## Fast Multiscale Image Segmentation

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Citations: | 121 - 13 self |

### BibTeX

@MISC{Sharon_fastmultiscale,

author = {Eitan Sharon and et al.},

title = {Fast Multiscale Image Segmentation},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

We introduce a fast, multiscale algorithm for image segmentation. Our algorithm uses modern numeric techniques to nd an approximate solution to normalized cut measures in time that is linear in the size of the image with only a few dozen operations per pixel. In just one pass the algorithm provides a complete hierarchical decomposition of the image into segments. The algorithm detects the segments by applying a process of recursive coarsening in which the same minimization problem is represented with fewer and fewer variables producing an irregular pyramid. During this coarsening process we may compute additional internal statistics of the emerging segments and use these statistics to facilitate the segmentation process. Once the pyramid is completed it is scanned from the top down to associate pixels close to the boundaries of segments with the appropriate segment. The algorithm is inspired by algebraic multigrid (AMG) solvers of minimization problems of heat or electric networks. We demonstrate the algorithm by applying it to real images.

### Citations

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Citation Context ...ecisions. F uzzy C-means clustering algorithms (e.g., [4]) avoid such premature decisions, but they in volve aslowiterative process. Also related are algorithms motivated by physical processes (e.g., =-=[8, 15]-=-). The paperis divided as follo ws. Section 2formulates the segmentation problem and describes the principles of our method. Section 3 describes the algorithm. Section 4 discusses how more global prop... |

2590 | Normalized cuts and image segmentation - Shi, Malik - 1997 |

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Citation Context ...ings") between nearby pixels. The image is segmented b y minimizing a cost associated with cutting the graph into subgraphs. In the simpler version, the cost is the sum of the a nities across the cut =-=[20]-=-. Other versions normalize this cost by dividing it by theoverall area of the segments [6] or b y a measure derived from the a nities betw een nodes within the segments [17, 13 , 19 ]. Normalizing the... |

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(Show Context)
Citation Context ...de ciencies will be muc h reduced with each improvement, so that normally very few such improvements (if at all) would be needed. (Such improved interpolation rules are widely used in AMG, see, e.g., =-=[2]-=-.) With the improved in terpolation weights (18), the coarse-variable selection criterion (11) can be relaxed, replacing it by the more general criterion di 1 ; . Condition (16) can similarly be relax... |

52 | Ratio regions: A technique for image segmentation - Cox, Rao, et al. - 1996 |

48 | A pyramid framework for early vision - Jolion, Rosenfeld - 1994 |

32 | Rigorous quantitative analysis of multigrid, I. Constant coefficients two-level cycle with L2-norm
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Citation Context ...sure that for any low-energy con gurations the values of u indeed depend, to a good approximation, on those of the subset U. This choice of C is common in applying fast, multiscale AMG solvers (e.g., =-=[3]-=-). We now discuss the in terpolation rule in Eq. (5). Given a segment Sm, we de ne U (m) as U (m) k = 1 if ck 2 Sm 0 if ck =2 Sm � (12) and de ne ~u (m) as the con guration interpolated from U (m) b y... |

29 | Image Segmentation from Consensus Information
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Citation Context ...see reviews in [7, 9, 11 ]). How ev er,methods that use regular p yramids (e.g., [10]) have di culties in extracting regions of irregular structures. Methods that construct irregular p yramids (e.g., =-=[1, 5,12,18]-=-) are strongly a ected by local decisions. F uzzy C-means clustering algorithms (e.g., [4]) avoid such premature decisions, but they in volve aslowiterative process. Also related are algorithms motiva... |

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Citation Context ...ecisions. F uzzy C-means clustering algorithms (e.g., [4]) avoid such premature decisions, but they in volve aslowiterative process. Also related are algorithms motivated by physical processes (e.g., =-=[8, 15]-=-). The paperis divided as follo ws. Section 2formulates the segmentation problem and describes the principles of our method. Section 3 describes the algorithm. Section 4 discusses how more global prop... |

11 |
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Citation Context ...see reviews in [7, 9, 11 ]). How ev er,methods that use regular p yramids (e.g., [10]) have di culties in extracting regions of irregular structures. Methods that construct irregular p yramids (e.g., =-=[1, 5,12,18]-=-) are strongly a ected by local decisions. F uzzy C-means clustering algorithms (e.g., [4]) avoid such premature decisions, but they in volve aslowiterative process. Also related are algorithms motiva... |

8 | Learning to Form Large Groups of Salient Image Features - Sarkar - 1998 |

8 |
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(Show Context)
Citation Context ...see reviews in [7, 9, 11 ]). How ev er,methods that use regular p yramids (e.g., [10]) have di culties in extracting regions of irregular structures. Methods that construct irregular p yramids (e.g., =-=[1, 5,12,18]-=-) are strongly a ected by local decisions. F uzzy C-means clustering algorithms (e.g., [4]) avoid such premature decisions, but they in volve aslowiterative process. Also related are algorithms motiva... |

7 |
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(Show Context)
Citation Context ...ies in extracting regions of irregular structures. Methods that construct irregular p yramids (e.g., [1, 5,12,18]) are strongly a ected by local decisions. F uzzy C-means clustering algorithms (e.g., =-=[4]-=-) avoid such premature decisions, but they in volve aslowiterative process. Also related are algorithms motivated by physical processes (e.g., [8, 15]). The paperis divided as follo ws. Section 2formu... |

4 | Bezdek, "Efficient implementation of fuzzy c-means clustering algorithms - Cannon, Dave, et al. - 1986 |

2 | Faster algorithms for finding small separators in planar graphs - Rao - 1971 |

2 | ter haar Romeny, ed., "Geometry-Driven Diffusion in Computer Vision - M - 1994 |

1 |
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(Show Context)
Citation Context ... globally optimal solution when the cost is normalized exist when the graph is planar, but the runtime complexity of these methods is O(N 2 log N), where N denotes the numberofpixelsin the image (see =-=[14, 6]-=-). When the graph is non-planar the problem of nding a globally optimal solution is NP-hard. Therefore, approximation methods are emplo yed.The most common of these uses spectral techniques to nd an a... |

1 |
Ratio Regions: A T echnique for Image Segmentation
- Cox, Rao, et al.
- 1996
(Show Context)
Citation Context ...cutting the graph into subgraphs. In the simpler version, the cost is the sum of the a nities across the cut [20]. Other versions normalize this cost by dividing it by theoverall area of the segments =-=[6]-=- or b y a measure derived from the a nities betw een nodes within the segments [17, 13 , 19 ]. Normalizing the cost of a cut preven ts over-segmentation of the image. Polynomial methods for nding a gl... |

1 |
Apyramid framework for early vision. Klu w er
- Jolion, Rosenfeld
(Show Context)
Citation Context ...ture than that traditionally solved b y AMG. Pyramidal structures ha ve been used in many algorithms for segmentation (see reviews in [7, 9, 11 ]). How ev er,methods that use regular p yramids (e.g., =-=[10]-=-) have di culties in extracting regions of irregular structures. Methods that construct irregular p yramids (e.g., [1, 5,12,18]) are strongly a ected by local decisions. F uzzy C-means clustering algo... |

1 |
Integrating region gro wing and edge detection
- avlidis, Liow
- 1990
(Show Context)
Citation Context |

1 |
Learning to Form Large Groups of Salient Image Features
- ar
- 1998
(Show Context)
Citation Context ...r of S (m).) In con trast, setting >0:5 will create preference for large segments. In our implementation weused = 1, which is equivalent to the so called \average" or \normalized" cut measures (e.g., =-=[6, 16, 17]-=-). Finally, the v olume ofu can be generalized by replacing V (u) by V (u) = NX i=1 iui � NX i=1 i = N � (4) where i is a \mass" assigned to the pixel i. This will become important in coarser steps wh... |

1 |
Normalized Cuts and Image Segmentation," Pr oc
- Shi, Malik
- 1997
(Show Context)
Citation Context ...solution. These spectral methods are analogous to nding the principal modes of certain physical systems. With these methods, and exploiting the sparseness of the graph, a cut can be found in O(N 3=2 )=-=[17]-=-. Below weintroduce a fast algorithm for segmentation. Our algorithm too nds an approximate solution to a normalized cut problem, but it does so in time that is linear in the number of pixels in the i... |