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## Active Contours for Tracking Distributions (2002)

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### Other Repositories/Bibliography

Venue: | IEEE Trans. Image Processing |

Citations: | 66 - 4 self |

### Citations

12415 |
Elements of information theory
- Cover, Thomas
(Show Context)
Citation Context ...ity . There are a variety of criteria which can be used to compare the two densities. One obvious candidate is the Kullback–Leibler distance This measure plays an important role in information theor=-=y [27]. -=-Note that the Kullback–Leibler distance is not truly a metric, as it is not symmetric in its argument. Nonetheless, it is referred to as a distance, as the smaller it is, the closer are the two dist... |

3948 | Snakes: Active contour models
- Kass, Witkin, et al.
- 1988
(Show Context)
Citation Context ...he advantage of dealing directly with two difficulties that often confound such algorithms. First, the tracker does not rely on edges. Many trackers use edge information exclusively; examples include =-=[8, 2, 7]-=-. The problems associated with using edges are well-known. For instance, edge-detectors may be inaccurate, leading to the detection of spurious edges; edges may not be detected when contrast between a... |

1629 |
Applications of the Lie Groups to Differential Equations
- Olver
- 1986
(Show Context)
Citation Context ... c 0 (s))ds where in the second line, the parameterization of c = @! has been substituted. In order to calculate c , we may use results from the calculus of variations. In particular, it can be shown [13] that c = @ @c d ds @ @c 0 5 Now, @ @c 1 d ds @ @c 0 1 = @P 1 @c 1 c 0 2 + @P 2 @c 1 c 0 1 d ds P 2 = @P 1 @c 1 c 0 2 + @P 2 @c 1 c 0 1 @P 2 @c 1 c 0 1 + @P 2 @c 2 c 0 2 = @P 1 @c 1 ... |

1503 | CONDENSATION -- conditional density propagation for visual tracking,
- Isard, Blake
- 1998
(Show Context)
Citation Context ...he advantage of dealing directly with two difficulties that often confound such algorithms. First, the tracker does not rely on edges. Many trackers use edge information exclusively; examples include =-=[8, 2, 7]-=-. The problems associated with using edges are well-known. For instance, edge-detectors may be inaccurate, leading to the detection of spurious edges; edges may not be detected when contrast between a... |

1473 |
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
- Osher, Sethian
- 1988
(Show Context)
Citation Context ...s geometric curve evolution [3, 9, 10, 4], and this paper will follow in that tradition. Many of these recent papers have focused on the novel level-set approach to implementing geometric curve flows =-=[14]-=-, which allows for a stable numerical scheme, as well as for changes in topology to be handled without difficulty. There are several recent papers in the active contour literature which bear closer re... |

1425 | Geodesic active contours,
- Caselles, Kimmel, et al.
- 1992
(Show Context)
Citation Context ...e field originated with the snake formulation of Kass, Witkin, and Terzopoulos [8], and many papers in a similar vein followed [1, 17, 19]. The recent trend has been towards geometric curve evolution =-=[3, 9, 10, 4]-=-, and this paper will follow in that tradition. Many of these recent papers have focused on the novel level-set approach to implementing geometric curve flows [14], which allows for a stable numerical... |

1292 | Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems
- Mumford, Shah
- 1989
(Show Context)
Citation Context ...y. There are several recent papers in the active contour literature which bear closer relation to the current paper. Chan and Vese [5] solve a restricted form of the Mumford-Shah segmentation problem =-=[11]-=-, assuming only two regions whose segments are piecewise constant. Yezzi et al. [22, 21] and Tsai et al. [18] also solve a number of segmentation problems, including the fullblown Mumford-Shah segment... |

1206 | Active contours without edges
- Chan, Vese
- 2001
(Show Context)
Citation Context ...e, as well as for changes in topology to be handled without difficulty. There are several recent papers in the active contour literature which bear closer relation to the current paper. Chan and Vese =-=[5]-=- solve a restricted form of the Mumford-Shah segmentation problem [11], assuming only two regions whose segments are piecewise constant. Yezzi et al. [22, 21] and Tsai et al. [18] also solve a number ... |

815 | Real-time tracking of non-rigid objects using mean shift. In:
- Comaniciu, Ramesh, et al.
- 2000
(Show Context)
Citation Context ...is presented in this paper. However, before attempting to include geometric concerns, it is instructive to see how well a pure photometric tracker can do. A recent general-purpose photometric tracker =-=[6]-=-, to be discussed at greater length shortly, demonstrates the ability of such trackers to succeed. The active contour literature is vast, so no attempt will be made to review it comprehensively. The f... |

808 | Shape modeling with front propagation: a level set approach
- Malladi, Sethian, et al.
- 1995
(Show Context)
Citation Context ...e field originated with the snake formulation of Kass, Witkin, and Terzopoulos [8], and many papers in a similar vein followed [1, 17, 19]. The recent trend has been towards geometric curve evolution =-=[3, 9, 10, 4]-=-, and this paper will follow in that tradition. Many of these recent papers have focused on the novel level-set approach to implementing geometric curve flows [14], which allows for a stable numerical... |

773 | Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multi-Band Image Segmentation
- Zhu, Yuille
- 1996
(Show Context)
Citation Context ...al papers in the active contour literature which bear closer relation to the current paper. An early paper which uses probabilistic region-based information for segmentation is that of Zhu and Yuille =-=[17]. -=-More recently, Chan and Vese [18] solve a restricted form of the Mumford–Shah segmentation problem [19], assuming only two regions whose segments are piecewise constant; they have also examined the ... |

487 |
CONDENSATION—conditional density propagation for visual tracking
- Isard, Blake
- 1998
(Show Context)
Citation Context ...d be unfair.) With regard to comparison with other algorithms, it is also worth commenting on the performance comparison between the proposed flows and two popular methods: the condensation algorithm =-=[2]-=- and mean-shift technique [6], [26]. The condensation algorithm has been shown to have difficulty in following the motion of the finger in the third experiment without a great deal of explicit modelin... |

293 |
Vese “Active Contours Without Edges”
- Chan, Luminita
- 2001
(Show Context)
Citation Context ...erature which bear closer relation to the current paper. An early paper which uses probabilistic region-based information for segmentation is that of Zhu and Yuille [17]. More recently, Chan and Vese =-=[18] sol-=-ve a restricted form of the Mumford–Shah segmentation problem [19], assuming only two regions whose segments are piecewise constant; they have also examined the full-blown Mumford–Shah segmentatio... |

280 |
The divergence and Bhattacharyya distance measures in signal selection
- Kailath
- 1967
(Show Context)
Citation Context ...tric in its argument. Nonetheless, it is referred to as a distance, as the smaller it is, the closer are the two distributions. A second criterion for comparing densities is the Bhattacharyya measure =-=[28]-=- This measure varies between 0 and 1, where 0 indicates complete mismatch, and 1 indicates a complete match. In other words, it is an affinity measure, rather than a distance. This is the matching mea... |

271 | Geodesic active contours and level sets for the detection and tracking of moving objects,
- Paragios, Deriche
- 2000
(Show Context)
Citation Context ...kers, to assume knowledge of the background, as the tracker must be able to work in as many situations as possible. Paragios and Deriche have extended this work to the context of motion estimation in =-=[16]-=-. All of the above mentioned papers are similar in spirit to the current paper, in that they use information contained in the interior of the contours within the geometric curve evolution 2 framework.... |

256 |
A geometric model for active contours in image processing.
- Caselles, Catte, et al.
- 1993
(Show Context)
Citation Context ...e field originated with the snake formulation of Kass, Witkin, and Terzopoulos [8], and many papers in a similar vein followed [1, 17, 19]. The recent trend has been towards geometric curve evolution =-=[3, 9, 10, 4]-=-, and this paper will follow in that tradition. Many of these recent papers have focused on the novel level-set approach to implementing geometric curve flows [14], which allows for a stable numerical... |

239 | Gradient flows and geometric active contour models,” in
- Kichenassamy, Kumar, et al.
- 1995
(Show Context)
Citation Context |

128 | A statistical approach to snakes for bimodal and trimodal imagery,”
- Yezzi, Tsai, et al.
- 1999
(Show Context)
Citation Context ...r relation to the current paper. Chan and Vese [5] solve a restricted form of the Mumford-Shah segmentation problem [11], assuming only two regions whose segments are piecewise constant. Yezzi et al. =-=[22, 21]-=- and Tsai et al. [18] also solve a number of segmentation problems, including the fullblown Mumford-Shah segmentation. Noteworthy as well is the paper of Paragios and Deriche [15], which solves a segm... |

125 |
Deformable boundary finding in medical images by integrating gradient and region information,”
- Chakraborty, Staib, et al.
- 1996
(Show Context)
Citation Context ...e exists a parameterization of for which where is the normal to . This result relies on Green’s Theorem, and was demonstrated in the work of Zhu and Yuille [17], as well as that of Chakraborty et al=-=. [29]-=-. In the next two sections, we will use this proposition. In the first case case, we will use a gradient descent approach to find an optimum of in terms of , i.e., a curve for which is 0. In the secon... |

118 |
Tracking with kalman snakes.
- Terzopoulos, Szeliski
- 1992
(Show Context)
Citation Context ...ture is vast, so no attempt will be made to review it comprehensively. The field originated with the snake formulation of Kass, Witkin, and Terzopoulos [8], and many papers in a similar vein followed =-=[1, 17, 19]-=-. The recent trend has been towards geometric curve evolution [3, 9, 10, 4], and this paper will follow in that tradition. Many of these recent papers have focused on the novel level-set approach to i... |

106 | An algorithm for data-driven bandwidth selection",
- Comaniciu
- 2003
(Show Context)
Citation Context ...iven by so-called “mean-shift analysis”; however, the way in which the ellipse shrinks or enlarges is incorporated in an ad hoc fashion. (This was treated in a more rigorous fashion in another pap=-=er, [26]-=-.) Nonetheless, this tracker performs very well experimentally, and does so in real time. III. THEORY A. Notation Let be the photometric variable of interest. For example, could be an intensity, color... |

77 | Tracking with Kalman Snakes, Active Vision, - Terzopoulos, Szeliski - 1992 |

72 | Geodesic active regions for supervised texture segmentation
- Paragios, Deriche
- 1999
(Show Context)
Citation Context ...nt. Yezzi et al. [22, 21] and Tsai et al. [18] also solve a number of segmentation problems, including the fullblown Mumford-Shah segmentation. Noteworthy as well is the paper of Paragios and Deriche =-=[15]-=-, which solves a segmentation problem using both boundary and region information. While the approach taken in this paper may appear superficially similar to the current approach, a key difference is t... |

67 | Lafter: Lips and Face Real Time Tracker",
- Oliver, Pentland, et al.
- 1997
(Show Context)
Citation Context ... headway may be made in the design of a lip-tracker by noticing that human lips tend to come in a small number of colours. Indeed, colour-based methods are often used in special-purpose trackers (e.g =-=[20, 12]-=- present colour-based face-trackers), mostly to excellent effect. The second problem which is directly addressed by this tracker is the difficulty of tracking successfully through cluttered scenes. Fi... |

53 |
Real time face and object tracking as a component of a perceptual user interface,
- Bradski
- 1998
(Show Context)
Citation Context ...ormation used are quite different, as are the techniques used in deriving the flows. Finally, it is worth mentioning the work of Comaniciu et al. [6], [7], which builds on earlier research of Bradski =-=[25]-=-, and which is in a sense most in keeping with the present work. This algorithm attempts to follow a distribution by maximizing the Bhattacharyya measure between a model distribution and an empirical ... |

26 |
Robust active contours with insensitive parameters,”
- Xu, Segawa, et al.
- 1994
(Show Context)
Citation Context ...ture is vast, so no attempt will be made to review it comprehensively. The field originated with the snake formulation of Kass, Witkin, and Terzopoulos [8], and many papers in a similar vein followed =-=[1, 17, 19]-=-. The recent trend has been towards geometric curve evolution [3, 9, 10, 4], and this paper will follow in that tradition. Many of these recent papers have focused on the novel level-set approach to i... |

23 | A curve evolution approach to smoothing and segmentation using the Mumford-Shah functional
- Tsai, Yezzi, et al.
- 2000
(Show Context)
Citation Context ... paper. Chan and Vese [5] solve a restricted form of the Mumford-Shah segmentation problem [11], assuming only two regions whose segments are piecewise constant. Yezzi et al. [22, 21] and Tsai et al. =-=[18]-=- also solve a number of segmentation problems, including the fullblown Mumford-Shah segmentation. Noteworthy as well is the paper of Paragios and Deriche [15], which solves a segmentation problem usin... |

8 |
Binary and ternary flows for image segmentation
- Yezzi, Tsai, et al.
- 1999
(Show Context)
Citation Context ...r relation to the current paper. Chan and Vese [5] solve a restricted form of the Mumford-Shah segmentation problem [11], assuming only two regions whose segments are piecewise constant. Yezzi et al. =-=[22, 21]-=- and Tsai et al. [18] also solve a number of segmentation problems, including the fullblown Mumford-Shah segmentation. Noteworthy as well is the paper of Paragios and Deriche [15], which solves a segm... |

4 | Provably fast algorithms for contour tracking - Freedman, Brandstein - 2000 |

4 | object tracking - “Kernel-based - 2003 |

3 |
Using dynamic programming for minimizing the enegy of active contours in the presence of hard constraints
- Amini, Tehrani, et al.
- 1988
(Show Context)
Citation Context ...ture is vast, so no attempt will be made to review it comprehensively. The field originated with the snake formulation of Kass, Witkin, and Terzopoulos [8], and many papers in a similar vein followed =-=[1, 17, 19]-=-. The recent trend has been towards geometric curve evolution [3, 9, 10, 4], and this paper will follow in that tradition. Many of these recent papers have focused on the novel level-set approach to i... |

2 |
Snakes: Active contour models,” presented at the Int
- Kass, Witkin, et al.
- 1987
(Show Context)
Citation Context ...he advantage of dealing directly with two difficulties that often confound such algorithms. First, the tracker does not rely on edges. Many trackers use edge information exclusively; examples include =-=[1]��-=-�[3]. The problems associated with using edges are well-known. For instance, edge-detectors may be inaccurate, leading to the detection of spurious edges; edges may not be detected when contrast betwe... |

1 |
A real-time face tracer
- Yang, Waibel
- 1996
(Show Context)
Citation Context ... headway may be made in the design of a lip-tracker by noticing that human lips tend to come in a small number of colours. Indeed, colour-based methods are often used in special-purpose trackers (e.g =-=[20, 12]-=- present colour-based face-trackers), mostly to excellent effect. The second problem which is directly addressed by this tracker is the difficulty of tracking successfully through cluttered scenes. Fi... |

1 |
Vese, “A level-set algorithm for minimizing te mumford-shah functional in image processing
- Chan, A
(Show Context)
Citation Context ...olve a restricted form of the Mumford–Shah segmentation problem [19], assuming only two regions whose segments are piecewise constant; they have also examined the full-blown Mumford–Shah segmentat=-=ion [20]. -=-Yezzi et al. [21], [22] and Tsai et al. [23] also solve a number of segmentation problems, including the full Mumford–Shah segmentation. Noteworthy as well is the paper of Paragios and Deriche [24],... |

1 |
and ternary flows for image segmentation
- “Binary
- 1999
(Show Context)
Citation Context ... the Mumford–Shah segmentation problem [19], assuming only two regions whose segments are piecewise constant; they have also examined the full-blown Mumford–Shah segmentation [20]. Yezzi et al. [2=-=1], [22] a-=-nd Tsai et al. [23] also solve a number of segmentation problems, including the full Mumford–Shah segmentation. Noteworthy as well is the paper of Paragios and Deriche [24], which solves a segmentat... |