We address the problem of articulated posture estimation in its general form. Namely, the recovery of full 3D articulated posture parameters from an uncontrolled scene. Stochastic modeling of low-level segmented image...
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We address the problem of articulated posture estimation in its general form. Namely, the recovery of full 3D articulated posture parameters from an uncontrolled scene. Stochastic modeling of low-level segmented image data is unified with models of object kinematic structure through a constrained mixture of observation processes. A modified expectation-maximization algorithm is proposed for this purpose. Early experiments qualitatively demonstrate the efficacy of our approach, and provide a context for integration for more sophisticated image cues.
In this paper we address the problem of image restoration when the point-spread function (PSF) of the imaging process is not known exactly, a situation which arises regularly in practice. The algorithm based on the ex...
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In this paper we address the problem of image restoration when the point-spread function (PSF) of the imaging process is not known exactly, a situation which arises regularly in practice. The algorithm based on the expectation-maximization (EM) algorithm is proposed which has the capability to identify the unknown statistics of the image and the image-dependent noise while restoring the image. The convergence properties of the resulting estimators are examined.
Conventional training of a hidden Markov model (HMM) is performed by an expectation-maximization algorithm using a maximum likelihood (ML) criterion. It was reported that, using an incremental variant of maximum a pos...
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Conventional training of a hidden Markov model (HMM) is performed by an expectation-maximization algorithm using a maximum likelihood (ML) criterion. It was reported that, using an incremental variant of maximum a posteriori estimation, substantial speed improvements could be obtained. The approach requires a prior distribution when the training starts, although it is difficult to find an appropriate prior for some cases. This paper presents a new approach for achieving an efficient training of HMM parameters using the standard ML criterion. A prior distribution is not required. The algorithm sequentially selects a subset of data from the training set, updates the parameters from the subset, then iterates until convergence. There is a solid theoretical foundation that ensures a monotone likelihood improvement; thus stable convergence is guaranteed. Experimental results indicate substantially faster convergence than the standard batch training algorithm while holding the same level of recognition performance.
A maximum a posteriori (MAP) algorithm is presented for the estimation of spin-density and spin-spin decay distributions from frequency and phase-encoded magnetic resonance imaging data. Linear spatial localization gr...
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A maximum a posteriori (MAP) algorithm is presented for the estimation of spin-density and spin-spin decay distributions from frequency and phase-encoded magnetic resonance imaging data. Linear spatial localization gradients are assumed: the y-encode gradient applied during the phase preparation time of duration tau before measurement collection, and the x-encode gradient applied during the full data collection time t greater than or equal to 0, The MRT signal model developed in [22] is used in which a signal resulting from M phase encodes (rows) and N frequency encode dimensions (columns) is modeled as a superposition of MN sine-modulated exponentially decaying sinusoids with unknown spin-density and spin-spin decay parameters, The nonlinear least-squares MAP estimate of the spin density and spin-spin decay distributions solves for the 2MN spin-density and decay parameters minimizing the squared-error between the measured data and the sine-modulated exponentially decay signal model using an iterative expectation-maximization algorithm. A covariance diagonalizing transformation is derived which decouples the joint estimation of MN sinusoids into M separate N sinusoid optimizations, yielding an order of magnitude speed up in convergence, The MAP solutions are demonstrated to deliver a decrease in standard deviation of image parameter estimates on brain phantom data of greater than a factor of two over Fourier-based estimators of the spin density and spin-spin decay distributions. A parallel processor implementation is demonstrated which maps the N sinusoid coupled minimization to separate individual simple minimizations, one for each processor.
The estimation of the intensity function of a Poisson-driven shot-noise process is addressed using a regularization technique, where the data is modeled as a signal term plus a signal-dependent noise term. A new data-...
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The estimation of the intensity function of a Poisson-driven shot-noise process is addressed using a regularization technique, where the data is modeled as a signal term plus a signal-dependent noise term. A new data-based method for selecting a pair of regularization parameters is presented and compared with the minimum unbiased risk method. The detail in the intensity function can be recovered by both methods, but the new method does a better job at suppressing spurious oscillations.
This work investigates the application of stochastic optimization in the development of a new paradigm, polydistributional mixtures, for automated data modeling. This new paradigm increases the generality of mixture m...
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This work investigates the application of stochastic optimization in the development of a new paradigm, polydistributional mixtures, for automated data modeling. This new paradigm increases the generality of mixture methods by allowing for the automated simultaneous optimization of the number of components, the distributional form of each component, the proportionality associated with each component, as well as the parameters of each component. A general evolutionary approach, based on the mutation and selection from a population of potential solutions, is used as the optimization procedure. The approach is applied to modeling texture features extracted from digitized mammograms of cancerous and noncancerous regions. The resulting polydistributional mixtures are compared to optimal (in terms of model fitness) normal mixtures optimized via the expectation-maximization algorithm.
The max-min propagation neural network model is considered as a hierarchical mixture of experts by replacing the max (min) units with softmax functions. The resulting mixture is different from the model of Jordan and ...
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The max-min propagation neural network model is considered as a hierarchical mixture of experts by replacing the max (min) units with softmax functions. The resulting mixture is different from the model of Jordan and Jacobs, but we exploit the similarities between both models to derive a probability model. Learning is treated as a maximum-likelihood problem, in particular we present a gradient ascent algorithm and an expectation-maximization algorithm. Simulation results on the parity problem and the majority problem are reported.
The multigram model assumes that language can be described as the output of a memoryless source that emits variable-length sequences of words. The estimation of the model parameters can be formulated as a maximum like...
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The multigram model assumes that language can be described as the output of a memoryless source that emits variable-length sequences of words. The estimation of the model parameters can be formulated as a maximum likelihood estimation problem from incomplete data. We show that estimates of the model parameters can be computed through an iterative expectation-maximization algorithm and we describe a forward-backward procedure for its implementation. We report the results of a systematical evaluation of multigrams for language modeling on the ATIS database. The objective performance measure is the test set perplexity. Our results show that multigrams outperform conventional n-grams for this task.
The expectation-maximization (EM) method can facilitate maximizing likelihood functions that arise in statistical estimation problems. In the classical EM paradigm, one iteratively maximizes the conditional log-likeli...
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The expectation-maximization (EM) method can facilitate maximizing likelihood functions that arise in statistical estimation problems. In the classical EM paradigm, one iteratively maximizes the conditional log-likelihood of a single unobservable complete data space, rather than maximizing the intractable likelihood function for the measured or incomplete data. EM algorithms update all parameters simultaneously, which has two drawbacks: 1) slow convergence, and 2) difficult maximization steps due to coupling when smoothness penalties are used. This paper describes the space-alternating generalized EM (SAGE) method, which updates the parameters sequentially by alternating between several small hidden-data spaces defined by the algorithm designer. We prove that the sequence of estimates monotonically increases the penalized-likelihood objective, we derive asymptotic convergence rates, and we provide sufficient conditions for monotone convergence in norm. Two signal processing applications illustrate the method: estimation of superimposed signals in Gaussian noise, and image reconstruction from Poisson measurements. In both applications, our SAGE algorithms easily accommodate smoothness penalties and converge faster than the EM algorithms.
The use of the expectation-maximization algorithm to obtain pseudo-maximum likelihood estimates (i.e. the EM-ML algorithm) of radiopharmaceutical distributions based on data collected from emission computed tomography...
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The use of the expectation-maximization algorithm to obtain pseudo-maximum likelihood estimates (i.e. the EM-ML algorithm) of radiopharmaceutical distributions based on data collected from emission computed tomography (ECT) systems is now a well developed area, as witnessed by a number of recent articles on that topic, including the detailed study of the relative performance of EM-ML and FBP reconstructions provided in J. Llacer et al. (ibid., vol. 12, p. 215-31, 1993). However, there remains considerable confusion in the field regarding appropriate stopping rules for EM-ML algorithms, and in this correspondence the author attempts to detail a shortcoming of one of the more recent and innovative stopping rule criteria. In particular, the author discusses the effect of total photon counts on stopping criteria based on cross-validation.< >
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