Bayesian Image Segmentations by Potts Prior and Loopy Belief Propagation

Tanaka, Kazuyuki; Kataoka, Satoshi; Yasuda, Muneki; Waizumi, Yuji; Hsu, Chiou Ting

doi:10.7566/jpsj.83.124002

Cited by 4 publications

(7 citation statements)

References 33 publications

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“…4. Our proposed method can reduce the computational time of the hyperparameter estimations significantly.…”

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confidence: 92%

“…2) Loopy belief propagations (LBP's) have been applied to construct certain practical algorithms for application in Bayesian image segmentations. 3,4) In the present short note, we improve the Bayesian image segmentation algorithm in Ref. 4 by using a real space renormalization group (RSRG) transformation in order to reduce the computational time.…”

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confidence: 99%

“…Markov random fields are regarded as classical spin systems in statistical mechanics 2) . Loopy belief propagations (LBP's) have been applied to construct certain practical algorithms for application in Bayesian image segmentations 3,4) .…”

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confidence: 99%

“…The estimates α (R) and { m(ξ), C(ξ)|ξ∈Q} of α (R) and {m(ξ), C(ξ)|ξ∈Q}. are approximately computed by means of the LBP algorithm for the conditional maximum entropy framework 4) . After obtaining these estimates, we calculate α (0) from α (R) by using the following inverse RSRG transformations of Eq.…”

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confidence: 99%

“…In the present short note, we have presented a novel algorithm that involve the combination of the inverse RSRG transformation with the Bayesian image segmentation method proposed in Ref. 4) . Our proposed method can reduce the computational time of the hyperparameter estimations significantly.…”

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confidence: 99%

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Inverse Renormalization Group Transformation in Bayesian Image Segmentations

et al. 2015

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A new Bayesian image segmentation algorithm is proposed by combining a loopy belief propagation with an inverse real space renormalization group transformation to reduce the computational time. In results of our experiment, we observe that the proposed method can reduce the computational time to less than one-tenth of that taken by conventional Bayesian approaches.Bayesian segmentation modeling based on Markov random fields (MRF's) is one of the interesting research topics. 1) Image segmentations are required to classify pixels in an observed image into several regions, and such segmentations are regarded as a kind of clustering of pixels. Markov random fields are regarded as classical spin systems in statistical mechanics. 2) Loopy belief propagations (LBP's) have been applied to construct certain practical algorithms for application in Bayesian image segmentations. 3,4) In the present short note, we improve the Bayesian image segmentation algorithm in Ref. 4 by using a real space renormalization group (RSRG) transformation in order to reduce the computational time.We consider an image as defined on a set of pixels arranged on a square grid graph ðV; EÞ. Here V fiji ¼ 1; 2; . . . ; jVjg denotes the set of all the pixels and E is the set of all the nearest-neighbour pairs of pixels fi; jg. The total numbers of elements in the sets V and E are denoted by jVj and jEj, respectively. The square grid graph has the periodic boundary conditions along the x-and y-directions. The label at each pixel i is regarded as a state variable, and it is denoted by a i . Each state variable a i (i 2 V) takes on the values of all the possible integers in the set Q f0; 1; 2; . . . ; q À 1g as its region label. The state vector of labels is represented by a ¼ ða i ji 2 VÞ ¼ ða 1 ; a 2 ; . . . ; a jVj Þ T . The prior probability of a labeling configuration a is assumed to be specified by a constant α asup to the normalization constant. For the prior probability distribution PðaÞ, we introduce the following RSRG transformation:a 1 ;a 3 / X a 2 2Q X a 4 2Q exp 1 2 ðrÀ1Þ ð a 1 ;a 2 þ a 2 ;a 3 þ a 1 ;a 4 þ a 4 ;a 3 Þ ðr ¼ 1; 2; . . . ; RÞ;where ð0Þ . The square grid graph G ðrÞ ¼ ðV ðrÞ ; E ðrÞ Þ is defined as shown in Fig. 1(b). Here V ðrÞ is the set of all the pixels and E ðrÞ represents the set of all the nearest-neighbour pairs of pixels fi; jg in the graph G ðrÞ . Here, we remark that V ðrÞ is the subset of V. The prior probability distribution P ðrÞ ða ðrÞ Þ for a ðrÞ ða i ji 2 V ðrÞ Þ on G ðrÞ ¼ ðV ðrÞ ; E ðrÞ Þ after the r-iteration of the RSRG transformation is expressed as P ðrÞ ða ðrÞ Þ /

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“…4. Our proposed method can reduce the computational time of the hyperparameter estimations significantly.…”

mentioning

confidence: 92%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Inverse Renormalization Group Transformation in Bayesian Image Segmentations

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Review of Sublinear Modeling in Probabilistic Graphical Models by Statistical Mechanical Informatics and Statistical Machine Learning Theory

Tanaka¹

2021

Sublinear Computation Paradigm

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We review sublinear modeling in probabilistic graphical models by statistical mechanical informatics and statistical machine learning theory. Our statistical mechanical informatics schemes are based on advanced mean-field methods including loopy belief propagations. This chapter explores how phase transitions appear in loopy belief propagations for prior probabilistic graphical models. The frameworks are mainly explained for loopy belief propagations in the Ising model which is one of the elementary versions of probabilistic graphical models. We also expand the schemes to quantum statistical machine learning theory. Our framework can provide us with sublinear modeling based on the momentum space renormalization group methods.

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Potts Clustering with Complete Shrinkage: a novel clustering methodology with its Software Package pottscompleteshrinkage in Python

Alahassa¹

2021

Preprint

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We have modified the Potts Model Swendsen-Wang algorithm to insert some clusters constraints by applying a modified agglomerative clustering approach (Kurita, 1991). We have called the induced Potts Model, the Potts Clustering with Complete Shrinkage (PCCS), under the Python package pottscompleteshrinkage deployed on PyPi Index under its current release. In this approach, we deal with the increasing number of small clusters generated in a given partition by merging all small clusters of size ≤ h with their closest cluster in terms of minimal distance respectively, where h is an integer greater or equal to 2. The algorithm uses a technique in which distances of all pairs of observations are stored. Then the nearest cluster (with size ≥ h) is given by the cluster with the closest node in terms of minimal distance to the cluster to be merged using complete linkage. This approach is truly effective as it helps to control the clusters size, and we have found empirical evidence of Chi-Square and Gamma density curves for the constrained cluster size distribution of PCCS, when applied to some datasets taken from the multiple-output benchmark datasets available in the Mulan project website (Tsoumakas et al., 2020). We add a last framework based on Frequency of frequency distribution (FoF) to find the conditional bonds distribution given the clusters size constraints which results in an intractable distribution for large datasets, but its computation framework is a land of rich mathematical developments.

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Bayesian Image Segmentations by Potts Prior and Loopy Belief Propagation

Cited by 4 publications

References 33 publications

Inverse Renormalization Group Transformation in Bayesian Image Segmentations

Inverse Renormalization Group Transformation in Bayesian Image Segmentations

Review of Sublinear Modeling in Probabilistic Graphical Models by Statistical Mechanical Informatics and Statistical Machine Learning Theory

Potts Clustering with Complete Shrinkage: a novel clustering methodology with its Software Package pottscompleteshrinkage in Python

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