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2-D Hidden Markov Model
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Jia Li, Amir Najmi, Robert M. Gray, "Image classification by a two
dimensional hidden Markov model," IEEE Transactions on Signal Processing,
48(2):517-33, February 2000.
Abstract:
For block-based classification, an image is divided into blocks and a
feature vector is formed for each block by grouping statistics
extracted from the block. Conventional block-based classification
algorithms decide the class of a block by examining only the feature
vector of this block and ignoring context information. In order to
improve classification by context, a new algorithm models images by
two dimensional hidden Markov models (HMMs). The HMM considers feature
vectors statistically dependent through an underlying state process
assumed to be a Markov mesh, which has transition probabilities
conditioned on the states of neighboring blocks from both horizontal
and vertical directions. Thus, the dependency in two dimensions is
reflected simultaneously. The HMM parameters are estimated by the EM
algorithm. To classify an image, the classes with maximum a posteriori
probability are searched jointly for all the blocks. Applications of
the HMM algorithm to documentary and aerial image segmentation show
that the algorithm outperforms CART, LVQ, and Bayes VQ.
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2-D Multiresolution Hidden Markov Model
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Jia Li, Robert M. Gray, Richard A. Olshen, "Multiresolution image
classification by hierarchical modeling with two dimensional hidden Markov
models," IEEE Transactions on Information Theory, 46(5):1826-41, August 2000.
Abstract:
This paper treats a multiresolution hidden Markov model for classifying
images. Each image is represented by feature vectors at several resolutions,
which are statistically dependent as modeled by the underlying state process,
a multiscale Markov mesh. Unknowns in the model are estimated by maximum
likelihood, in particular by employing the expectation-maximization
algorithm. An image is classified by finding the optimal set of states with
maximum a posteriori probability. States are then mapped into classes. The
multiresolution model enables multiscale information about context to be
incorporated into classification. Suboptimal algorithms based on the model
provide progressive classification that is much faster than the algorithm
based on single-resolution hidden Markov models.
Applications
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Image annotation
the Automatic Linguistic Indexing for Pictures system
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Distinguishing stroke styles of fine art paintings
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Computationally efficient estimation of 2- and 3-D HMMs
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Dhiraj Joshi, Jia Li, James Z. Wang, "A computationally efficient approach to
the estimation of two- and three-dimensional hidden Markov models," IEEE
Transactions on Image Processing, 2005, to appear.
Abstract:
Statistical modeling methods are becoming indispensable in today's
large-scale image analysis. In this paper, we explore a computationally
efficient parameter estimation algorithm for two and three dimensional hidden
Markov models and show applications to satellite image segmentation. The
proposed parameter estimation algorithm is compared with the first proposed
algorithm for 2-D HMMs based on variable state Viterbi. We also propose a 3-D
hidden Markov model (3-D HMM) for volume image modeling and apply it to
volume image segmentation using a large number of synthetic images with
ground truth. Experiments have demonstrated the computational efficiency of
the proposed parameter estimation technique for 2-D HMMs and a potential of
3-D HMM as a stochastic modeling tool for volume images.
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