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## Global Minimum for Active Contour Models: A Minimal Path Approach (1997)

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Citations: | 238 - 70 self |

### Citations

4675 | A Computational Approach to Edge Detection
- Canny
- 1986
(Show Context)
Citation Context ...Closed contour: Medical Image In this third example, we want to extract the left ventricle in an MR image of the heart area. The potential is a function of the distance to the closest edge in a Canny =-=[7]-=- edge detection image (see Figure 14). Since it is a closed contour we use the saddle points classification in closing the boundaries of a single object in the heart image (see Figures 15 and 16). Giv... |

3948 | Snakes: Active contour models
- Kass, Witkin, et al.
- 1988
(Show Context)
Citation Context ...l Image : : : : : : : : : : : : : 29 7 Concluding RemarkssL. Cohen, R. Kimmel, March 26, 1996. 1 1 Introduction An active contour model for boundary integration and features extraction, introduced in =-=[26]-=-, has been considerably used and studied during the last decade. Most of the approaches that were introduced since then try to overcome the main drawbacks of this model: initialization, minimization a... |

1425 | Geodesic active contours,
- Caselles, Kimmel, et al.
- 1992
(Show Context)
Citation Context ...btained in the previous section with paths starting at p 0 and p 1 respectively. A natural combination is to use the above method in order to locate the minimal set, and then let the model defined in =-=[9]-=- take over and refine the result. However, we recommend an easier way to compute the path by back propagation. 3.5.2 Back propagation from p 1 In order to determine the minimal path between p 0 and p ... |

1388 | User’s guide to viscosity solutions of second order partial differential equations - Crandall, Ishii, et al. - 1992 |

1181 | Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations - Osher, Sethian - 1988 |

1087 |
A note on two problems in connection with graphs
- Dijkstra
- 1959
(Show Context)
Citation Context ...same looking two initial contours with different control points may lead to completely different solutions. One may argue that using previously mentioned graph search algorithms like the A , Dijkstra =-=[19, 48]-=-, or F as proposed in [22] for road tracking, might be sufficient. These algorithms are indeed efficient, yet suffer from `metrication errors'. The graph based algorithms consider the image as a graph... |

808 | Shape modeling with front propagation: a level set approach
- Malladi, Sethian, et al.
- 1995
(Show Context)
Citation Context ...n [12] and detailed in Section 4.2, previous local edge detection might be taken into account as data for defining the potential. A geometric approach for deformable models was recently introduced in =-=[8, 37]. A leve-=-l set approach for curve evolution [44, 49] is used to implement a planar curve evolution of the form: @C(s; �� ) @�� = P (C)(C ss + w ~n); (5) where s is the arc-length parameter of the curve... |

626 | A fast marching level set method for monotonically advancing fronts
- Sethian
- 1996
(Show Context)
Citation Context ...ution scheme that provides at each image pixel an output of the energy along the path of minimal integrated energy joining that pixel to the given start point. We use the Sethian fast marching method =-=[51, 50, 1]-=-. The search for a global minimum is then done efficiently. While this minimum is restricted to connect two given points, we also present a topology--based saddle search that helps in automatically cl... |

607 |
A level set approach for computing solutions to incompressible two-phase flow
- Sussman, Smereka, et al.
- 1994
(Show Context)
Citation Context ...ub-pixel estimation of the distance using a parallel algorithm was presented in [30]. It gives a high sub-pixel precision of the distance. This is one possible application of shortest path estimation =-=[28, 54]-=- presented briefly in Section 3.2. Note also that the distance potential selection P may be also considered as the normalized force introduced in [12] for stabilizing the results (i.e. for P = d E we ... |

588 | On active contour models and balloons
- Cohen
- 1991
(Show Context)
Citation Context ... initialization is made for the first image, it is possible to use the resulting contour of the first image as initial condition for the second and so on, as proposed in [26]. Using the balloon model =-=[12]-=- allows a less demanding initialization since any initial closed curve inside an object may be used to obtain its complete boundary. It enables in some cases, to obtain a completely automatic initiali... |

516 |
Algorithms in C++.
- Sedgewick
- 1995
(Show Context)
Citation Context ...same looking two initial contours with different control points may lead to completely different solutions. One may argue that using previously mentioned graph search algorithms like the A , Dijkstra =-=[19, 48]-=-, or F as proposed in [22] for road tracking, might be sufficient. These algorithms are indeed efficient, yet suffer from `metrication errors'. The graph based algorithms consider the image as a graph... |

423 | A fast level set method for propagating interfaces
- Adalsteinsson, Sethian
- 1995
(Show Context)
Citation Context ...ctive contours without the constant term and fixed end points is the right flow for this case. Observe that it should operate only within the "fat" set, which can be considered as a fixed na=-=rrow band [2]-=-, thereby reducing drastically the computational complexity of this refining. When there are two or more minimal paths, as will be seen in Section 5, the destination point p 1 is a saddle point and ea... |

373 | Efficient algorithms for globally optimal trajectories - Tsitsiklis - 1995 |

357 |
Using dynamic programming for solving variational problems in Vision,”
- Amini, Weymouth, et al.
- 1990
(Show Context)
Citation Context ...each pixel or vertex is considered as a start point and the algorithm should find simultaneously all interesting feature curves. Dynamic programming has also been used for snakes, first by authors of =-=[3]-=-. Although a complete theoretical description of continuous dynamic programming is reviewed, the proposed application to active contours is different from the ones above and our approach. The dynamic ... |

291 | Intelligent scissors for image composition. In: - Mortensen, Barrett - 1995 |

247 |
Distance Transformations in Arbitrary Dimensions”,
- Borgefors
- 1984
(Show Context)
Citation Context ... either when there is no more change in the process (this has to happen in a finite number of iterations) or after a given number of passes. This kind of approach was used to compute distance maps in =-=[5, 17]-=-. It was also used for road detection in [39, 40], using some improvements in the potential definition. The authors also add some constraint on the curvature by taking into account sets of three verti... |

247 |
A viscosity solutions approach to shape-from-shading
- Rouy, Tourin
- 1992
(Show Context)
Citation Context ... the front and \Deltat is the time step of the scheme, of the above approach we refer to [2]. 3.4.3 Rouy-Tourin Shape from Shading Approach The second approach is based on a shape from shading method =-=[45, 21]-=- and searches for the surface U itself instead of tracking its level sets. In this case the surface may be found according to the following minimization procedure: Given U = 0 at the start point as bo... |

239 | Gradient flows and geometric active contour models,” in
- Kichenassamy, Kumar, et al.
- 1995
(Show Context)
Citation Context ...v, for the arbitrary parameter v). The curve evolution equation is then reformulated and implemented using the Osher-Sethian [44] numerical algorithm. Similar geometric models were also introduced in =-=[27, 61, 53]-=- and extended to color and texture in [47]. Although our work is related to [9], it is a totally independent approach. Actually, the geodesic active contours may be considered as a natural refinement ... |

233 | Euclidean distance mapping”,
- Danielsson
- 1980
(Show Context)
Citation Context ... either when there is no more change in the process (this has to happen in a finite number of iterations) or after a given number of passes. This kind of approach was used to compute distance maps in =-=[5, 17]-=-. It was also used for road detection in [39, 40], using some improvements in the potential definition. The authors also add some constraint on the curvature by taking into account sets of three verti... |

216 | Surface modeling with oriented particle systems. Computer Graphics,
- Szeliski, Tonnesen
- 1992
(Show Context)
Citation Context ...e motivated many other recent works like [9, 10, 61, 27, 57] for 2D and 3D implicit deformable models. Other models that can handle topology changes have also been used for curves in [38] or surfaces =-=[33, 55, 56]-=-. In this paper we present a new approach for finding the global minimum of energy minimizing curves given only one or two end points. Our goal is to help the user in solving the problem in hand by ma... |

196 | Finite Element Methods for Active Contour Models and balloons for 2D and 3D Images”,
- Cohen, Cohen
- 1993
(Show Context)
Citation Context ...oundary conditions. These may be free boundaries, as in the original snakes [26], cyclic boundaries by using periodic closed curves [58], or fixed boundaries by giving C(0), C v (0), C(1) and C v (1) =-=[12, 15]-=-. The mechanical properties of the model are controlled by the functions or constants w j . If C is a local minimum of E, it satisfies the associated Euler-Lagrange equation: ( \Gamma(w 1 C v ) v + (w... |

193 |
Tracking deformable objects in the plane using an active contour model,
- Leymarie, Levine
- 1993
(Show Context)
Citation Context ... This constant term is thus similar to the pressure force introduced for the balloon model [12]. It is also related to the dilatation transform in mathematical morphology and the grass-fire transform =-=[34]-=-. It was shown that the geometric snakes model performs better than the classical snakes in some cases like topology changes when implemented by the implicit embedding function technique proposed by O... |

186 | An active testing model for tracking roads in satellite images,”
- Geman, Jedynak
- 1996
(Show Context)
Citation Context ...ws the middle of the road. This example illustrates the efficiency of our approach compared to classical snakes. We do not claim that this is a road detection algorithm as one can find for example in =-=[22, 25]-=-. For such an application, if the two edges of the road are needed rather than the middle way, our result could be refined using either ribbon snakes [43] or a thick contour model like in [18]. Given ... |

176 | Dynamic programming for detecting, tracking and matching deformable contours - Geiger, Gupta, et al. - 1995 |

172 |
A geometric model for active contours,”
- Caselles, Catte, et al.
- 1993
(Show Context)
Citation Context ...ic initialization. For example, in [12] preprocessing is used to get an initial guess that has to be inside the desired area. The same property can be realized using the geometric model introduced in =-=[8, 36]-=- and recently improved in [9]. In [43], only two end points on the boundary are needed to follow the contour. Although the smoothing effect of the snakes may overcome small defaults in the data, spuri... |

160 | Structural saliency: the detection of globally salient structures using a locally connected network - Sha’Ashua, Ullman - 1988 |

125 |
Detection of roads and linear structures in low-resolution aerial imagery using a multisource knowledge integration technique. Computer Graphics and Image Processing,
- Fischler, Tenenbaum, et al.
- 1981
(Show Context)
Citation Context ...th integration, it also incorporates the regularization of the path like a "snake" model. Qualitatively, the relation between the potential and the smoothness of the result was understood an=-=d used in [22]-=-, long before the age of snakes. Here, we introduce a quantitative bound expressing the connection between the curvature and the generated potential. This bound is useful in many applications. Section... |

92 | A common framework for curve evolution, segmentation and anisotropic diffusion. - Shah - 1996 |

83 | Model Driven Edge Detection - Fua, Leclerc - 1988 |

74 |
Dynamic Programming and Modern Control Theory
- Bellman, Kalaba
- 1965
(Show Context)
Citation Context ...nt of the level set L(t) is dt ~ P from (11). So the derivative @U @~n = hrU;~ni = krUk is equal to dt= dt ~ P = ~ P . A rigorous proof of this idea can be found for example in [6]. (see also Bellman =-=[4] for a n-=-ice proof on the orthogonality of the wave fronts and the geodesics). Here, boundary conditions are given in the form of fixing the point C(0) = p 0 , i.e. U(p 0 ; �� ) = 0 for all �� . Author... |

74 |
Vector-valued active contours
- Sapiro
(Show Context)
Citation Context ...tion equation is then reformulated and implemented using the Osher-Sethian [44] numerical algorithm. Similar geometric models were also introduced in [27, 61, 53] and extended to color and texture in =-=[47]-=-. Although our work is related to [9], it is a totally independent approach. Actually, the geodesic active contours may be considered as a natural refinement procedure to the proposed approach. We not... |

69 |
A review of recent numerical algorithms for hypersurfaces moving with curvature-dependent speed.
- Sethian
- 1989
(Show Context)
Citation Context ... edge detection might be taken into account as data for defining the potential. A geometric approach for deformable models was recently introduced in [8, 37]. A level set approach for curve evolution =-=[44, 49] is used-=- to implement a planar curve evolution of the form: @C(s; �� ) @�� = P (C)(C ss + w ~n); (5) where s is the arc-length parameter of the curve C in this case. Therefore, C ss j ~n is the curvat... |

68 |
On the optimal detection of curves in noisy pictures
- Montanari
- 1971
(Show Context)
Citation Context ...ur, by using the surface of minimal action. To find the surface of minimal action, graph search and dynamic programming techniques were often used, considering the image pixels as vertices in a graph =-=[42, 22, 11]-=-. A description of A and F algorithms, applied to road detection, can be found in [22]. The distance image is initialized with value 1 everywhere except at a start point with value zero. At each itera... |

67 |
Finding shortest paths on surfaces using level set methods,”
- Kimmel, Amir, et al.
- 1995
(Show Context)
Citation Context ...oblem to the type of boundary conditions with fixed end points, however, as we will see in Section 5, the proposed approach may also be used for closed contours. Motivated by the ideas put forward in =-=[28, 30]-=- we develop an efficient and consistent method to find the path of minimal cost between two points, using the surface of minimal action [46, 30, 60] and the fact that operating on a given potential (c... |

61 |
Global Shape from Shading
- Kimmel, Bruckstein
- 1994
(Show Context)
Citation Context ...es L(v; t) construct the level sets of the surface U(x; y) : IR 2 ! IR + defined in (9). The t level set of U is exactly the curve L(:; t). Although a rigorous proof of this statement can be found in =-=[6]-=-, it can be understood simply by the following geometric interpretation. Observe that adding to a path ending at a point of L(:; t) a small segment in the normal direction to L(:; t) and of length 1 ~... |

55 |
B.C.: Evolutionary fronts for topology-independent shape modeling and recovery
- Malladi, Sethian, et al.
- 1994
(Show Context)
Citation Context ...ic initialization. For example, in [12] preprocessing is used to get an initial guess that has to be inside the desired area. The same property can be realized using the geometric model introduced in =-=[8, 36]-=- and recently improved in [9]. In [43], only two end points on the boundary are needed to follow the contour. Although the smoothing effect of the snakes may overcome small defaults in the data, spuri... |

55 | Image segmentation by reaction-diffusion bubbles
- Tek, Kimia
- 1995
(Show Context)
Citation Context ... with holes, it is possible [8, 36] to model the contour as a level set of a surface, allowing it to change its topology in a natural way. These approaches have motivated many other recent works like =-=[9, 10, 61, 27, 57]-=- for 2D and 3D implicit deformable models. Other models that can handle topology changes have also been used for curves in [38] or surfaces [33, 55, 56]. In this paper we present a new approach for fi... |

53 |
An Optimal Control Formulation and Related Numerical Methods for a Problem in Shape Reconstruction,
- Dupuis, Oliensis
- 1993
(Show Context)
Citation Context ...rithm (so L. Cohen, R. Kimmel, March 26, 1996. 9 called in [22]) computes the distance with a sequential update of the pixels. It is similar in spirit to the algorithm used in Section 3.4.3 (see also =-=[21]-=-), except that Equation (16) is again consistent. Using the F , the global minimum is reached only after the image is scanned iteratively top to bottom, row by row, left to right followed by right to ... |

42 | Medical image segmentation using topologically adaptable surface’;
- McInerney, Terzopoulos
- 1997
(Show Context)
Citation Context ...se approaches have motivated many other recent works like [9, 10, 61, 27, 57] for 2D and 3D implicit deformable models. Other models that can handle topology changes have also been used for curves in =-=[38]-=- or surfaces [33, 55, 56]. In this paper we present a new approach for finding the global minimum of energy minimizing curves given only one or two end points. Our goal is to help the user in solving ... |

39 | Auxiliary variables and two-step iterative algorithms in computer vision problems
- Cohen
- 1995
(Show Context)
Citation Context ...tion [37, 36, 35]. The difficulty here is that there is no order in the set of points and that it is unknown in advance which points belong to the boundary. This is defined as implicit constraints in =-=[13]-=-. Denote by E(x; y) : D ! f0; 1g a binary function representing the result of applying a standard edge detector on the image I, where 1 corresponds to a detected edge point. One possible way of defini... |

38 | Algorithms for implicit deformable models,” in
- Whitaker
- 1995
(Show Context)
Citation Context ... with holes, it is possible [8, 36] to model the contour as a level set of a surface, allowing it to change its topology in a natural way. These approaches have motivated many other recent works like =-=[9, 10, 61, 27, 57]-=- for 2D and 3D implicit deformable models. Other models that can handle topology changes have also been used for curves in [38] or surfaces [33, 55, 56]. In this paper we present a new approach for fi... |

37 | Surface reconstruction using active contour models - Cohen, Bardinet, et al. - 1992 |

34 | Sub-pixel distance maps and weighted distance transforms
- Kimmel, Kiryati, et al.
- 1996
(Show Context)
Citation Context ...oblem to the type of boundary conditions with fixed end points, however, as we will see in Section 5, the proposed approach may also be used for closed contours. Motivated by the ideas put forward in =-=[28, 30]-=- we develop an efficient and consistent method to find the path of minimal cost between two points, using the surface of minimal action [46, 30, 60] and the fact that operating on a given potential (c... |

34 | Brownian Strings: Segmenting Images with Stochastically Deformable Contours - Grzeszczuk, Levin - 1997 |

31 | Dibos A geometric model for active contours. Numerische Mathematik - Caselles, Catte, et al. - 1993 |

28 |
A Review of the Theory, Algorithms, and Applications of Level Set Methods for Propagating Interfaces, Acta Numerica,
- Sethian
- 1996
(Show Context)
Citation Context ...ution scheme that provides at each image pixel an output of the energy along the path of minimal integrated energy joining that pixel to the given start point. We use the Sethian fast marching method =-=[51, 50, 1]-=-. The search for a global minimum is then done efficiently. While this minimum is restricted to connect two given points, we also present a topology--based saddle search that helps in automatically cl... |

28 |
Shading from shape, the eikonal equation solved by grayweighted distance transform. Patt Recogn Lett 11:68190
- Verbeek, Verwer
- 1990
(Show Context)
Citation Context ... closed contours. Motivated by the ideas put forward in [28, 30] we develop an efficient and consistent method to find the path of minimal cost between two points, using the surface of minimal action =-=[46, 30, 60]-=- and the fact that operating on a given potential (cost) function helps in finding the solution for our path of minimal action (also known as minimal geodesic, or path of minimal potential). Thereby, ... |

28 | Level Set Methods: Evolving - Sethian - 1996 |

24 |
G.: Estimating shortest paths and minimal distances on digitized three-dimensional surfaces
- Kiryati, Székely
- 1993
(Show Context)
Citation Context ... to the true one as the grid is refined. This is known not to be the case in general graph search algorithms that suffer from digitization bias due to the metrication error when implemented on a grid =-=[41, 32]-=-. This gives a clear advantage to our method over minimal path estimation using graph search. Before introducing the proposed method, let us review the graph search based methods that try to minimize ... |

23 | Minimal surfaces: A three dimensional segmentation approach
- Caselles, Kimmel, et al.
- 1997
(Show Context)
Citation Context ... with holes, it is possible [8, 36] to model the contour as a level set of a surface, allowing it to change its topology in a natural way. These approaches have motivated many other recent works like =-=[9, 10, 61, 27, 57]-=- for 2D and 3D implicit deformable models. Other models that can handle topology changes have also been used for curves in [38] or surfaces [33, 55, 56]. In this paper we present a new approach for fi... |

22 |
Data structures for operations on digital images
- RUTOVITZ
- 1968
(Show Context)
Citation Context ... closed contours. Motivated by the ideas put forward in [28, 30] we develop an efficient and consistent method to find the path of minimal cost between two points, using the surface of minimal action =-=[46, 30, 60]-=- and the fact that operating on a given potential (cost) function helps in finding the solution for our path of minimal action (also known as minimal geodesic, or path of minimal potential). Thereby, ... |

22 |
Matching deformable models to images: Direct and iterative solutions
- Terzopoulos
- 1987
(Show Context)
Citation Context ... from images. The extraction of local features is specified by initial conditions that lead to the selection of one of the local minima. Snakes are a special case of deformable models as presented in =-=[58]-=-. The deformable contour model is a mapping: C(v) :\Omega \Gamma! IR 2 (1) v 7\Gamma! (x(v); y(v)) where\Omega = [0; 1] is the parameterization interval. In some cases v is chosen to be the arclength ... |

22 | Three dimensional object modeling via minimal surfaces - Caselles, Kimmel, et al. - 1996 |

19 |
Planning and reasoning for autonomous vehicle control
- Mitchell, Payton, et al.
- 1986
(Show Context)
Citation Context ... to the true one as the grid is refined. This is known not to be the case in general graph search algorithms that suffer from digitization bias due to the metrication error when implemented on a grid =-=[41, 32]-=-. This gives a clear advantage to our method over minimal path estimation using graph search. Before introducing the proposed method, let us review the graph search based methods that try to minimize ... |

18 | Finding shortest paths on surfaces by fast global approximation and precise local refinement
- Kimmel, Kiryati
- 1996
(Show Context)
Citation Context ...ion, which is not the case in the approach we use. Also, some fixes that minimize the average error by modifying the weights along the connections between the pixels were proposed in [32] and used in =-=[29]-=-. We show the example of Figures 1 and 2 for the simplest case of graph search, to clarify the metrication error effect. Our philosophy here is different. We propose to deal with the continuous proble... |

12 |
Fast marching method for computing solutions to static Hamilton-Jacobi equations
- Adalsteinsson, Kimmel, et al.
- 1996
(Show Context)
Citation Context ...ution scheme that provides at each image pixel an output of the energy along the path of minimal integrated energy joining that pixel to the given start point. We use the Sethian fast marching method =-=[51, 50, 1]-=-. The search for a global minimum is then done efficiently. While this minimum is restricted to connect two given points, we also present a topology--based saddle search that helps in automatically cl... |

12 | Adaptive active contour algorithms for extracting and mapping thick curves
- Davatzikos, Prince
- 1993
(Show Context)
Citation Context ... in [22, 25]. For such an application, if the two edges of the road are needed rather than the middle way, our result could be refined using either ribbon snakes [43] or a thick contour model like in =-=[18]-=-. Given a start point p 0 on the bottom left, the image of minimal action U(x; y) from this point is shown in Figure 8. Observe the way the level curves propagate faster along the road. In the top exa... |

11 |
Fast marching methods for computing distance maps and shortest paths
- Kimmel, Sethian
- 1996
(Show Context)
Citation Context ...mma minfU k\Gamma1;l ; U k+1;l g; 0g) 2 +(maxfu \Gamma minfU k;l\Gamma1 ; U k;l+1 g; 0g) 2 = P 2 k;l ;(17) and let U k;l = u. For efficiency, the trial list is kept as min heap structure. We refer to =-=[51, 50, 1, 31]-=- for further details on the above algorithm, as well as a proof of correct construction. Using a min-heap structure for the trial list, the algorithm computational complexity is O(N logN) where N is t... |

11 | Curvature and continuity control in particle-based surface models
- Szeliski, Tonnesen
- 1993
(Show Context)
Citation Context ...e motivated many other recent works like [9, 10, 61, 27, 57] for 2D and 3D implicit deformable models. Other models that can handle topology changes have also been used for curves in [38] or surfaces =-=[33, 55, 56]-=-. In this paper we present a new approach for finding the global minimum of energy minimizing curves given only one or two end points. Our goal is to help the user in solving the problem in hand by ma... |

10 | Making Snakes Converge from Minimal Initialization
- Neuenschwander, Fua, et al.
- 1994
(Show Context)
Citation Context ...reprocessing is used to get an initial guess that has to be inside the desired area. The same property can be realized using the geometric model introduced in [8, 36] and recently improved in [9]. In =-=[43]-=-, only two end points on the boundary are needed to follow the contour. Although the smoothing effect of the snakes may overcome small defaults in the data, spurious edges generated by noise or in a c... |

10 |
Chamfer masks: discrete distance functions, geometrical properties and optimization
- Thiel, Montanvert
- 1992
(Show Context)
Citation Context ...optimal no matter how much we refine the (4-neighboring) grid. larger neighborhood as structuring element, giving better approximations of the distance in some directions (like p 2 for the diagonals) =-=[5, 59]-=-. These give a different polygonal approximation of the circle, but there will always be an error in some direction that will be invariant to the grid resolution, which is not the case in the approach... |

8 |
Dynamic segmentation: Detecting complex topology 3D objects
- Leitner, Cinquin
- 1991
(Show Context)
Citation Context ...e motivated many other recent works like [9, 10, 61, 27, 57] for 2D and 3D implicit deformable models. Other models that can handle topology changes have also been used for curves in [38] or surfaces =-=[33, 55, 56]-=-. In this paper we present a new approach for finding the global minimum of energy minimizing curves given only one or two end points. Our goal is to help the user in solving the problem in hand by ma... |

8 |
Recovery of shapes by evolution of zero-crossings,”
- Shah
- 1995
(Show Context)
Citation Context ...v, for the arbitrary parameter v). The curve evolution equation is then reformulated and implemented using the Osher-Sethian [44] numerical algorithm. Similar geometric models were also introduced in =-=[27, 61, 53]-=- and extended to color and texture in [47]. Although our work is related to [9], it is a totally independent approach. Actually, the geodesic active contours may be considered as a natural refinement ... |

8 | Curve Evolution on Surfaces - Kimmel - 1995 |

8 |
Gradient and geometric active contour models
- Kichenassamy, Kumar, et al.
- 1995
(Show Context)
Citation Context ...v, for the arbitrary parameter v). The curve evolution equation is then reformulated and implemented using the Osher-Sethian [44] numerical algorithm. Similar geometric models were also introduced in =-=[27, 61, 53]-=- and extended to color and texture in [47]. Although our work is related to [9], it is a totally independent approach. Actually, the geodesic active contours may be considered as a natural renement p... |

5 | New prospects in line detection for remote sensing images - Merlet, Zerubia - 1994 |

4 | Edge integration using minimal geodesics
- Cohen, Kimmel
- 1995
(Show Context)
Citation Context ... path is introduced. This justify the fact that although our approach is a path integration, it also incorporate the regularization of the path like a "snake" model. 2 Deformable Contours We=-= refer to [10] for an ov-=-erview of the different approaches for active contour models. Since the introduction of "snakes" [1], deformable models have been extensively used to integrate boundaries and extract feature... |

4 |
Image segmentation by reaction-diusion bubbles
- Tek, Kimia
- 1995
(Show Context)
Citation Context ... with holes, it is possible [8, 36] to model the contour as a level set of a surface, allowing it to change its topology in a natural way. These approaches have motivated many other recent works like =-=[9, 10, 61, 27, 57]-=- for 2D and 3D implicit deformable models. Other models that can handle topology changes have also been used for curves in [38] or surfaces [33, 55, 56]. In this paper we present a new approach forsnd... |

2 |
Global minima via dynamic programming: Energy minimizing active contours
- Chandran, Meajima, et al.
- 1991
(Show Context)
Citation Context ...ur, by using the surface of minimal action. To find the surface of minimal action, graph search and dynamic programming techniques were often used, considering the image pixels as vertices in a graph =-=[42, 22, 11]-=-. A description of A and F algorithms, applied to road detection, can be found in [22]. The distance image is initialized with value 1 everywhere except at a start point with value zero. At each itera... |

2 |
A uni framework for shape segmentation representation, and recognition
- Malladi, Sethian
- 1994
(Show Context)
Citation Context ...e domain and serve as the key points in generating a single boundary contour. Finding such a contour is usually referred to as `shape modeling' that is used for object segmentation and classification =-=[37, 36, 35]-=-. The difficulty here is that there is no order in the set of points and that it is unknown in advance which points belong to the boundary. This is defined as implicit constraints in [13]. Denote by E... |

2 |
A curvature dependent energy function for detecting lines in satellite images
- Merlet, Zerubia
- 1993
(Show Context)
Citation Context ...ess (this has to happen in a finite number of iterations) or after a given number of passes. This kind of approach was used to compute distance maps in [5, 17]. It was also used for road detection in =-=[39, 40]-=-, using some improvements in the potential definition. The authors also add some constraint on the curvature by taking into account sets of three vertices instead of two in the graph search to update ... |

2 |
Merlet and Josiane Zerubia. New prospects in line detection for remote sensing images
- Nicolas
- 1994
(Show Context)
Citation Context ...ess (this has to happen in a finite number of iterations) or after a given number of passes. This kind of approach was used to compute distance maps in [5, 17]. It was also used for road detection in =-=[39, 40]-=-, using some improvements in the potential definition. The authors also add some constraint on the curvature by taking into account sets of three vertices instead of two in the graph search to update ... |

1 |
Eric Bardinet, and Nicholas Ayache. Surface reconstruction using active contour models
- Cohen
- 1993
(Show Context)
Citation Context ...ignificant local minimum of the energy. The inflation or expansion force [12] may help the contour to avoid being trapped by isolated edges into a local minimum. A region based approach introduced in =-=[14]-=- also makes the solution less sensitive to local minima and initialization. It considers a mixed energy including a snake like term on the boundary and an homogeneous value constraint inside the regio... |

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Motion tracking of deformable objects based on energy minimization using multiscale dynamic programming
- Fujimura, Yokoya, et al.
- 1992
(Show Context)
Citation Context ...y the size of the graph, since the vertices are the nodes on the curve and the possible values for these are only the eight neighbors L. Cohen, R. Kimmel, March 26, 1996. 10 of the initial vertex. In =-=[24]-=-, the range of possible local deformations is broadened using a multiscale dynamic programming algorithm. However, in both approaches, this kind of graph search does not avoid undesirable local minima... |

1 | Variational Methods for Image Processing (in French). Université Paris Dauphine. “Mémoire d’Habilitation à diriger des recherches” Presented together with 10 main publications (in English) during - Cohen - 1995 |

1 | Annals of Applied Probability, 4(2):287–346. Minimum for Active Contour Models 77 - Fischler, Tenenbaum, et al. - 1981 |