Probabilistic Labeling in a Hidden Second Order Markov Mesh

Hidden Markov Model Approaches for Biological Studies

“…One of the major shortcomings is that the dependence of a node on its neighbors in a fully connected multi-dimensional HMM does not guarantee to be explored. Several attempts have also been done to heuristically reduce the complexity of the HMM algorithms by making simplifying assumptions [34,36,42,43,[49][50][51][52]. The main disadvantage of these approaches is that they only provide approximate computations, such that the probabilistic model is no longer theoretically sound.…”

“…One solution is to convert a multi-dimensional model into a 1-D multidimensional vector Markov model by considering the set of nodes with a fixed coordinate along a given direction (e.g., horizontal, vertical, or diagonal in a regular plane) as a new vector node. For example, the rows, the columns, and the anti-diagonal and its parallelisms of a 2-D lattice respectively form super nodes, generating a vector Markov chain [34][35][36][37][38]. Generalization to the 3-D case is also straightforward [39][40][41].…”

Automatic Semantic Annotation of Images using Spatial Hidden Markov Model

“…For the frequency λ and orientation θ, the outputs of a pair of corresponding Gabor filters with initial phases 0 and −π/2 are denoted by γ λ,θ,0 and γ λ,θ,−pi/2 respectively. The combination of these two quantities yields the so called Gabor energy [6].…”

“…The underlying idea is that the state of a block only depends on the states of two previously observed neighbor blocks in a raster scan. This assumption,which is appropriate for horizontally layered natural images, differs dramatically from that used in second-order Markov mesh models [6]. The complete specification of a spatial HMM λ requires a specification of the number of states N(the collection of available hidden states is denoted by S), and the four probability measures such as H(horizontal transition matrix), V(vertical transition matrix), B and π.…”

Multiresolution image classification by hierarchical modeling with two-dimensional hidden Markov models

“…Context-dependent classification algorithms based on two-dimensional hidden Markov models (2-D HMMs) have been developed [14], [24], [25] to overcome the overlocalization of con- ventional block-based classification algorithms. In this paper, a multiresolution extension of the 2-D HMMs described in [25] is proposed so that more global context information can be used efficiently.…”