## Unsupervised Texture Segmentation in a Deterministic Annealing Framework (1998)

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Citations: | 91 - 9 self |

### BibTeX

@MISC{Hofmann98unsupervisedtexture,

author = {Thomas Hofmann and Jan Puzicha and Joachim M. Buhmann},

title = {Unsupervised Texture Segmentation in a Deterministic Annealing Framework},

year = {1998}

}

### Years of Citing Articles

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### Abstract

We present a novel optimization framework for unsupervised texture segmentation that relies on statistical tests as a measure of homogeneity. Texture segmentation is formulated as a data clustering problem based on sparse proximity data. Dissimilarities of pairs of textured regions are computed from a multi-scale Gabor filter image representation. We discuss and compare a class of clustering objective functions which is systematically derived from invariance principles. As a general optimization framework we propose deterministic annealing based on a mean-field approximation. The canonical way to derive clustering algorithms within this framework as well as an efficient implementation of mean-field annealing and the closely related Gibbs sampler are presented. We apply both annealing variants to Brodatz-like micro-texture mixtures and real-word images.

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Citation Context ...ed to cover the reflexive case to get a true identity. T. Hofmann et.al.: Unsupervised Texture Segmentation. IEEE PAMI, 1998, to appear. 8 4 Clustering Algorithms In seminal papers Kirkpatrick et al. =-=[33]-=- and, independently, Cerny [34] have proposed the stochastic optimization strategy Simulated Annealing. Simulated Annealing determines solutions to combinatorial optimization problems by a random sear... |

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Citation Context ...ning schemes [3, 4, 5], is shift invariance, i.e., invariance with respect to additive shifts of the proximity scale. In particular, this yields a natural generalization of the K--means cost function =-=[6]-=- to proximity data. Section 4 presents an introduction to the concept of deterministic annealing, a general framework to derive efficient heuristic algorithms for a variety of problems in combinatoria... |

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Citation Context ... space. As a consequence, these approaches have to solve the difficult problem of specifying a metric that appropriately represents visual dissimilarities between textures in the chosen feature space =-=[1, 2]-=-. In contrast to this widely appreciated approach, we follow the ideas of Geman et al. [3] to avoid a vector space representation by utilizing non--parametric statistical tests. As we will show, stati... |

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Citation Context ...to get a true identity. T. Hofmann et.al.: Unsupervised Texture Segmentation. IEEE PAMI, 1998, to appear. 8 4 Clustering Algorithms In seminal papers Kirkpatrick et al. [33] and, independently, Cerny =-=[34]-=- have proposed the stochastic optimization strategy Simulated Annealing. Simulated Annealing determines solutions to combinatorial optimization problems by a random search, which is formally modeled b... |

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Citation Context ...been applied to the traveling salesman problem [7], graph partitioning [8], quadratic assignment and graph T. Hofmann et.al.: Unsupervised Texture Segmentation. IEEE PAMI, 1998, to appear. 2 matching =-=[9, 10]-=-, vector quantization [11, 12], surface reconstruction [13], image restoration [14, 15], and edge detection [16]. A deterministic annealing approach for clustering and visualization of complete proxim... |

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Citation Context ... For the zero temperature limit a deterministic greedy optimization algorithm known as Iterative Conditional Mode (ICM) [36] is obtained. While the general convergence results for simulated annealing =-=[37]-=- demonstrate the universality of this optimization principle, the inherently slow convergence of stochastic techniques compared to deterministic algorithms is perceived as a major disadvantage. Theref... |

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Citation Context ... surface reconstruction [13], image restoration [14, 15], and edge detection [16]. A deterministic annealing approach for clustering and visualization of complete proximity data has been presented in =-=[17]-=-. More specifically, we use mean--field theory as an approximation principle [18, 19, 20, 21] to obtain computationally tractable algorithms. Astonishingly, deterministic annealing algorithms have onl... |

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Citation Context ...itioning [8], quadratic assignment and graph T. Hofmann et.al.: Unsupervised Texture Segmentation. IEEE PAMI, 1998, to appear. 2 matching [9, 10], vector quantization [11, 12], surface reconstruction =-=[13]-=-, image restoration [14, 15], and edge detection [16]. A deterministic annealing approach for clustering and visualization of complete proximity data has been presented in [17]. More specifically, we ... |

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Citation Context .... A deterministic annealing approach for clustering and visualization of complete proximity data has been presented in [17]. More specifically, we use mean--field theory as an approximation principle =-=[18, 19, 20, 21]-=- to obtain computationally tractable algorithms. Astonishingly, deterministic annealing algorithms have only been derived independently for highly specific optimization instances despite these widespr... |

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Citation Context ...ithm, (c) a texture segmentation with K = 4. The image partitioning is visualized in (d) - (g). in autonomous robotics and the presented algorithms have been implemented on the autonomous robot RHINO =-=[46]-=-. An example image of a typical office environment is presented in Fig. 12. The achieved segmentation is both visually and semantically satisfying. Untextured parts of the image are grouped together i... |

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Citation Context ...sample problem [28]. We have examined the performance of the mutual information [4], the Kolmogorov--Smirnov statistic [3, 29], tests of the Cramer/von Mises type, and the �� 2 --statistics in det=-=ail [30, 31]. Empiri-=-cally, the �� 2 test and the mutual information test have been shown to yield the best results. In the following we focus on the �� 2 --statistics which is defined by D (r) ij = L X k=1 i f r ... |

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Citation Context ...ed on the distribution of coefficients in either window, i.e., D (r) ij = d(f r (\Delta; ~x i ); f r (\Delta; ~x j )). Several non--parametric test statistics are available for the two-sample problem =-=[28]. We-=- have examined the performance of the mutual information [4], the Kolmogorov--Smirnov statistic [3, 29], tests of the Cramer/von Mises type, and the �� 2 --statistics in detail [30, 31]. Empirical... |

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Citation Context ... salesman problem [7], graph partitioning [8], quadratic assignment and graph T. Hofmann et.al.: Unsupervised Texture Segmentation. IEEE PAMI, 1998, to appear. 2 matching [9, 10], vector quantization =-=[11, 12]-=-, surface reconstruction [13], image restoration [14, 15], and edge detection [16]. A deterministic annealing approach for clustering and visualization of complete proximity data has been presented in... |

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Citation Context ... salesman problem [7], graph partitioning [8], quadratic assignment and graph T. Hofmann et.al.: Unsupervised Texture Segmentation. IEEE PAMI, 1998, to appear. 2 matching [9, 10], vector quantization =-=[11, 12]-=-, surface reconstruction [13], image restoration [14, 15], and edge detection [16]. A deterministic annealing approach for clustering and visualization of complete proximity data has been presented in... |

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Citation Context ...been applied to the traveling salesman problem [7], graph partitioning [8], quadratic assignment and graph T. Hofmann et.al.: Unsupervised Texture Segmentation. IEEE PAMI, 1998, to appear. 2 matching =-=[9, 10]-=-, vector quantization [11, 12], surface reconstruction [13], image restoration [14, 15], and edge detection [16]. A deterministic annealing approach for clustering and visualization of complete proxim... |

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Citation Context ...nt heuristic algorithms for a variety of problems in combinatorial optimization and computer vision. Deterministic Annealing has been applied to the traveling salesman problem [7], graph partitioning =-=[8]-=-, quadratic assignment and graph T. Hofmann et.al.: Unsupervised Texture Segmentation. IEEE PAMI, 1998, to appear. 2 matching [9, 10], vector quantization [11, 12], surface reconstruction [13], image ... |

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Citation Context ...assignment and graph T. Hofmann et.al.: Unsupervised Texture Segmentation. IEEE PAMI, 1998, to appear. 2 matching [9, 10], vector quantization [11, 12], surface reconstruction [13], image restoration =-=[14, 15]-=-, and edge detection [16]. A deterministic annealing approach for clustering and visualization of complete proximity data has been presented in [17]. More specifically, we use mean--field theory as an... |

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Citation Context .... A deterministic annealing approach for clustering and visualization of complete proximity data has been presented in [17]. More specifically, we use mean--field theory as an approximation principle =-=[18, 19, 20, 21]-=- to obtain computationally tractable algorithms. Astonishingly, deterministic annealing algorithms have only been derived independently for highly specific optimization instances despite these widespr... |

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Citation Context ...ly accelerated using the concept of multiscale optimization. The resulting optimization times are in the range of less then 5 seconds 8 for the examples shown here without loss in performance quality =-=[45]-=-. In Fig. 9 deterministic annealing is compared with the ICM algorithm and the Gibbs 8 For deterministic annealing on a SUN UltraSparc, less then 2 seconds for ICM. The multiscale annealing scheme is ... |

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Citation Context ...elta; ~x j )). Several non--parametric test statistics are available for the two-sample problem [28]. We have examined the performance of the mutual information [4], the Kolmogorov--Smirnov statistic =-=[3, 29], tests -=-of the Cramer/von Mises type, and the �� 2 --statistics in detail [30, 31]. Empirically, the �� 2 test and the mutual information test have been shown to yield the best results. In the followi... |

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Citation Context ...a convergent iteration scheme. The following statements which are proven in the appendix summarize the most important results for factorial distributions. A more detailed presentation can be found in =-=[30, 38]-=-. T. Hofmann et.al.: Unsupervised Texture Segmentation. IEEE PAMI, 1998, to appear. 10 Theorem 1 Let H be an arbitrary partitioning cost function, H : M! IR. The factorial distribution Q 2 QM , which ... |

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Citation Context .... 2 the misclassified sites mainly correspond to errors at texture borders, which contain more then one texture. Misclassifications at the boundary are unavoidable due to the support of Gabor filters =-=[43]-=-, as statistics from different textures are mixed. The post-processing step improves the segmentations by a significant noise reduction. T. Hofmann et.al.: Unsupervised Texture Segmentation. IEEE PAMI... |

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Citation Context ...mework to derive efficient heuristic algorithms for a variety of problems in combinatorial optimization and computer vision. Deterministic Annealing has been applied to the traveling salesman problem =-=[7]-=-, graph partitioning [8], quadratic assignment and graph T. Hofmann et.al.: Unsupervised Texture Segmentation. IEEE PAMI, 1998, to appear. 2 matching [9, 10], vector quantization [11, 12], surface rec... |

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