Two-dimensional Hidden Markov Model Research Articles

Model Checking for Hidden Markov Models

Residual analysis is a useful tool for checking lack of fit and for providing insight into model improvement. However, literature on residual analysis and the goodness of fit for hidden Markov models (HMMs) is limited. As HMMs with complex structures are increasingly used to accommodate different types of data, there is a need for further tools to check the validity of models applied to real world data. We review model checking methods for HMMs and develop new methods motivated by a particular case study involving a two-dimensional HMM developed for time series with many null events. We propose new residual analysis and stochastic reconstruction methods, which are adapted from model checking techniques for point process models. We apply the new methods to the case study model and discuss their adequacy. We find that there is not one “best” test for diagnostics but that our new methods have some advantages over previously developed tools. The importance of multiple tests for complex HMMs is highlighted and we use the results of our model checking to provide suggestions for possible improvements to the case study model. Supplementary materials for this article are available online.

Two-dimensional hidden semantic information model for target saliency detection and eyetracking identification

Saliency detection has been applied to the target acquisition case. This paper proposes a two-dimensional hidden Markov model (2D-HMM) that exploits the hidden semantic information of an image to detect its salient regions. A spatial pyramid histogram of oriented gradient descriptors is used to extract features. After encoding the image by a learned dictionary, the 2D-Viterbi algorithm is applied to infer the saliency map. This model can predict fixation of the targets and further creates robust and effective depictions of the targets’ change in posture and viewpoint. To validate the model with a human visual search mechanism, two eyetrack experiments are employed to train our model directly from eye movement data. The results show that our model achieves better performance than visual attention. Moreover, it indicates the plausibility of utilizing visual track data to identify targets.

Multimodal face recognition method with two-dimensional hidden Markov model

Abstract The paper presents a new solution for the face recognition based on two-dimensional hidden Markov models. The traditional HMM uses one-dimensional data vectors, which is a drawback in the case of 2D and 3D image processing, because part of the information is lost during the conversion to one-dimensional features vector. The paper presents a concept of the full ergodic 2DHMM, which can be used in 2D and 3D face recognition. The experimental results demonstrate that the system based on two dimensional hidden Markov models is able to achieve a good recognition rate for 2D, 3D and multimodal (2D+3D) face images recognition, and is faster than ICP method.

Road signs recognition with two-dimensional hidden Markov models

The automatic road sign recognition system is presented. The system uses two-dimensional hidden Markov models. The system is able to recognize the road signs, which were detected earlier in the image. The system uses wavelet transform for features extraction of road signs. In recognition process system uses two dimensional hidden Markov models. The experimental results demonstrate that the system is able to gain an average recognition rate of 83%. Streszczenie. Zaprezentowano automatyczny system rozpoznawania znakow drogowych. System wykorzystuje dwuwymiarowe uryte modele Markowa. System rozponaje znaki drogowe, ktore byly wczewykryte nas obrazie. Do ekstrakcji cech znakow drogowych system u˙ zywa transfor- maty falkowej. W procesie rozpoznawania zastosowano dwuwymiarowe modele Markowa. Wyniki eksperymentu pokazuj ˛ a, ˙ ze system jest w stanie osi ˛ agn ˛ a´ c poziom rozpoznania 83% . (Rozpoznawanie znakow drogowych z dwuwymiarowymi ukrytymi modelami Markowa)

Automatic 3D Model Annotation by a Two-Dimensional Hidden Markov Model

In this paper, a new method of 3D model automatic annotation is proposed based on a two-dimensional Hidden Markov Model(2-D HMM). Growing importance in the last years Hidden Markov Models are a widely used methodology for sequential data modeling. Recent years, HMMs are applied to research of automatic annotation, such as images and models annotation. The three basic problems with HMM-liked model are also solved in our model. Our modeling process has two steps, those are training and testing. In the proposed approach, each object is separated into several bins by a spiderweb model and a shape function D2 is computed for each bin. These feature vectors are then arranged in a sequential fashion to compose a sequence vector, which is used to train HMMs. In 2-D HMM, we assume that feature vectors are statistically dependent on an underlying state process which has transition probabilities conditioning the states of two neighboring bins. Thus the dependency of two dimensions is reflected simultaneously. To classify an object, the maximized posteriori probability is calculated by a given model and the observed sequence of an unknown object. Comparing with the general HMM, 2-D HMM gets more information from the neighboring bins. So the system of 2-D HMM performs well on images and model annotation. Analysis and experimental results show that the proposed approach performs better than existing ones in database. DOI : http://dx.doi.org/10.11591/telkomnika.v12i5.4946

3D Object Classification Using a Two-Dimensional Hidden Markov Model

In this paper, we develop a novel method of 3D object classification based on a Two-Dimensional Hidden Markov Model (2D HMM). Hidden Markov Models are a widely used methodology for sequential data modeling, of growing importance in the last years. In the proposed approach, each object is decomposed by a spiderweb model and a shape function D2 is computed for each bin. These feature vectors are then arranged in a sequential fashion to compose a sequence vector, which is used to train HMMs. In 2D HMM, we assume that feature vectors are statistically dependent on an underlying state process which has transition probabilities conditioning the states of two neighboring bins. Thus the dependency of two dimensions is reflected simultaneously. To classify an object, the maximized posteriori probability is calculated by a given model and the observed sequence of an unknown object. Comparing with 1D HMM, the 2D HMM gets more information from the neighboring bins. Analysis and experimental results show that the proposed approach performs better than existing ones in database.

Two-Dimensional Hidden Markov Model for Classification of Continuous-Valued Noisy Vector Fields

In this paper we present a statistical model with a nonsymmetric half-plane (NSHP) region of support for two-dimensional continuous-valued vector fields. It has the simplicity, efficiency, and ease of use of the well-known hidden Markov model (HMM) and associated Baum-Welch algorithms for time-series and other one-dimensional problems. At the same time it is able to learn textures on a two-dimensional field. We describe a fast approximate forward procedure for computation of the joint probability density function (pdf) of the vector field as well as an approximate Baum-Welch algorithm for parameter reestimation. Radar and sonar applications include classification of two-dimensional fields such as range versus azimuth or range versus aspect angle data wherein each data point in the field consists of a multi-dimensional feature vector. We test the method using synthetic textures.

New Learning Algorithms for Third-Order 2-D Hidden Markov Models

Abstract One-dimensional Hidden Markov models (1-D HMMs) are statistical models of sequential data that have been used successfully in many machine learning applications, especially for speech recognition. Two-dimensional hidden Markov model (2-D HMM) is an extension of 1-D HMM to 2-D, it provides a reasonable statistical method to model matrix data. This paper describes the structure of third-order 2-D HMM in which probability of a transition not only depends immediate vertical and horizontal states but also depends on immediate diagonal state, and gives a study of learning algorithms for third-order 2-D HMM. By using the ideal that the sequences of states on columns or rows of a third-order 2-D HMM can be seen as states of a 1-D HMM and building up an associated objective function using Lagrange multiplier method, several new formulae solving model learning algorithms are theoretically derived.

Image Classification With Kernelized Spatial-Context

The goal of image classification is to classify a collection of unlabeled images into a set of semantic classes. Many methods have been proposed to approach this goal by leveraging visual appearances of local patches in images. However, the spatial context between these local patches also provides significant information to improve the classification accuracy. Traditional spatial contextual models, such as two-dimensional hidden Markov model, attempt to construct one common model for each image category to depict the spatial structures of the images in this class. However due to large intra-class variances in an image category, one single model has difficulties in representing various spatial contexts in different images. In contrast, we propose to construct a prototype set of spatial contextual models by leveraging the kernel methods rather than only one model. Such an algorithm combines the advantages of rich representation ability of spatial contextual models as well as the powerful classification ability of kernel method. In particular, we propose a new distance measure between different spatial contextual models by integrating joint appearance-spatial image features. Such a distance measure can be efficiently computed in a recursive formulation that scales well to image size. Extensive experiments demonstrate that the proposed approach significantly outperforms the state-of-the-art approaches.

Analysis and Synthesis of Formant Spaces of British, Australian, and American Accents

In this paper, the probability distribution functions (pdf's) of the formant spaces of three major accents of the English language, namely, British Received Pronunciation (RP), General American, and Broad Australian, are modeled and compared. The statistical differences across the formant spaces of these accents are employed for accent conversion. An improved formant tracking method, based on linear prediction (LP) feature analysis and a two-dimensional hidden Markov model (2-D-HMM) of format trajectories, is used for estimation of the formant trajectories of vowels and diphthongs of each accent. Comparative analysis of the formant spaces of the three accents indicates that these accents are partly conveyed by the differences of the formants of vowels. The estimates of the probability distributions of the formants for each accent are used in a speech synthesis system for accent conversion. Accent synthesis, through modification of the acoustic parameters of speech, provides a means of assessing the perceptual contribution of each formant parameter on conveying an accent. The results of perceptual evaluations of accent conversion illustrate that formants play an important role in conveying accents

Parametric Formant Modelling and Transformation in Voice Conversion

This paper presents a method for the estimation and mapping of parametric models of speech resonance at formants for voice conversion. The spectral features at formants that contribute to voice characteristics are the trajectories of the frequencies, the bandwidths and intensities of the resonance at formants. The formant features are extracted from the poles of a linear prediction (LP) model of speech. The statistical distributions of formants are modelled by a two-dimensional hidden Markov model (HMM) spanning the time and frequency dimensions. Experimental results are presented which show a close match between HMM-based formant models and the histograms of formants. For voice conversion two alternative methods are explored for mapping the formants of a source speaker to those of a target speaker. The first method is based on an adaptive formant-tracking warping of the frequency response of the LP model and the second method is based on the rotation of the poles of the LP model of speech. Both methods transform all spectral parameters of the resonance at formants of the source speaker towards those of the target speaker. In addition, the issues affecting the selection of the warping ratios for the mapping functions are investigated. Experimental results of formant estimation and perceptual evaluation of voice morphing based on parametric formant models are presented.

Evaluation of formant-like features on an automatic vowel classification task.

Numerous attempts have been made to find low-dimensional, formant-related representations of speech signals that are suitable for automatic speech recognition. However, it is often not known how these features behave in comparison with true formants. The purpose of this study was to compare two sets of automatically extracted formant-like features, i.e., robust formants and HMM2 features, to hand-labeled formants. The robust formant features were derived by means of the split Levinson algorithm while the HMM2 features correspond to the frequency segmentation of speech signals obtained by two-dimensional hidden Markov models. Mel-frequency cepstral coefficients (MFCCs) were also included in the investigation as an example of state-of-the-art automatic speech recognition features. The feature sets were compared in terms of their performance on a vowel classification task. The speech data and hand-labeled formants that were used in this study are a subset of the American English vowels database presented in Hillenbrand et al. [J. Acoust. Soc. Am. 97, 3099-3111 (1995)]. Classification performance was measured on the original, clean data and in noisy acoustic conditions. When using clean data, the classification performance of the formant-like features compared very well to the performance of the hand-labeled formants in a gender-dependent experiment, but was inferior to the hand-labeled formants in a gender-independent experiment. The results that were obtained in noisy acoustic conditions indicated that the formant-like features used in this study are not inherently noise robust. For clean and noisy data as well as for the gender-dependent and gender-independent experiments the MFCCs achieved the same or superior results as the formant features, but at the price of a much higher feature dimensionality.

A Probabilistic Model for Face Transformation with Application to Person Identification

A novel approach for content-based image retrieval and its specialization to face recognition are described. While most face recognition techniques aim at modeling faces, our goal is to model the transformation between face images of the same person. As a global face transformation may be too complex to be modeled directly, it is approximated by a collection of local transformations with a constraint that imposes consistency between neighboring transformations. Local transformations and neighborhood constraints are embedded within a probabilistic framework using two-dimensional hidden Markov models (2D HMMs).We further introduce a new efficient technique, called turbo-HMM (T-HMM) for approximating intractable 2D HMMs. Experimental results on a face identification task show that our novel approach compares favorably to the popular eigenfaces and fisherfaces algorithms.

Image classification by a two-dimensional hidden Markov model

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, an algorithm is proposed that models images by two dimensional (2-D) 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 document and aerial image segmentation show that the algorithm outperforms CART/sup TM/, LVQ, and Bayes VQ.

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

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.

Pseudo Two-Dimensional Hidden Markov Models for Document Recognition

Hidden Markov models (HMM) have become the most popular technique for automatic speech recognition. Extending this technique to the two-dimensional domain is a promising approach to solving difficult problems in optical character recognition (OCR), such as recognizing poorly printed text. Hidden Markov models are robust for OCR applications due to: — Their inherent tolerance to noise and distortion, — Their ability to segment blurred and connected text into words and characters as an integral part of the recognition process, — Their invariance to size, slant, and other transformations of the basic characters, and — The ease with which contextual information and language models can be incorporated into the recognition algorithms. We give a brief overview of OCR algorithms based on two-dimensional hidden Markov models, and we present three case studies that show their remarkable strengths.