## A robust snake implementation; a dual active contour (1997)

### Cached

### Download Links

- [users.ecs.soton.ac.uk]
- [www.ecs.soton.ac.uk]
- DBLP

### Other Repositories/Bibliography

Venue: | IEEE Transactions on Pattern Analysis and Machine Intelligence |

Citations: | 51 - 3 self |

### BibTeX

@ARTICLE{Gunn97arobust,

author = {Steve Fl Gunn and Mark S. Nixon},

title = {A robust snake implementation; a dual active contour},

journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},

year = {1997},

volume = {19},

pages = {63--68}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract-A conventional active contour formulation suffers difficulty in appropriate choice of an initial contour and values of parameters. Recent approaches have aimed to resolve these problems but can compromise other performance aspects. To relieve the problem in initialization, we use a dual active contour, which is combined with a local shape model to improve the parameterization. One contour expands from inside the target feature, the other contracts from the outside. The two contours are interlinked to provide a balanced technique with an ability to reject “weak ” local energy minima. Index Terms-Snakes, active contours, regularization, feature extraction, local shape.

### Citations

3310 | Snakes: Active contour models
- Kass, Witkin, et al.
- 1988
(Show Context)
Citation Context ...echnique with an ability to reject “weak” local energy minima. Index Terms—Snakes, active contours, regularization, feature extraction, local shape. ———————— ✦ ———————— 1 INTRODUCTION ACTIVE contours =-=[10]-=-, also termed snakes by the nature of their evolution, are a sophisticated approach to contour extraction and image interpretation. They advocate the paradigm that the presence of an edge depends not ... |

495 | On active contour models and balloons
- Cohen
- 1991
(Show Context)
Citation Context ...y and consideration of all appropriate image data. The external forces, F, are derived from the external image energy E ext . F i F G HG =-k ∂Eext ∂x vi ∂Eext ∂y vi I J KJ (12) Bilinear interpolation =-=[3]-=- ensures that a stable convergence is attainable. The constant, k, is chosen to normalise the external forces so that they lie within the interval [–1, 1]. Then the contour, v, is evolved according to... |

298 |
Finite-element methods for active contour models and balloons for 2-D and 3-D images
- Cohen, Cohen
- 1993
(Show Context)
Citation Context ...ated weighting parameters. The technique requires the initial contour to lie outside the feature of interest and relies on an inherent contraction force to move the contour towards the feature. Cohen =-=[2]-=- proposed an inflating contour that reduced the sensitivity to initialization, but increased the number of parameters. Berger [1] proposed a, similar, expanding contour. These techniques are constrain... |

286 | Boundary finding with parametrically deformable models
- Staib, Duncan
- 1992
(Show Context)
Citation Context ...n-trivial equilibrium provided it does not expand (or contract) indefinitely, which is possible provided: N -1 ji= bN- 2g p and 0 < ji < 2p (10) Â i= 0 Including higher level shape information, [12], =-=[16]-=-, other than low overall curvature can be advantageous. The local shape model allows such information to be integrated within the contour, by modifying the values of T, to change the contour’s natural... |

252 |
Regularization of inverse visual problems involving discontinuities
- Terzopoulos
- 1986
(Show Context)
Citation Context ... a selected image functional, to measure desired features such as edges, lines, regions [14] and, recently, texture [9]. The internal energy, the a priori information, regularises the external energy =-=[18]-=-, the a posteriori information. The technique refines an estimated initial contour by an energy minimization technique. The original technique [10] defines the snake energy, Esnake , of a contour, v, ... |

205 |
Shape discrimination using Fourier descriptors
- Persoon, Fu
- 1977
(Show Context)
Citation Context ... a better fit than a circle, the curvature was taken to be zero. To assess similarity between two contours u and v, we used the Euclidean feature distance d(u, v) of the contours’ Fourier Descriptors =-=[13]-=-, m and n, \\CA_NET1\SYS\LIBRARY\SHARE\TRANS\TPAMI\2-INPROD\P96106\P96106_1.DOC cores-96.dot JPR 19,968 12/04/96 3:11 PM 3 / 54 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 19... |

161 |
Dynamic programming for detecting, tracking, and matching deformable contours
- Geiger, Gupta, et al.
- 1995
(Show Context)
Citation Context ... solution that is highly dependent on the initial contour due to many local minima within a typical external energy function. Use of simulated annealing for minimization [17], and dynamic programming =-=[5]-=- have been proposed to reduce problems caused by local minima. However, these techniques are restricted by difficulty in choosing appropriate parameters due to scale variance and parameter interdepend... |

135 |
Region-based strategies for active contour models
- Ronfard
- 1994
(Show Context)
Citation Context ... desired properties of a contour’s shape, such as smoothness and continuity. The external energy is derived from a selected image functional, to measure desired features such as edges, lines, regions =-=[14]-=- and, recently, texture [9]. The internal energy, the a priori information, regularises the external energy [18], the a posteriori information. The technique refines an estimated initial contour by an... |

77 | G.: Model driven edge detection
- Fua, Leclerc
- 1988
(Show Context)
Citation Context ...which expands from inside. This reduces the sensitivity to initialization, by enabling a comparison between the contours’ energy, which is used to objectively reject weak minima, as advocated earlier =-=[4]-=-. The scale-variance of the internal energy function in a conventional snake makes it difficult to compare the behaviour of contracting and expanding contours. This also illustrates the main difficult... |

57 | A bayesian approach to dynamic contours through stochastic sampling and simulated annealing
- Storvik
- 1994
(Show Context)
Citation Context ...ce IEEECS Log Number P96106. 2 solution that is highly dependent on the initial contour due to many local minima within a typical external energy function. Use of simulated annealing for minimization =-=[17]-=-, and dynamic programming [5] have been proposed to reduce problems caused by local minima. However, these techniques are restricted by difficulty in choosing appropriate parameters due to scale varia... |

32 | The organization of curve detection: coarse tangent fields and fine spline covering - Zucker, David, et al. - 1989 |

23 |
Robust active contours with insensitive parameters: Pattern Recognition
- Xu, Segawa, et al.
- 1994
(Show Context)
Citation Context ... unwanted contraction force. The new contour has no preference to expand or contract, other than to acquire its natural shape. This is similar to a recent approach which removed the contraction force =-=[20]-=-, but it is more efficient by the use of a direct implementation, and moreover it enables prior shape information to be integrated within the contour. This is achieved by a simple relationship between... |

22 |
Active Mesh—A Feature Seeking and Tracking Image Sequence Representation Scheme
- Wang, Lee
- 1994
(Show Context)
Citation Context ...t contraction force compounds the parameter problem and makes the generalization to open contours difficult. Alternative approaches to the problem of initialization can use exhaustive initializations =-=[19]-=-, [21], but their computationally expensive nature is not justified for many applications. The generalised Hough transform has recently been used [11] to provide initial contours when substantial prio... |

21 |
Active region models for segmenting textures and colours
- Ivins, Porrill
- 1995
(Show Context)
Citation Context ...tour’s shape, such as smoothness and continuity. The external energy is derived from a selected image functional, to measure desired features such as edges, lines, regions [14] and, recently, texture =-=[9]-=-. The internal energy, the a priori information, regularises the external energy [18], the a posteriori information. The technique refines an estimated initial contour by an energy minimization techni... |

5 | Improving Snake Performance Via a Dual Active
- Gunn, Nixon
- 1995
(Show Context)
Citation Context ...ficulty in determining appropriate values for the parameters. To overcome difficulty in this choice, and to enable a comparison between contours, we develop a scale invariant internal energy function =-=[6]-=-, that retains the conventional continuity and smoothness constraints, but removes the unwanted contraction force. The new contour has no preference to expand or contract, other than to acquire its na... |

4 |
Towards Dynamic Adaption of Snake Contours
- Berger
- 1991
(Show Context)
Citation Context ...erent contraction force to move the contour towards the feature. Cohen [2] proposed an inflating contour that reduced the sensitivity to initialization, but increased the number of parameters. Berger =-=[1]-=- proposed a, similar, expanding contour. These techniques are constrained by their gradient descent nature, with a ———————————————— • The authors are with the ISIS research group, Dept. of Electronics... |

3 |
A Dual Active Contour
- Gunn, Nixon
- 1994
(Show Context)
Citation Context ...t minimum. However the contour is now sensitive to local minima and consequently sensitive to initialization. A strategy which finds a “good” minimum is now required. Accordingly, we use two contours =-=[7]-=-, one inside and one outside the feature of interest. The two contours aim to find a local energy minimum according to a trade-off between the prior shape constraints and the image. When both contours... |

3 |
Deformable contours:modeling and extraction
- Lai, R
- 1994
(Show Context)
Citation Context ...initialization can use exhaustive initializations [19], [21], but their computationally expensive nature is not justified for many applications. The generalised Hough transform has recently been used =-=[11]-=- to provide initial contours when substantial prior knowledge is available. Here, we introduce a new dual active contour that confronts the two primary problems of initialization and parameterization.... |

3 |
Active Contour Models: Overview
- Menet, Saint-Marc, et al.
- 1990
(Show Context)
Citation Context ...e a non-trivial equilibrium provided it does not expand (or contract) indefinitely, which is possible provided: N -1 ji= bN- 2g p and 0 < ji < 2p (10) Â i= 0 Including higher level shape information, =-=[12]-=-, [16], other than low overall curvature can be advantageous. The local shape model allows such information to be integrated within the contour, by modifying the values of T, to change the contour’s n... |

1 | Deformable Contours-Modeling and Extraction,” Trans. Pattern Analysis and - Lai, Chin |

1 | tiersoon and-K.S. Fu; “Shape &criminaiion Using Fourier Descriptors - unknown authors |

1 |
Kinematics of Interface Evolution with Application to ActiveContour Models
- Rougon
- 1991
(Show Context)
Citation Context ...e driving force. 3.3 Implementation The minimization process is implemented by the method of gradient descent. The rate of evolution controls the stability and convergence of the minimization process =-=[15]-=-. The evolution must be controlled to ensure that a contour cannot move by more than one pixel, in one iteration, ensuring stability and consideration of all appropriate image data. The external force... |

1 | Regula&ti& of Inverse %;a1 Problems involving Discontinuities,” Trans - T&opoulos - 1986 |

1 |
Filtering Closed Curves,” Trans
- Horn, Weldon
- 1972
(Show Context)
Citation Context ...el. The original technique implements the internal continuity and smoothness constraints by two regularising functions [18], which effectively low-pass filter the contour. These result in contraction =-=[8]-=-: Closed and open contours shrink to a point without the support of external forces. Modification of the continuity and curvature constraints to remove the unwanted contraction force, produces a solut... |