Since the introduction by Shepp and Vardi [Shepp, L. A. & Vardi, Y. (1982) IEEE Trans. Med. Imaging 1, 113-121] of the expectation-maximization algorithm for the generation of maximum-likelihood images in emission tomography, a number of investigators have applied the maximum-likelihood method to imaging problems. Though this approach is promising, it is now well known that the unconstrained ma...

The known factorization algorithm for the maximum likelihood affine reconstruction requires that all the feature points used must be visible in all views. We derive here a closed-form-expression for the 3D coordinates of the feature points and translation vectors given the inhomogeneous affine projection matrices, but no single feature point is required to be visible in all views. The expressio...

More sophisticated fuzzy clustering algorithms, like the Gustafson–Kessel algorithm [11] and the fuzzy maximum likelihood estimation (FMLE) algorithm [10] offer the possibility of inducing clusters of ellipsoidal shape and different sizes. The same holds for the expectation maximization (EM) algorithm for a mixture of Gaussians. However, these additional degrees of freedom can reduce the robust...

Maximum-likelihood range imaging is considered for pulsed-imager operation of a coherent laser radar. The expectation-maximization (EM) algorithm is used to develop an explicit procedure for maximum-likelihood fitting of a multiresolution (wavelet) basis-at a sequence of increasingly fine resolutions-to laser radar range data. Specialization to the Haar-wavelet basis yields a procedure that is ...

Recently, analysis of structural equation models with polytomous and continuous variables has received a lot of attention. However, contributions to the selection of good models are limited. The main objective of this article is to investigate the maximum likelihood estimation of unknown parameters in a general LISREL-type model with mixed polytomous and continuous data and propose a model sele...

We present a noise-injected version of the Expectation-Maximization (EM) algorithm: the Noisy Expectation Maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that additive noise speeds up the average convergence of the EM algorithm to a local maximum of the likelihood surface if a positivity condition holds. Corollary...

In this paper, an improved expectation maximization (EM) algorithm called statistical histogram based expectation maximization (SHEM) algorithm is presented. The algorithm is put forward to overcome the drawback of standard EM algorithm, which is extremely computationally expensive for calculating the maximum likelihood (ML) parameters in the statistical segmentation. Combining the SHEM algorit...

Expectation-maximization (EM) algorithm has been used to maximize the likelihood function or posterior when the model contains unobserved latent variables. One main important application of EM algorithm is to find the maximum likelihood estimator for mixture models. In this article, we propose an EM type algorithm to maximize a class of mixture type objective functions. In addition, we prove th...

The approach proposed in this paper takes into account the uncertainty in colour modelling by employing variational Bayesian estimation. Mixtures of Gaussians are considered for modelling colour images. Distributions of parameters characterising colour regions are inferred from data statistics. The Variational Expectation-Maximization (VEM) algorithm is used for estimating the hyperparameters c...