## A review of statistical approaches to level set segmentation: Integrating color, texture, motion and shape (2007)

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Venue: | International Journal of Computer Vision |

Citations: | 85 - 4 self |

### BibTeX

@ARTICLE{Cremers07areview,

author = {Daniel Cremers and Mikael Rousson and Rachid Deriche},

title = {A review of statistical approaches to level set segmentation: Integrating color, texture, motion and shape},

journal = {International Journal of Computer Vision},

year = {2007},

volume = {72},

pages = {215}

}

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### Abstract

Abstract. Since their introduction as a means of front propagation and their first application to edge-based segmentation in the early 90’s, level set methods have become increasingly popular as a general framework for image segmentation. In this paper, we present a survey of a specific class of region-based level set segmentation methods and clarify how they can all be derived from a common statistical framework. Region-based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity, color, texture or motion in each of a set of regions. In contrast to edge-based schemes such as the classical Snakes, region-based methods tend to be less sensitive to noise. For typical images, the respective cost functionals tend to have less local minima which makes them particularly well-suited for local optimization methods such as the level set method. We detail a general statistical formulation for level set segmentation. Subsequently, we clarify how the integration of various low level criteria leads to a set of cost functionals and point out relations between the different segmentation schemes. In experimental results, we demonstrate how the level set function is driven to partition the image plane into domains of coherent color, texture, dynamic texture or motion. Moreover, the Bayesian formulation allows to introduce prior shape knowledge into the level set method. We briefly review a number of advances in this domain.

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164 | Shape priors for level set representations
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Citation Context ...tudied in [33]. Chen et al. [14] proposed to impose shape information on the zero crossing (rather than on the level set function). Rousson et al. proposed variational integrations of the shape prior =-=[78, 79]-=- based on the assumption of a Gaussian distribution. The use of nonparametric density estimation to model larger classes of level set based shape distributions was developed in [20, 74]. This approach... |

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Citation Context ... separate textures which 2 It should be pointed out that based on various heuristics, one can successfully incorporate regriding mechanisms and topological changes into explicit representations – cf. =-=[62, 48, 28, 25]-=-. 3 IJCV.tex; 19/09/2005; 19:10; p.3s4 have identical spatial characteristics but differ in their temporal dynamics. In Section 7 we detail how to integrate motion information as a criterion for segme... |

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Citation Context ...ectly optimizing in the linear subspace spanned by the principal components. A detailed analysis of various shape distances and statistical shape analysis in the level set formulation can be found in =-=[13]-=-. Figure 15 shows the effect of variation along the first principal component on the embedding function and the implicitly represented contour. The use of principal component analysis to model level s... |

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Citation Context ...he shape prior [78, 79] based on the assumption of a Gaussian distribution. The use of nonparametric density estimation to model larger classes of level set based shape distributions was developed in =-=[20, 74]-=-. This approach allows to model distributions of shape which are not Gaussian – such as the various views of a 3D object [19] or the silhouettes of a walking person [20]. Moreover, in the limit of lar... |

76 | Dynamical statistical shape priors for level set based tracking
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Citation Context ...n and to induce a recognition-driven segmentation through the competition of shape priors was developed in [24]. Dynamical statistical shape priors for implicit shape representations were proposed in =-=[18]-=-. The latter approach takes into account that in the context of image sequence segmentation, the probability of a contour IJCV.tex; 19/09/2005; 19:10; p.28sFigure 16. Sample segmentations using statis... |

74 |
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Citation Context ...ined from a Minimum Description Length (MDL) criterion. The link with the Mumford-Shah functional and the equivalence to Bayesian maximum a posteriori (MAP) estimation is provided in [100]. Following =-=[66]-=-, an optimal partition P(Ω) of the image plane Ω (i.e. a partition of the image plane into pairwise disjoint regions) can be computed by maximizing the a posteriori probability p(P(Ω) | I) for a given... |

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Citation Context ...ations (pdes). Such pde-based segmentation methods became popular with the seminal paper on Snakes by Kass et al. [44]. In this paper, the contour is implemented by an explicit (parametric) curve C : =-=[0, 1]-=- → Ω which is evolved by locally minimizing the functional � E(C) = − |∇I(C)| 2 � ds + ν1 |Cs| 2 � ds + ν2 |Css| 2 ds, (1) where Cs and Css denote the first and second derivative with respect to the c... |

69 |
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Citation Context ... separate textures which 2 It should be pointed out that based on various heuristics, one can successfully incorporate regriding mechanisms and topological changes into explicit representations – cf. =-=[62, 48, 28, 25]-=-. 3 IJCV.tex; 19/09/2005; 19:10; p.3s4 have identical spatial characteristics but differ in their temporal dynamics. In Section 7 we detail how to integrate motion information as a criterion for segme... |