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## Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multi-band Image Segmentation (1996)

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

Citations: | 774 - 20 self |

### Citations

5126 | Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images
- Geman, Geman
- 1984
(Show Context)
Citation Context ..., (ii) Snake [19] and Balloon methods [6], [7], [37], [32](iii) Region growing and merging techniques [2], [1],[26], and (iv) Global optimization approaches based on energy functions [28] or Bayesian =-=[10]-=- [3], [11] and MDL (Minimum Description Length) criteria [23] [20] [18]. A common property of these approaches is that they all make hypotheses about the image, test features and make decisions by app... |

4675 | A Computational Approach to Edge Detection.”
- Canny
- 1986
(Show Context)
Citation Context ...roblem of early vision and it has been intensively studied. Approaches to image segmentation can be roughly classified into four groups: (i) Local filtering approaches such as the Canny edge detector =-=[4]-=-, (ii) Snake [19] and Balloon methods [6], [7], [37], [32](iii) Region growing and merging techniques [2], [1],[26], and (iv) Global optimization approaches based on energy functions [28] or Bayesian ... |

3951 | Snakes: Active contour models,
- Kass, Witkin, et al.
- 1988
(Show Context)
Citation Context ...vision and it has been intensively studied. Approaches to image segmentation can be roughly classified into four groups: (i) Local filtering approaches such as the Canny edge detector [4], (ii) Snake =-=[19]-=- and Balloon methods [6], [7], [37], [32](iii) Region growing and merging techniques [2], [1],[26], and (iv) Global optimization approaches based on energy functions [28] or Bayesian [10] [3], [11] an... |

3784 |
Introduction to Statistical Pattern Recognition
- Fukunaga
- 1990
(Show Context)
Citation Context ...e. n 2 = 1 and n 1 is very large (say n 1 ? 100). In this case we can treat �� =s�� 1 ; oe 2 =soe 2 1 , and �� 2 = I (x;y) (the intensity at point (x; y)), and approximate the squared Fish=-=er distance [8] by:-=- (I \Gamma��) 2 oe 2 . A variant of region growing [26] is to fit the intensity within each region to a parameterized model, such as a plane or a quadratic form. Then tests like Equation (4) can b... |

1294 | Optimal approximations by piecewise smooth functions and associated variational problems.
- Mumford, Shah
- 1989
(Show Context)
Citation Context ...edge detector [4], (ii) Snake [19] and Balloon methods [6], [7], [37], [32](iii) Region growing and merging techniques [2], [1],[26], and (iv) Global optimization approaches based on energy functions =-=[28]-=- or Bayesian [10] [3], [11] and MDL (Minimum Description Length) criteria [23] [20] [18]. A common property of these approaches is that they all make hypotheses about the image, test features and make... |

898 | Visual Reconstruction.
- Blake, Zisserman
- 1987
(Show Context)
Citation Context ...) Snake [19] and Balloon methods [6], [7], [37], [32](iii) Region growing and merging techniques [2], [1],[26], and (iv) Global optimization approaches based on energy functions [28] or Bayesian [10] =-=[3]-=-, [11] and MDL (Minimum Description Length) criteria [23] [20] [18]. A common property of these approaches is that they all make hypotheses about the image, test features and make decisions by applyin... |

588 | On Active Contour Models and Balloons”,
- Cohen
- 1991
(Show Context)
Citation Context ...vely studied. Approaches to image segmentation can be roughly classified into four groups: (i) Local filtering approaches such as the Canny edge detector [4], (ii) Snake [19] and Balloon methods [6], =-=[7]-=-, [37], [32](iii) Region growing and merging techniques [2], [1],[26], and (iv) Global optimization approaches based on energy functions [28] or Bayesian [10] [3], [11] and MDL (Minimum Description Le... |

568 |
Seeded region growing
- Adams, Bischof
- 1994
(Show Context)
Citation Context ...assified into four groups: (i) Local filtering approaches such as the Canny edge detector [4], (ii) Snake [19] and Balloon methods [6], [7], [37], [32](iii) Region growing and merging techniques [2], =-=[1]-=-,[26], and (iv) Global optimization approaches based on energy functions [28] or Bayesian [10] [3], [11] and MDL (Minimum Description Length) criteria [23] [20] [18]. A common property of these approa... |

270 | Constructing simple stable descriptions for image partitioning.
- Leclerc
- 1989
(Show Context)
Citation Context ...i) Region growing and merging techniques [2], [1],[26], and (iv) Global optimization approaches based on energy functions [28] or Bayesian [10] [3], [11] and MDL (Minimum Description Length) criteria =-=[23]-=- [20] [18]. A common property of these approaches is that they all make hypotheses about the image, test features and make decisions by applying thresholds explicitly or implicitly. As shown by the sh... |

233 | Filters, random fields and maximum entropy (frame): Towards a unified theory for texture modeling.
- Zhu, Wu, et al.
- 1998
(Show Context)
Citation Context ...theory to derive alternative costs [31] [20]. However, we argue that these costs should be determined by the properties of real images, rather than from coding theory, and should be found empirically =-=[39]-=-, [40]. rule This corresponds to setting 4 : ff i = arg min ff i f\Gamma Z Z R i log P (ff i j I (x;y) )dxdyg; 8 i (8) In the discrete case: ff i = arg max ff i Y (x;y)2R i P (ff i j I (x;y) ); 8 i (9... |

211 | A physical approach to color image understanding.
- Klinker
- 1993
(Show Context)
Citation Context ...nge dramatically due to the changes of the geometric configuration. 5.1 The Color Model If we include specularity in the image formation process then the standard color dichromatic reflection model is=-=[21]-=-: I(;~r i ) = ae(; ~r s )F b (~v; ~n; ~s)E(; ~n; ~s) + F s (~v; ~n; ~s)E(; ~n; ~s) + noise(~r i ) (26) where I is the image as function of the image position ~r i and wavelength , ae is the surface al... |

174 | FORMS: A flexible object recognition and modeling system.
- Zhu, Yuille
- 1996
(Show Context)
Citation Context ...ntegrating grey level, color and texture cues, (ii) integrating the filtering approaches to locate the edge more precisely, (iii) using this algorithm as a front end for our object recognition systems=-=[38]-=-. Acknowledgments It is a pleasure to acknowledge many highly stimulating discussions with David Mumford and Tai Sing Lee. Tai Sing Lee worked with us on the texture section and is a co-author for the... |

171 |
Region-based strategies for active contour models.
- Ronfard
- 1994
(Show Context)
Citation Context ...d. Approaches to image segmentation can be roughly classified into four groups: (i) Local filtering approaches such as the Canny edge detector [4], (ii) Snake [19] and Balloon methods [6], [7], [37], =-=[32]-=-(iii) Region growing and merging techniques [2], [1],[26], and (iv) Global optimization approaches based on energy functions [28] or Bayesian [10] [3], [11] and MDL (Minimum Description Length) criter... |

111 |
Automatic extraction of deformable parts models,”
- Pentland
- 1990
(Show Context)
Citation Context ...ture, but will often have sharp shadows due to creases. Finally we run our algorithm on texture images using filters to provide multi-band input. This paper has some similarities to work described by =-=[29]-=- and [26]. Both approaches use statistical tests to grow multiple seed regions independently, and then use the MDL criterion to compress the overlapping between regions. By contrast, our method minimi... |

87 | A multiscale algorithm for image segmentation by variational method
- Koepfler, Lopez, et al.
- 1994
(Show Context)
Citation Context ...rion to compress the overlapping between regions. By contrast, our method minimizes the MDL criterion for the entire image directly. Our work also has some similarities to ideas discussed in [28] and =-=[22]-=- [27]. These works differ from ours by not using a statistical criterion. This paper is organized as follows. Section (2) sets the scene by briefly describing Snakes and Balloons, Region Growing and E... |

86 |
Segmentation of Range Images as the Search for Geometric Parametric Models,”
- Leonardis, Gupta, et al.
- 1995
(Show Context)
Citation Context ...fied into four groups: (i) Local filtering approaches such as the Canny edge detector [4], (ii) Snake [19] and Balloon methods [6], [7], [37], [32](iii) Region growing and merging techniques [2], [1],=-=[26]-=-, and (iv) Global optimization approaches based on energy functions [28] or Bayesian [10] [3], [11] and MDL (Minimum Description Length) criteria [23] [20] [18]. A common property of these approaches ... |

77 |
Another interpretation of the EM algorithm for mixture distributions,”
- Hathaway
- 1986
(Show Context)
Citation Context ...d homogeneity criterion, and the background region as R 0 (so that 6 This two step iteration process is similar to the well-known EM algorithm which can be re-expressed as two steepest descent stages =-=[14]-=-. R 1 [ R 0 = R) with uniform probability distribution P 0 . Then the motion equation for each point ~v along the boundary is: d~v dt = (logP (I (~v) jff 1 ) \Gamma logP 0 )~ n (~v) (15) where ~ n is ... |

62 |
A finite element method applied to new active contour models and 3-D reconstruction from crossing sections. In:
- Cohen, Cohen
- 1990
(Show Context)
Citation Context ...tensively studied. Approaches to image segmentation can be roughly classified into four groups: (i) Local filtering approaches such as the Canny edge detector [4], (ii) Snake [19] and Balloon methods =-=[6]-=-, [7], [37], [32](iii) Region growing and merging techniques [2], [1],[26], and (iv) Global optimization approaches based on energy functions [28] or Bayesian [10] [3], [11] and MDL (Minimum Descripti... |

61 |
Segmenting images using normalized color,”
- Healey
- 1992
(Show Context)
Citation Context ... component, and the (e r ; e g ; e b ) (x;y) are the residuals (or noise). Although there have been many attempts to separate the body color (r; g; b) from the specular color (r s ; g s ; b s ) [21], =-=[15]-=-, [34], these approaches have been demonstrated on plastic and metal objects with nice illumination. If the noise level is quite high and the intensity around the specular regions are approximately sa... |

38 |
The uncertainty principle in image processing.
- Wilson, Granlund
- 1984
(Show Context)
Citation Context ...e size of these windows depends on a tradeoff between the conflicting goals of maximizing the signal to noise ratio and locating the boundaries accurately. This gives rise to an uncertaincy principle =-=[36]-=-. We describe how optimally sized windows can be chosen to minimize this uncertainty. Like many algorithms, the performance of region competition will depends on the initial conditions -- more precise... |

36 | Deformable boundary finding influenced by region homogeneity, - Chakraborty, Staib, et al. - 1994 |

31 | Foundations of Applied Mathematics, - Greenberg - 1978 |

29 |
Compact Region Extraction Using Weighted Pixel Linking in a Pyramid
- Hong, Rosenfeld
- 1984
(Show Context)
Citation Context ...n tries to maximize its area while smoothing its bounding contour and maximizing the intensity gradient along the contour. 2.2 Region Growing and Merging The goal of region merging and region growing =-=[16], [26-=-] is to divide the domain R of the image I into regions fR i : i = 1; :::; Mg so that R = [ M i=1 R i , R i " R j = OE if i 6= j, and I satisfies a homogeneity criterion on each R i . Region merg... |

26 |
Robust active contours with insensitive parameters,”
- Xu, Segawa, et al.
- 1994
(Show Context)
Citation Context ...studied. Approaches to image segmentation can be roughly classified into four groups: (i) Local filtering approaches such as the Canny edge detector [4], (ii) Snake [19] and Balloon methods [6], [7], =-=[37]-=-, [32](iii) Region growing and merging techniques [2], [1],[26], and (iv) Global optimization approaches based on energy functions [28] or Bayesian [10] [3], [11] and MDL (Minimum Description Length) ... |

12 |
A vector signal processing approach to color
- Sung
- 1992
(Show Context)
Citation Context ...nent, and the (e r ; e g ; e b ) (x;y) are the residuals (or noise). Although there have been many attempts to separate the body color (r; g; b) from the specular color (r s ; g s ; b s ) [21], [15], =-=[34]-=-, these approaches have been demonstrated on plastic and metal objects with nice illumination. If the noise level is quite high and the intensity around the specular regions are approximately saturate... |

11 | Modeling by Shortest Data Description," Automatica 14 - Rissanen - 1978 |

10 |
0(log n) bimodality analysis.
- Phillips, Rosenfeld, et al.
- 1989
(Show Context)
Citation Context ..., and I satisfies a homogeneity criterion on each R i . Region merging builds up complicated regions by combining smaller regions using a statistical similarity test. A popular choice is Fisher's test=-=[33]. For ex-=-ample, suppose there are two adjacent regions R 1 and R 2 , where n 1 ; n 2 ;s�� 1 ;s�� 2 ;soe 2 1 ;soe 2 2 are the sizes, sample means and sample variances of R 1 ; R 2 respectively. Then in ... |

8 |
Map Representations and Coding-Based Priors for Segmentation. CVPR
- Keeler
- 1991
(Show Context)
Citation Context ...gion growing and merging techniques [2], [1],[26], and (iv) Global optimization approaches based on energy functions [28] or Bayesian [10] [3], [11] and MDL (Minimum Description Length) criteria [23] =-=[20]-=- [18]. A common property of these approaches is that they all make hypotheses about the image, test features and make decisions by applying thresholds explicitly or implicitly. As shown by the shadowe... |

6 |
Modeling light reflection for color computer vision
- Lee, Breneman, et al.
- 1990
(Show Context)
Citation Context ...~n and ~s. In general, the first term corresponds to the body reflectance and the second term corresponds to specularities (typically highlights). This model has been tested over a range of materials =-=[25]-=- and is shown to be a good approximation in many cases, though it fails for some dielectrics. If we assume red, green, and blue color bands, then we can simplify Equation (26) at each point (x; y) to:... |

3 |
Applied Multivariate Statsitical Analysis
- Johnson, Wichem
- 1982
(Show Context)
Citation Context ... 2 2 = noe 2 n 1soe 2 1 + n 2soe 2 2 \Gamma 1; (4) where n = n 1 + n 2 andsoe 2 is the sample variance of the mixture region (a generalization to the multi-dimensional case is called Hotelling's test =-=[17]-=-). If this statistic is below a certain threshold then the regions are merged. Region growing can be considered as a special case of region merging, where R 1 is the growing region and R 2 is a single... |

2 |
A.L.Yuille. "A common framework for image segmentation
- Geiger
- 1991
(Show Context)
Citation Context ...region. It is usually very difficult to minimize the energy functions resulting from Bayes or MDL. Algorithms such as simulated annealing [10], graduated non-convexity [3] and deterministic annealing =-=[9]-=- are perhaps the most successful. 3 Region Competition for Grey Level Images In this section, we first derive our region competition algorithm from a global optimization criterion. Then we show how th... |

2 |
P.Dong. "Boundary Detection by Constrained Optimization
- Geman
- 1990
(Show Context)
Citation Context ...ke [19] and Balloon methods [6], [7], [37], [32](iii) Region growing and merging techniques [2], [1],[26], and (iv) Global optimization approaches based on energy functions [28] or Bayesian [10] [3], =-=[11]-=- and MDL (Minimum Description Length) criteria [23] [20] [18]. A common property of these approaches is that they all make hypotheses about the image, test features and make decisions by applying thre... |

2 |
The Heat Equation Shrinking Convex Plane Curves
- Grayson
- 1987
(Show Context)
Citation Context ...it is equal to the following heat diffusion equation. d\Gamma dt = @ 2 \Gamma @s 2 (14) where s is the arc length of the curve \Gamma. Detailed discussions of properties of this equation are given in =-=[12]-=-. Besides the smoothing term, the motion of ~v is determined by the likelihood ratio test. If P (I (~v) jff i ) ? P (I (~v) jff j ) -- i.e. if the intensity at ~v fits better to the distribution of re... |

2 |
B.Dom, W.Niblack and D.Steele. "A fast algorithm for MDL-based multi-band image segmentation
- Kanungo
- 1994
(Show Context)
Citation Context ...growing and merging techniques [2], [1],[26], and (iv) Global optimization approaches based on energy functions [28] or Bayesian [10] [3], [11] and MDL (Minimum Description Length) criteria [23] [20] =-=[18]-=-. A common property of these approaches is that they all make hypotheses about the image, test features and make decisions by applying thresholds explicitly or implicitly. As shown by the shadowed are... |

2 | A.P.Pentland, "Cooperative Robust Estimation Using Layers of Support - Darrell - 1994 |

1 | Existence and Regularity of Solutions to a Variational Problem of Mumford and Shah
- Wang
- 1991
(Show Context)
Citation Context ...ng on the contour, both pointing along the normal. The first term, the smoothing 4 We assume ff i has uniform a priori distribution. 5 Recently we noticed that a similar equation (11) was reported in =-=[35]-=-. But it was not derived from MDL and the statistical meaning was not analyzed there. force, is strongest at points of high curvature. Figure (2.a) shows the smoothing force at points along the region... |

1 |
Learning and sampling the prior distribution for visual computation". Harvard Robotics Laboratory
- Zhu, Mumford
- 1995
(Show Context)
Citation Context ... to derive alternative costs [31] [20]. However, we argue that these costs should be determined by the properties of real images, rather than from coding theory, and should be found empirically [39], =-=[40]-=-. rule This corresponds to setting 4 : ff i = arg min ff i f\Gamma Z Z R i log P (ff i j I (x;y) )dxdyg; 8 i (8) In the discrete case: ff i = arg max ff i Y (x;y)2R i P (ff i j I (x;y) ); 8 i (9) In o... |

1 |
A Unified Theory for Image Segmenation: Region Competition and its Analysis". Harvard Robotics Laboratory
- Zhu, Yuille
- 1995
(Show Context)
Citation Context ...lgorithm will have difficulty in classifying pixels, because of sample fluctuations, and so faulty segmentations may occur even if the global minimum of the MDL has been reached. It can be shown, see =-=[41]-=-, that if the data in a region is generated by a Gaussian with variance oe 2 then the variance of the sample variance in the region is of order oe 4 =N . For small regions, with N !! oe 4 , it will of... |