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

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Citations: | 96 - 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 ...cay rate for T , which is too fast to guarantee convergence to a global minimum. 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 c... |

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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 ...lation [25]. In addition to the theoretical justification in a scale space framework, Gabor filters have empirically proven to possess excellent discrimination properties for a wide range of textures =-=[26, 27]-=-. The multi--scale representation of images with a Gabor filter bank is especially useful for unsupervised texture segmentation, where little is known a priori about the characteristic frequencies of ... |

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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 .... 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 ...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 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, statistical tests are reliable measures of local texture similarity which are generally applica... |

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Citation Context ...lation [25]. In addition to the theoretical justification in a scale space framework, Gabor filters have empirically proven to possess excellent discrimination properties for a wide range of textures =-=[26, 27]-=-. The multi--scale representation of images with a Gabor filter bank is especially useful for unsupervised texture segmentation, where little is known a priori about the characteristic frequencies of ... |

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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 ... 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 ... very small and thin regions as described in [3]. Since additional hard constraints restrict the development of efficient optimization algorithms and may lead to forbiddingly heavy computational load =-=[32]-=-, we enforce these constraints in a separate post-processing stage which follows the clustering procedure and determines the closest valid partitioning by eliminating components and smoothing borders,... |

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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 ...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 ...rs fq i g given their previous values and an asynchronous update with respect to a site visitation schedule. Most of the work on mean--field annealing has either favored the synchronous update (e.g., =-=[39, 20, 40]-=-) or has at least been indifferent to this distinction (e.g., [8, 14, 16]). The synchronous scheme has the advantage of being amenable to a parallel implementation as already proposed by [39]. On the ... |

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Citation Context ... aerial image of San Francisco in Fig. 10. We believe a hierarchical clustering model to be more appropriate for many purposes and have extended our work in that direction in more recent publications =-=[44]-=-. 5.2 Mean-field Approximation and Gibbs Sampling Another important question is concerned with the quality of deterministic annealing algorithms compared to stochastic procedures. The quality of the p... |

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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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