## 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 ...es. As it turns out, the key idea is to choose an appropriate normalization in measuring cluster compactness. The main property, which distinguishes our approach from other graph partitioning 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.... |

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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 ...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... |

202 | Texture classification and segmentation using multiresolution simultaneous autoregressive models - Mao, Jain - 1992 |

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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 ...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 ...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 ... 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 ...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 ...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 ...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 ...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 .... 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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