Theory of Segmentation

Lember, Jüri; Kuljus, Kristi; Koloydenko, Alexey

doi:10.5772/14214

Cited by 9 publications

(10 citation statements)

References 37 publications

(68 reference statements)

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“…One possible direction could be combining regression with segmentation and atlasbased approach. With HMMs it is easy to perform segmentation and this can be done in different ways (Lember et al, 2011). In the current application, when underlying states have physical meaning (tissue classes), it is realistic to assume that in some regions of the head the underlying states can be revealed.…”

Section: Discussionmentioning

confidence: 99%

Comparison of hidden Markov chain models and hidden Markov random field models in estimation of computed tomography images

Kuljus

Bayisa

Bolin

et al. 2018

Communications in Statistics: Case Studies, Data Analysis and A

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There is an interest to replace computed tomography (CT) images with magnetic resonance (MR) images for a number of diagnostic and therapeutic workflows. In this article, predicting CT images from a number of magnetic resonance imaging (MRI) sequences using regression approach is explored. Two principal areas of application for estimated CT images are dose calculations in MRI based radiotherapy treatment planning and attenuation correction for positron emission tomography (PET)/MRI. The main purpose of this work is to investigate the performance of hidden Markov (chain) models (HMMs) in comparison to hidden Markov random field (HMRF) models when predicting CT images of head. Our study shows that HMMs have clear advantages over HMRF models in this particular application. Obtained results suggest that HMMs deserve a further study for investigating their potential in modeling applications where the most natural theoretical choice would be the class of HMRF models.

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Section: Discussionmentioning

confidence: 99%

Comparison of hidden Markov chain models and hidden Markov random field models in estimation of computed tomography images

Kuljus

Bayisa

Bolin

et al. 2018

Communications in Statistics: Case Studies, Data Analysis and A

Self Cite

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“…For using the Viterbi algorithm, find the optimal path as the main path [13][14][15][16][17]. In the process of finding the main path, that is, starting from the network element of the sink node S, find the optimal path to the network element of the sink node E and find an optimal solution for the main and backup paths.…”

Section: Applicationmentioning

confidence: 99%

A Method of Optimizing Network Topology Structure Combining Viterbi Algorithm and Bayesian Algorithm

Shi

2021

Wireless Communications and Mobile Computing

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With Internet entering all walks of life, development of internet and usage expansion demand better performance, especially the application of 5G network that adopts NAS networking mode. Some of the network bandwidth cannot fully support the current network demand, which causes network fluctuations and other concerns. In this paper, a method for optimizing the topological structure of the bottom layer of the communication network is proposed that has outage performance close to optimal routing scheme. In specific, path in areas with poor network conditions is first optimized using Viterbi algorithm. Then, network element nodes on the path are optimized using Bayes recommendation algorithm for reasonable flow distribution. Dual planning of improved Viterbi algorithm is used to realize the main and standby path planning, and then, Bayesian recommendation algorithm based on the average value is used to optimize the network elements. Therefore, it is very efficient to realize overall performance optimization.

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“…and rise above zero i.o. Together with (7) this implies that almost no realization of X has an infinite Viterbi path. It is easy to confirm that this model is HMM with…”

Section: Viterbi Pathmentioning

confidence: 99%

“…On the other hand, Viterbi path is not in general the one that minimizes the expected number of errors, when the number of errors between two sequences are measured entry by entry (Hamming metric). For more detailed discussion about the segmentation problem and the properties of different estimates, we refer to [7][8][9][10][11]. Although these papers deal with HMM's only, the general theory applies for any model including PMM's.…”

Section: Viterbi Pathmentioning

confidence: 99%

Existence of infinite Viterbi path for pairwise Markov models

Lember

Sova

2020

Stochastic Processes and their Applications

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For hidden Markov models one of the most popular estimates of the hidden chain is the Viterbi path -the path maximising the posterior probability. We consider a more general setting, called the pairwise Markov model, where the joint process consisting of finite-state hidden regime and observation process is assumed to be a Markov chain. We prove that under some conditions it is possible to extend the Viterbi path to infinity for almost every observation sequence which in turn enables to define an infinite Viterbi decoding of the observation process, called the Viterbi process. This is done by constructing a block of observations, called a barrier, which ensures that the Viterbi path goes trough a given state whenever this block occurs in the observation sequence.

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Theory of Segmentation

Cited by 9 publications

References 37 publications

Comparison of hidden Markov chain models and hidden Markov random field models in estimation of computed tomography images

Comparison of hidden Markov chain models and hidden Markov random field models in estimation of computed tomography images

A Method of Optimizing Network Topology Structure Combining Viterbi Algorithm and Bayesian Algorithm

Existence of infinite Viterbi path for pairwise Markov models

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