is a continuous form of the propagation rule of the "forward algorithm" Isard and Blake. IJCV, in press, (1998). 27 for Hidden Markov Model=-=s (HMMs) (Rabiner and Bing-Hwang, 1993-=-). The integral over continuous states in (5) becomes a summation over discrete states in the HMM, with p(x t jx t\Gamma1 ) represented by a transition matrix. This suggests a natural opportunity to c... |

1694 |
Novel approach to non-linear/non-gaussian bayesian state estimation
- Gordon, Salmond, et al.
(Show Context)
Citation Context ...ation algorithm The Condensation algorithm is based on factored sampling but extended to apply iteratively to successive images in a sequence. The same sampling strategy has been developed elsewhere (=-=Gordon et al., 1993-=-; Kitagawa, 1996), presented as developments of Monte-Carlo methods. Jump-diffusion tracking (Miller et al., 1995) may also be related to the approach described here. Given that the process at each ti... |

1190 | Applied Optimal Estimation - Gelb - 1980 |

1035 | Optimal Filtering - Anderson, Moore - 1979 |

921 |
Tracking and Data Association
- Bar-Shalom, Fortmann
- 1988
(Show Context)
Citation Context ... m g; m = 1; : : : ; M occurs, or else the target object is not visible with probability q = 1 \Gamma P m P (OE m ). Such reasoning about clutter and false alarms is commonly used in target tracking (=-=Bar-Shalom and Fortmann, 1988-=-). Now the observation density can be expressed as p(zjx) = qp(zjclutter) + M X m=1 p(zjx; OE m )P (OE m ): A reasonable functional form for this can be obtained by making some specific assumptions: t... |

887 | Linear Statistical Inference and Its Applications - Rao - 1973 |

649 | Contour tracking by stochastic propagation of conditional density
- Isard, Blake
- 1996
(Show Context)
Citation Context ...atistical variability of image data z given a curve state x, a posterior distribution can, in principle, be estimated for x t given z t at successive times t. 1 This paper has appeared in short form (=-=Isard and Blake, 1996-=-) as joint winner of the prize of the European Conference on Computer Vision, 1996. Isard and Blake. IJCV, in press, (1998). 3 1.2 Kalman filters and data-association Spatio-temporal estimation, the t... |

579 |
Monte-carlo filter and smoother for nonGaussian nonlinear state space models
- Kitagawa
- 1996
(Show Context)
Citation Context ...ondensation algorithm is based on factored sampling but extended to apply iteratively to successive images in a sequence. The same sampling strategy has been developed elsewhere (Gordon et al., 1993; =-=Kitagawa, 1996-=-), presented as developments of Monte-Carlo methods. Jump-diffusion tracking (Miller et al., 1995) may also be related to the approach described here. Given that the process at each time-step is a sel... |

557 |
Stochastic simulation
- Ripley
- 1987
(Show Context)
Citation Context ...sample sets. A third question concerns the random sampling scheme and its efficiency. Factored sampling can be inefficient as the modes of p(zjx) become narrow. One approach is "importance sampli=-=ng" (Ripley, 1987-=-) in which a heuristically chosen distribution, approximating p(zjx), is used to concentrate random sampling around modes. However, this has the drawback that the prior p(x) must be repeatedly evaluat... |

469 |
Recognition by linear combinations of models
- Ullman, Basri
- 1991
(Show Context)
Citation Context ...is allows too many degrees of freedom for stable tracking and it is necessary to restrict the curve to a low-dimensional parameter x, for example over an affine space (Koenderink and Van Doorn, 1991; =-=Ullman and Basri, 1991; Blake et-=- al., 1993), or more generally allowing a "shape-space" of non-rigid motion (Cootes et al., 1993). Finally, prior probability densities can be defined over the curves (Cootes et al., 1993) r... |

414 |
The representation and matching of pictorial structures
- Fischler, Elschlager
- 1973
(Show Context)
Citation Context ...nt computationally (Lowe, 1992), especially if motion is modelled as well as shape (Gennery, 1992; Harris, 1992). One important facility is the modelling of curve segments which interact with images (=-=Fischler and Elschlager, 1973-=-; Yuille and Hallinan, 1992) or image sequences (Kass et al., 1987; Dickmanns and Graefe, 1988). This is more general than modelling entire objects but more clutter-resistant than applying signalproce... |

391 |
Dynamic 3D models with local and global deformations: Deformable superquadrics
- Terzopoulos, Metaxas
- 1991
(Show Context)
Citation Context ...id motion (Cootes et al., 1993). Finally, prior probability densities can be defined over the curves (Cootes et al., 1993) represented by appropriate parameter vectors x, and also over their motions (=-=Terzopoulos and Metaxas, 1991-=-; Blake et al., 1993), and this constitutes a powerful facility for tracking. Reasonable defaults can be chosen for those densities. However, it is obviously more satisfactory to measure or estimate t... |

322 | Affine structure from motion - Koenderink, Doorn - 1991 |

319 |
Adaptive Filtering Prediction and Control
- Goodwin, Sin
- 1984
(Show Context)
Citation Context ... it is obviously more satisfactory to measure or estimate them from data-sequences (x 1 ; x 2 ; : : :). Algorithms to do this, assuming Gaussian densities, are known in the control-theory literature (=-=Goodwin and Sin, 1984-=-) and have been applied in computer vision (Blake and Isard, 1994; Baumberg and Hogg, 1995). Given the prior, and an observation density that characterises the statistical variability of image data z ... |

310 |
editors. An introduction to splines for use in computer graphics and geometric modeling
- Bartels, Beatty, et al.
- 1987
(Show Context)
Citation Context ...s but more clutter-resistant than applying signalprocessing to low-level corners or edges. The methods to be discussed here have been applied at this level, to segments of parametric B-spline curves (=-=Bartels et al., 1987-=-) tracking over image sequences (Menet et al., 1990; Cipolla and Blake, 1990). The B-spline curves could, in theory, be parameterised by their control points. In practice this allows too many degrees ... |

257 |
Model-based vision: A program to see a walking person
- Hogg
- 1983
(Show Context)
Citation Context ...sion for modelling shape and motion. When suitable geometric models of a moving object are available, they can be matched effectively to image data, though usually at considerable computational cost (=-=Hogg, 1983-=-; Lowe, 1991; Sullivan, 1992; Huttenlocher et al., 1993). Once an object has been located approximately, tracking it in subsequent images becomes more efficient computationally (Lowe, 1992), especiall... |

255 | Kalman filterbased algorithms for estimating depth from image sequences
- Matthies, Kanade, et al.
- 1989
(Show Context)
Citation Context ...y by Kalman filtering, in the relatively clutter-free case in which p(x t ) can satisfactorily be modelled as Gaussian (Dickmanns and Graefe, 1988; Harris, 1992; Gennery, 1992; Rehg and Kanade, 1994; =-=Matthies et al., 1989-=-) and can be applied to curves (Terzopoulos and Szeliski, 1992; Blake et al., 1993). These solutions work relatively poorly in clutter which causes the density for x t to be multi-modal and therefore ... |

209 |
Introduction to Stochastic Control Theory
- ˚Aström
- 2006
(Show Context)
Citation Context ...applying only to Gaussian densities, of a more general probability density propagation process. In continuous time this can be described in terms of diffusion, governed by a "Fokker-Planck" =-=equation (Astrom, 1970-=-), in which the density for x t drifts and spreads under the action of a stochastic model of its dynamics. In the simple Gaussian case, the diffusion is purely linear and the density function evolves ... |

207 |
A framework for spatio-temporal control in the tracking of visual contours
- Blake, Curwen, et al.
- 1993
(Show Context)
Citation Context ...es of freedom for stable tracking and it is necessary to restrict the curve to a low-dimensional parameter x, for example over an affine space (Koenderink and Van Doorn, 1991; Ullman and Basri, 1991; =-=Blake et al., 1993), or more-=- generally allowing a "shape-space" of non-rigid motion (Cootes et al., 1993). Finally, prior probability densities can be defined over the curves (Cootes et al., 1993) represented by approp... |

192 | Visual tracking of high dof articulated structures: an application to human hand tracking
- Rehg, Kanade
- 1994
(Show Context)
Citation Context ...en dealt with thoroughly by Kalman filtering, in the relatively clutter-free case in which p(x t ) can satisfactorily be modelled as Gaussian (Dickmanns and Graefe, 1988; Harris, 1992; Gennery, 1992; =-=Rehg and Kanade, 1994-=-; Matthies et al., 1989) and can be applied to curves (Terzopoulos and Szeliski, 1992; Blake et al., 1993). These solutions work relatively poorly in clutter which causes the density for x t to be mul... |

182 | Robust model-based motion tracking through the integration of search and estimation
- Lowe
- 1992
(Show Context)
Citation Context ...ional cost (Hogg, 1983; Lowe, 1991; Sullivan, 1992; Huttenlocher et al., 1993). Once an object has been located approximately, tracking it in subsequent images becomes more efficient computationally (=-=Lowe, 1992-=-), especially if motion is modelled as well as shape (Gennery, 1992; Harris, 1992). One important facility is the modelling of curve segments which interact with images (Fischler and Elschlager, 1973;... |

162 | Learning flexible models from image sequences
- Baumberg, Hogg
- 1994
(Show Context)
Citation Context ...capturing sequences of key frames of the object in different poses (Blake et al., 1995); 3. performing principal components analysis on a set of outlines of the deforming object (Cootes et al., 1993; =-=Baumberg and Hogg, 1994-=-) to derive a small set of representative contours. 5.2 Dynamical model Exploiting earlier work on dynamical modelling (Blake et al., 1993; Blake et al., 1995), object dynamics are modelled as a 2nd o... |

147 |
HANDS. A Pattern Theoretical Study of Biological Shapes
- Grenander, Chow, et al.
- 1991
(Show Context)
Citation Context ... x. In cases where p(zjx) is sufficiently complex that p(xjz) cannot be evaluated simply in closed form, iterative sampling techniques can be used (Geman and Geman, 1984; Ripley and Sutherland, 1990; =-=Grenander et al., 1991-=-; Storvik, 1994). The factored sampling algorithm (Grenander et al., 1991) generates a random variate x from a distribution ~ p(x) that approximates the posterior p(xjz). First a sample-set Isard and ... |

147 | Visual tracking of known three-dimensional objects - Gennery - 1992 |

146 | Recursive bayesian estimation using gaussian sums - Sorenson, Alspach - 1971 |

117 |
Tracking with Kalman snakes
- Terzopoulos, Szeliski
- 1992
(Show Context)
Citation Context ... case in which p(x t ) can satisfactorily be modelled as Gaussian (Dickmanns and Graefe, 1988; Harris, 1992; Gennery, 1992; Rehg and Kanade, 1994; Matthies et al., 1989) and can be applied to curves (=-=Terzopoulos and Szeliski, 1992-=-; Blake et al., 1993). These solutions work relatively poorly in clutter which causes the density for x t to be multi-modal and therefore non-Gaussian. With simple, discrete features such as points or... |

110 | Learning to track the visual motion of contours
- Blake, Isard, et al.
- 1995
(Show Context)
Citation Context ...joint angles (Rehg and Kanade, 1994). 5.1 Linear parameterisations of splines for tracking We represent the state of a tracked object following methods established for tracking using a Kalman filter (=-=Blake et al., 1995-=-). Objects are modelled as a curve (or set of curves), typically though not necessarily the occluding contour, and represented at time t by a parameterised image curve r(s; t). The parameterisation is... |

105 |
Tracking non-rigid objects in complex scenes
- Huttenlocher, Noh, et al.
- 1993
(Show Context)
Citation Context ...n suitable geometric models of a moving object are available, they can be matched effectively to image data, though usually at considerable computational cost (Hogg, 1983; Lowe, 1991; Sullivan, 1992; =-=Huttenlocher et al., 1993-=-). Once an object has been located approximately, tracking it in subsequent images becomes more efficient computationally (Lowe, 1992), especially if motion is modelled as well as shape (Gennery, 1992... |

101 |
Tracking with Rigid Models
- Harris
- 1992
(Show Context)
Citation Context ... Once an object has been located approximately, tracking it in subsequent images becomes more efficient computationally (Lowe, 1992), especially if motion is modelled as well as shape (Gennery, 1992; =-=Harris, 1992-=-). One important facility is the modelling of curve segments which interact with images (Fischler and Elschlager, 1973; Yuille and Hallinan, 1992) or image sequences (Kass et al., 1987; Dickmanns and ... |

91 |
Dynamic monocular machine vision
- Dickmanns, Graefe
- 1988
(Show Context)
Citation Context ...; Harris, 1992). One important facility is the modelling of curve segments which interact with images (Fischler and Elschlager, 1973; Yuille and Hallinan, 1992) or image sequences (Kass et al., 1987; =-=Dickmanns and Graefe, 1988-=-). This is more general than modelling entire objects but more clutter-resistant than applying signalprocessing to low-level corners or edges. The methods to be discussed here have been applied at thi... |

90 |
Probability and Statistics
- Papoulis
- 1990
(Show Context)
Citation Context ...or p(x), using data z from a single image. The posterior density p(xjz) represents all the knowledge about x that is deducible from the data. It can be evaluated in principle by applying Bayes' rule (=-=Papoulis, 1990-=-) to obtain p(xjz) = kp(zjx)p(x) (6) where k is a normalisation constant that is independent of x. In cases where p(zjx) is sufficiently complex that p(xjz) cannot be evaluated simply in closed form, ... |

69 | 3D position, attitude and shape input using video tracking of hands and lips - Blake, Isard - 1994 |

62 |
B-snakes: implementation and application to stereo
- Menet, Saint-Marc, et al.
- 1990
(Show Context)
Citation Context ...essing to low-level corners or edges. The methods to be discussed here have been applied at this level, to segments of parametric B-spline curves (Bartels et al., 1987) tracking over image sequences (=-=Menet et al., 1990-=-; Cipolla and Blake, 1990). The B-spline curves could, in theory, be parameterised by their control points. In practice this allows too many degrees of freedom for stable tracking and it is necessary ... |

62 | A Bayesian approach to dynamic contours through stochastic sampling and simulated annealing
- Storvik
- 1994
(Show Context)
Citation Context ...) is sufficiently complex that p(xjz) cannot be evaluated simply in closed form, iterative sampling techniques can be used (Geman and Geman, 1984; Ripley and Sutherland, 1990; Grenander et al., 1991; =-=Storvik, 1994-=-). The factored sampling algorithm (Grenander et al., 1991) generates a random variate x from a distribution ~ p(x) that approximates the posterior p(xjz). First a sample-set Isard and Blake. IJCV, in... |

60 |
The dynamic analysis of apparent contours
- Cipolla, Blake
- 1990
(Show Context)
Citation Context ...corners or edges. The methods to be discussed here have been applied at this level, to segments of parametric B-spline curves (Bartels et al., 1987) tracking over image sequences (Menet et al., 1990; =-=Cipolla and Blake, 1990-=-). The B-spline curves could, in theory, be parameterised by their control points. In practice this allows too many degrees of freedom for stable tracking and it is necessary to restrict the curve to ... |

59 |
Building and using flexible models incorporating grey-level information
- Cootes, Taylor, et al.
- 1993
(Show Context)
Citation Context ...dimensional parameter x, for example over an affine space (Koenderink and Van Doorn, 1991; Ullman and Basri, 1991; Blake et al., 1993), or more generally allowing a "shape-space" of non-rigi=-=d motion (Cootes et al., 1993-=-). Finally, prior probability densities can be defined over the curves (Cootes et al., 1993) represented by appropriate parameter vectors x, and also over their motions (Terzopoulos and Metaxas, 1991;... |

58 | Visual interpretation of known objects in constrained scenes
- Sullivan
- 1992
(Show Context)
Citation Context ... and motion. When suitable geometric models of a moving object are available, they can be matched effectively to image data, though usually at considerable computational cost (Hogg, 1983; Lowe, 1991; =-=Sullivan, 1992-=-; Huttenlocher et al., 1993). Once an object has been located approximately, tracking it in subsequent images becomes more efficient computationally (Lowe, 1992), especially if motion is modelled as w... |

49 | Learning dynamics of complex motions from image sequences
- Reynard, Wildenberg, et al.
- 1996
(Show Context)
Citation Context ...ken while the object performs typical motions. Methods for doing this via Maximum Likelihood Estimation are essential to the work described here and are described fully elsewhere (Blake et al., 1995; =-=Reynard et al., 1996-=-). The dynamical model can be re-expressed in such a way as to make quite clear that it is a temporal Markov chain: p(x t jx t\Gamma1 ) / exp \Gamma 1 2 kB \Gamma1 ((x t \Gamma x) \Gamma A(x t\Gamma1 ... |

44 | Sensor fusion and planning: a computational approach - Hager - 1990 |

41 |
Deformable templates
- Yuille, Hallinan
- 1992
(Show Context)
Citation Context ..., especially if motion is modelled as well as shape (Gennery, 1992; Harris, 1992). One important facility is the modelling of curve segments which interact with images (Fischler and Elschlager, 1973; =-=Yuille and Hallinan, 1992-=-) or image sequences (Kass et al., 1987; Dickmanns and Graefe, 1988). This is more general than modelling entire objects but more clutter-resistant than applying signalprocessing to low-level corners ... |

39 | Generating spatiotemporal models from examples
- Baumberg, Hogg
- 1995
(Show Context)
Citation Context ...; x 2 ; : : :). Algorithms to do this, assuming Gaussian densities, are known in the control-theory literature (Goodwin and Sin, 1984) and have been applied in computer vision (Blake and Isard, 1994; =-=Baumberg and Hogg, 1995-=-). Given the prior, and an observation density that characterises the statistical variability of image data z given a curve state x, a posterior distribution can, in principle, be estimated for x t gi... |

34 | Conditional-mean estimation via jump-diffusion processes in multiple target tracking/recognition
- Miller, Srivasta, et al.
- 1995
(Show Context)
Citation Context ...cessive images in a sequence. The same sampling strategy has been developed elsewhere (Gordon et al., 1993; Kitagawa, 1996), presented as developments of Monte-Carlo methods. Jump-diffusion tracking (=-=Miller et al., 1995-=-) may also be related to the approach described here. Given that the process at each time-step is a self-contained iteration of factored sampling, the output of an iteration will be a weighted, time-s... |

32 | A ne structure from motion - Koenderink, Doorn - 1991 |

17 |
Finding spiral structures in images of galaxies
- Ripley, Sutherland
- 1990
(Show Context)
Citation Context ...nstant that is independent of x. In cases where p(zjx) is sufficiently complex that p(xjz) cannot be evaluated simply in closed form, iterative sampling techniques can be used (Geman and Geman, 1984; =-=Ripley and Sutherland, 1990-=-; Grenander et al., 1991; Storvik, 1994). The factored sampling algorithm (Grenander et al., 1991) generates a random variate x from a distribution ~ p(x) that approximates the posterior p(xjz). First... |

17 | Kalman lter-based algorithms for estimating depth from image sequences - Matthies, Kanade, et al. - 1989 |

15 | Applications of dynamic monocular machine vision - Dickmanns, Graefe - 1988 |

13 | Data association methods for tracking systems - Rao - 1992 |

13 | Learning exible models from image sequences - Baumberg, Hogg - 1994 |

11 | Bayes theorem and digital realizations for non-linear lters - Bucy - 1969 |

10 | Conditional-mean estimation via jumpdi usion processes in multiple target tracking/recognition - Miller, Srivasta, et al. - 1995 |

9 |
Statistical feature modelling for active contours
- Rowe, Blake
- 1996
(Show Context)
Citation Context ...to obtain a sequence of outline curves that is usable as training data. Given the high level of clutter, adequate performance with the Kalman filter is obtained here by means of background modelling (=-=Rowe and Blake, 1996-=-), a statistical form of background subtraction, which effectively removes clutter from the image data before it is tracked. It transpires, for this particular training set, that the learned motions c... |

9 | Building and using exible models incorporating grey-level information - Cootes, Taylor, et al. - 1993 |

7 | Adaptive ltering prediction and control - Goodwin, Sin - 1984 |

5 |
Fitting parameterised 3D models to images
- Lowe
- 1991
(Show Context)
Citation Context ...elling shape and motion. When suitable geometric models of a moving object are available, they can be matched effectively to image data, though usually at considerable computational cost (Hogg, 1983; =-=Lowe, 1991-=-; Sullivan, 1992; Huttenlocher et al., 1993). Once an object has been located approximately, tracking it in subsequent images becomes more efficient computationally (Lowe, 1992), especially if motion ... |

4 | Optimal ltering - Anderson, Moore - 1979 |

1 | Visual tracking of known three-dimensional objects - IJCV - 1998 |

1 | 31 A Non-linear filtering There are four distinct probability distributions represented in a non-linear Bayesian filter. Three of them form part of the problem specification and the fourth constitutes the solution. The three specified distributions are: 1 - IJCV - 1998 |

1 | A.2 Non-Gaussian process density Non-Gaussian state densities can arise from the nature of the process either because the dynamics are driven by non-Gaussian process noise, or, more generally, because the deterministic dynamics are non-linear. One approac - IJCV - 1988 |

1 | A.3 Non-Gaussian observation density In the case of visual tracking in clutter, non-linearity of the tracking lter arises, as we have seen, because the observation density p(zjx) is non-Gaussian and, furthermore, is multi-modal so that it cannot be well a - Rao - 1988 |

1 | 33 B Derivation of the sampling rule The correctness of the sampling rule (4) on page 6 is proved by rst deriving two lemmas from the independence assumption (2). (This is similar to the derivation found in (Bar-Shalom and Fortmann - IJCV - 1998 |

1 | 34 C Asymptotic correctness of the Condensation Algorithm The Condensation algorithm is validated here by a probabilistic argument showing that the sample-set representation of conditional density is correct, asymptotically, as the size N of the sample se - IJCV - 1998 |

1 | 35 C.3 Propagation of approximated state density First note that the samples s (n) t generated by the algorithm can themselves be regarded as random variables. Using the corollary it is possible to establish that asymptotically the probability density of - IJCV - 1998 |

1 | Monte-carlo lter and smoother for non-Gaussian nonlinear state space models - Kitagawa - 1996 |

1 | 31 A Non-linear ltering There are four distinct probability distributions represented in a non-linear Bayesian lter. Three of them form part of the problem speci cation and the fourth constitutes the solution. The three speci ed distributions are: 1. the - IJCV - 1998 |