## Hierarchical Matching of Deformable Shapes (2007)

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Venue: | In Proceedings of CVPR |

Citations: | 75 - 0 self |

### BibTeX

@INPROCEEDINGS{Felzenszwalb07hierarchicalmatching,

author = {Pedro F. Felzenszwalb},

title = {Hierarchical Matching of Deformable Shapes},

booktitle = {In Proceedings of CVPR},

year = {2007},

pages = {1--8}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

1344 | Shape matching and object recognition using shape contexts
- BELONGIE, MALIK, et al.
- 2002
(Show Context)
Citation Context ... other methods for representing, matching and recognizing shapes. These include methods based on the medial axis transform and the shock graph [5], [25], [24], procrustes analysis [7], shape contexts =-=[3]-=- and the inner distance [16]. We experimentally compare our algorithm to several of these approaches in Section 5. 2. The Shape-Tree We start by describing our hierarchical representation for open cur... |

547 | Statistical Shape Analysis
- DRYDEN, MARDIA
- 1998
(Show Context)
Citation Context ...ours. There are many other methods for representing, matching and recognizing shapes. These include methods based on the medial axis transform and the shock graph [5], [25], [24], procrustes analysis =-=[7]-=-, shape contexts [3] and the inner distance [16]. We experimentally compare our algorithm to several of these approaches in Section 5. 2. The Shape-Tree We start by describing our hierarchical represe... |

448 | Learning to detect natural image boundaries using local brightness, color, and texture cues
- Martin, Fowlkes, et al.
- 2004
(Show Context)
Citation Context ...se these matches together, forming an optimal matching between the model and a subset of the image contours. These stages are illustrated in Figure 5. For the first stage, we use the PB edge operator =-=[18]-=- to compute an edge strength map. For the second stage, westrace smooth contours in the edge map using the method from [10]. The result is a set of salient contours in the image. An example can be fou... |

224 |
A theory of multiscale, curvature-based shape representation for planar curves
- Mokhtarian, Mackworth
- 1992
(Show Context)
Citation Context ...tandard method used for polygon simplification in computer graphics [22]. In vision, multiscale representations such as the curvature scale-space (CSS) have been previously used for shape recognition =-=[21, 20, 28]-=-. The CSS captures critical curvature points of a contour at different levels of smoothing. Our representation is also based on a multiresolution approach, but we rely only on subsampling to define co... |

224 | Shock graphs and shape matching
- Siddiqi, Shokoufandeh, et al.
- 1999
(Show Context)
Citation Context ...[12], works by linking edge contours. There are many other methods for representing, matching and recognizing shapes. These include methods based on the medial axis transform and the shock graph [5], =-=[25]-=-, [24], procrustes analysis [7], shape contexts [3] and the inner distance [16]. We experimentally compare our algorithm to several of these approaches in Section 5. 2. The Shape-Tree We start by desc... |

160 |
Biological shape and visual science
- Blum
- 1973
(Show Context)
Citation Context ...t of [12], works by linking edge contours. There are many other methods for representing, matching and recognizing shapes. These include methods based on the medial axis transform and the shock graph =-=[5]-=-, [25], [24], procrustes analysis [7], shape contexts [3] and the inner distance [16]. We experimentally compare our algorithm to several of these approaches in Section 5. 2. The Shape-Tree We start b... |

158 | Recognition of shapes by editing their shock graphs
- Sebastian, Klein, et al.
(Show Context)
Citation Context ...we obtain better recognition results than other methods on several shape datasets, including the MPEG-7 shape dataset [15], a Swedish leaf dataset [26], and a silhouette dataset from Brown University =-=[24]-=-. We have also used the ETHZ dataset [12] to demonstrate how hierarchical matching can be used for matching shapes to real, cluttered images. These experiments illustrate how the approach is not restr... |

139 |
Hands: A Pattern Theoretic Study of Biological Shapes
- Grenander, Chow, et al.
- 1991
(Show Context)
Citation Context ...Most of the previous elastic matching methods look for maps between two curves while minimizing a measure of local bending and stretching (see [2], [23] and references within). The methods in [6] and =-=[13]-=- use a similar idea to match a curve to cluttered images. Local deformation models are appealing from an algorithmic perspective. Usually dynamic programming can be used to find optimal matchings. How... |

134 | Efficient and robust retrieval by shape content through curvature scale space
- Mokhtarian, Abbasi, et al.
- 1996
(Show Context)
Citation Context ...tandard method used for polygon simplification in computer graphics [22]. In vision, multiscale representations such as the curvature scale-space (CSS) have been previously used for shape recognition =-=[21, 20, 28]-=-. The CSS captures critical curvature points of a contour at different levels of smoothing. Our representation is also based on a multiresolution approach, but we rely only on subsampling to define co... |

133 | Shape descriptors for non-rigid shapes with a single closed contour
- Latecki, Lakämper, et al.
- 2000
(Show Context)
Citation Context ...ariety of situations and obtained excellent performance. In classification tasks, we obtain better recognition results than other methods on several shape datasets, including the MPEG-7 shape dataset =-=[15]-=-, a Swedish leaf dataset [26], and a silhouette dataset from Brown University [24]. We have also used the ETHZ dataset [12] to demonstrate how hierarchical matching can be used for matching shapes to ... |

124 |
An iterative procedure for the polygonal approximation of plane curves
- Ramer
- 1972
(Show Context)
Citation Context ...h the only information kept at each node is the relative position of the selected midpoint. Recursive midpoint selection is also a standard method used for polygon simplification in computer graphics =-=[22]-=-. In vision, multiscale representations such as the curvature scale-space (CSS) have been previously used for shape recognition [21, 20, 28]. The CSS captures critical curvature points of a contour at... |

109 | Determining the Similarity of Deformable Shapes
- Basri, Costa, et al.
- 1995
(Show Context)
Citation Context ...organized set of contours extracted from natural images. Most of the previous elastic matching methods look for maps between two curves while minimizing a measure of local bending and stretching (see =-=[2]-=-, [23] and references within). The methods in [6] and [13] use a similar idea to match a curve to cluttered images. Local deformation models are appealing from an algorithmic perspective. Usually dyna... |

98 | On aligning curves
- Sebastian, Klein, et al.
(Show Context)
Citation Context ...ized set of contours extracted from natural images. Most of the previous elastic matching methods look for maps between two curves while minimizing a measure of local bending and stretching (see [2], =-=[23]-=- and references within). The methods in [6] and [13] use a similar idea to match a curve to cluttered images. Local deformation models are appealing from an algorithmic perspective. Usually dynamic pr... |

83 | Representation and detection of deformable shapes
- Felzenszwalb
- 2005
(Show Context)
Citation Context ...but this method is not compositional in contrast to ours. Other hierarchical methods include the hierarchical graphical models in [8] and hierarchical procrustes matching [19]. The methods in [1] and =-=[9]-=- use triangulated graphs to represent shapes and to model deformations of objects. Our work is related since we use the geometric arrangement of sets of three points to capture shape information. Our ... |

82 | L.V.: Object detection by contour segment networks
- Ferrari, Tuytelaars, et al.
(Show Context)
Citation Context ... other methods on several shape datasets, including the MPEG-7 shape dataset [15], a Swedish leaf dataset [26], and a silhouette dataset from Brown University [24]. We have also used the ETHZ dataset =-=[12]-=- to demonstrate how hierarchical matching can be used for matching shapes to real, cluttered images. These experiments illustrate how the approach is not restricted to matching pre-segmented shapes. I... |

66 |
A generalization of Dijkstra’s algorithm
- Knuth
- 1977
(Show Context)
Citation Context ...point, matchings Match(a, c, p, r) and Match(c, e, r, u) could be composed. Continuing in this way, we stitch together the boundary of the object. in P . In the future we plan to use the algorithm in =-=[14]-=- to compute optimal matches even faster. That method would compose matchings in order of their quality to avoid considering many possibilities that are considered by the dynamic programming procedure.... |

57 | Using the Inner-Distance for Classification of Articulated Shapes”, CVPR
- Ling, Jacobs
- 2005
(Show Context)
Citation Context ...ting, matching and recognizing shapes. These include methods based on the medial axis transform and the shock graph [5], [25], [24], procrustes analysis [7], shape contexts [3] and the inner distance =-=[16]-=-. We experimentally compare our algorithm to several of these approaches in Section 5. 2. The Shape-Tree We start by describing our hierarchical representation for open curves. Let A be an open curve ... |

55 | Graphical templates for model registration
- Amit, Kong
- 1996
(Show Context)
Citation Context ...ptions, but this method is not compositional in contrast to ours. Other hierarchical methods include the hierarchical graphical models in [8] and hierarchical procrustes matching [19]. The methods in =-=[1]-=- and [9] use triangulated graphs to represent shapes and to model deformations of objects. Our work is related since we use the geometric arrangement of sets of three points to capture shape informati... |

50 | An Efficient Earth Mover’s Distance Algorithm for Robust Histogram Comparison
- Ling, Okada
(Show Context)
Citation Context ...es from thissFigure 7. Some of the objects in the MPEG-7 dataset. One image per class for the first 40 classes (the database has 70 classes). Method Recognition rate Shape-tree 87.70% IDSC + DP + EMD =-=[17]-=- 86.56% Hierarchical Procrustes [19] 86.35% IDSC + DP [16] 85.40% Generative Models [27] 80.03% Curve Edit [23] 78.14% SC + TPS [3] 76.51% Visual Parts [15] 76.45% CSS [20] 75.44% Table 1. Classificat... |

49 | Efficient deformable template detection and localization without user initialization
- Coughlan, Yuille, et al.
(Show Context)
Citation Context ...images. Most of the previous elastic matching methods look for maps between two curves while minimizing a measure of local bending and stretching (see [2], [23] and references within). The methods in =-=[6]-=- and [13] use a similar idea to match a curve to cluttered images. Local deformation models are appealing from an algorithmic perspective. Usually dynamic programming can be used to find optimal match... |

47 |
Shape matching and recognition: Using generative models and informative features
- Tu, Yuille
- 2004
(Show Context)
Citation Context ...r the first 40 classes (the database has 70 classes). Method Recognition rate Shape-tree 87.70% IDSC + DP + EMD [17] 86.56% Hierarchical Procrustes [19] 86.35% IDSC + DP [16] 85.40% Generative Models =-=[27]-=- 80.03% Curve Edit [23] 78.14% SC + TPS [3] 76.51% Visual Parts [15] 76.45% CSS [20] 75.44% Table 1. Classification results on the MPEG-7 dataset. Method Recognition rate Shape-tree 96.28% IDSC + DP [... |

37 | Compositionality, MDL priors, and object recognition
- Bienenstock, Geman, et al.
- 1997
(Show Context)
Citation Context ...mming algorithm for matching. But, as opposed to these other methods, ours does not solve a shortest path problem due to its compositional nature. Our compositional approach is related to the work in =-=[4]-=-. Hierarchical representations have proven to be useful in a variety of situations. The arc-tree in [14] gives a hierarchical description of a curve based on recursive selection of midpoints. This rep... |

33 | The generalized A* architecture
- Felzenszwalb, McAllester
- 2007
(Show Context)
Citation Context ...he boundary of the object. gorithm runs in O(m 3 k 3 ) time, where m is the number of sample points in the model and k is the number of endpoints in P . In the future we plan to use the algorithms in =-=[11]-=- to compute optimal matches even faster. Those algorithms would compose matchings in order of their quality to avoid considering many possibilities that are considered by the dynamic programming proce... |

31 |
Learning visual models from shape contours using multiscale convex/concave structure matching
- Ueda, Suzuki
- 1993
(Show Context)
Citation Context ...tandard method used for polygon simplification in computer graphics [22]. In vision, multiscale representations such as the curvature scale-space (CSS) have been previously used for shape recognition =-=[21, 20, 28]-=-. The CSS captures critical curvature points of a contour at different levels of smoothing. Our representation is also based on a multiresolution approach, but we rely only on subsampling to define co... |

28 | Hierarchical procrustes matching for shape retrieval
- McNeill, Vijayakumar
- 2006
(Show Context)
Citation Context ...ing multiscale descriptions, but this method is not compositional in contrast to ours. Other hierarchical methods include the hierarchical graphical models in [8] and hierarchical procrustes matching =-=[19]-=-. The methods in [1] and [9] use triangulated graphs to represent shapes and to model deformations of objects. Our work is related since we use the geometric arrangement of sets of three points to cap... |

27 |
Computer vision classification of leaves from Swedish trees
- Söderkvist
- 2001
(Show Context)
Citation Context ...ined excellent performance. In classification tasks, we obtain better recognition results than other methods on several shape datasets, including the MPEG-7 shape dataset [15], a Swedish leaf dataset =-=[26]-=-, and a silhouette dataset from Brown University [24]. We have also used the ETHZ dataset [12] to demonstrate how hierarchical matching can be used for matching shapes to real, cluttered images. These... |

25 | A min-cover approach for finding salient curves
- Felzenszwalb, McAllester
- 2006
(Show Context)
Citation Context ...re illustrated in Figure 5. For the first stage, we use the PB edge operator [18] to compute an edge strength map. For the second stage, westrace smooth contours in the edge map using the method from =-=[10]-=-. The result is a set of salient contours in the image. An example can be found in Figure 5(c). Let M be a model curve, C be the set of contours extracted from an image and P denote the set of endpoin... |

12 |
The arc tree: An approximation scheme to represent arbitrary curved shapes
- Günther, Wong
- 1990
(Show Context)
Citation Context ...th problem due to its compositional nature. Our compositional approach is related to the work in [4]. Hierarchical representations have proven to be useful in a variety of situations. The arc-tree in =-=[14]-=- gives a hierarchical description of a curve based on recursive selection of midpoints. This representation was used to perform geometric queries such as detecting intersections between two curves. Ou... |

11 | Probabilistic contour extraction using hierarchical shape representation
- Fan, Qi, et al.
(Show Context)
Citation Context ...n [28] uses dynamic programming for matching multiscale descriptions, but this method is not compositional in contrast to ours. Other hierarchical methods include the hierarchical graphical models in =-=[8]-=- and hierarchical procrustes matching [19]. The methods in [1] and [9] use triangulated graphs to represent shapes and to model deformations of objects. Our work is related since we use the geometric ... |