scispace - formally typeset
Search or ask a question
Topic

Maximum a posteriori estimation

About: Maximum a posteriori estimation is a research topic. Over the lifetime, 7486 publications have been published within this topic receiving 222291 citations. The topic is also known as: Maximum a posteriori, MAP & maximum a posteriori probability.


Papers
More filters
Journal ArticleDOI
TL;DR: The general problem of determining the photoelectron "counting" distribution resulting from an electromagnetic field impinging on a quantum detector is formulated and various limiting forms of this distribution are derived, including the necessary conditions for those commonly accepted.
Abstract: In this paper we formulate the general problem of determining the photoelectron "counting" distribution resulting from an electromagnetic field impinging on a quantum detector. Although the detector model used was derived quantum mechanically, our treatment is wholly classical and includes all results known to date. This combination is commonly referred to as the semiclassical approach. The emphasis, however, lies in directing the problem towards optical communication. The electromagnetic field is assumed to be the sum of a deterministic signal and a zero-mean narrow-band Gaussian random process, and is expanded in a Karhunen-Loeve series of orthogonal functions. Several examples are given. It is shown that all the results obtainable can be written explicitly in terms of the noise covariance function. Particular attention is given to the case of a signal plus white Gaussian noise, both of which are band-limited to \pm B Hz. Since the result is a fundamental one, to add some physical insight, we show four methods by which it can be obtained. Various limiting forms of this distribution are derived, including the necessary conditions for those commonly accepted. The likelihood functional is established and is shown to be the product of Laguerre polynomials. For the problem of continuous estimation, the Fisher information kernel is derived and an important limiting form is obtained. The maximum a posteriori (MAP) and maximum-likelihood (ML) estimation equations are also derived. In the latter case the results are also functions of Laguerre polynomials.

68 citations

Journal ArticleDOI
TL;DR: The iterative extension to maximum a posteriori (MAP) supervised classification methods can be combined effectively with a stratification of the image, which is made on the basis of additional map data and relies on the sample sets being representative.
Abstract: The paper describes an iterative extension to maximum a posteriori (MAP) supervised classification methods. A posteriori probabilities per class are used for classification as well as to obtain class area estimates. From these, an updated set of prior probabilities is calculated and used in the next iteration. The process converges to statistically correct area estimates. The iterative process can be combined effectively with a stratification of the image, which is made on the basis of additional map data. Moreover, it relies on the sample sets being representative. Therefore, the method is shown to be well applicable in combination with an existing GIS. The paper gives a description of the procedure and provides a mathematical foundation. An example is presented to distinguish residential, industrial, and greenhouse classes. A significant improvement of the classification was obtained.

67 citations

Proceedings ArticleDOI
17 May 2004
TL;DR: This paper proposes to increase the performance of the GMM approach (without sacrificing its simplicity) through the use of local features with embedded positional information and shows that the performance obtained is comparable to 1D HMMs.
Abstract: It has been shown previously that systems based on local features and relatively complex generative models, namely 1D hidden Markov models (HMMs) and pseudo-2D HMMs, are suitable for face recognition (here we mean both identification and verification). Recently a simpler generative model, namely the Gaussian mixture model (GMM), was also shown to perform well. In this paper we first propose to increase the performance of the GMM approach (without sacrificing its simplicity) through the use of local features with embedded positional information; we show that the performance obtained is comparable to 1D HMMs. Secondly, we evaluate different training techniques for both GMM and HMM based systems. We show that the traditionally used maximum likelihood (ML) training approach has problems estimating robust model parameters when there is only a few training images available; we propose to tackle this problem through the use of maximum a posteriori (MAP) training, where the lack of data problem can be effectively circumvented; we show that models estimated with MAP are significantly more robust and are able to generalize to adverse conditions present in the BANCA database.

67 citations

Proceedings ArticleDOI
15 Jun 2002
TL;DR: A method is presented for segmentation of anatomical structures that incorporates prior information about the intensity and curvature profile of the structure from a training set of images and boundaries that model the intensity distribution as a function of signed distance from the object boundary.
Abstract: A method is presented for segmentation of anatomical structures that incorporates prior information about the intensity and curvature profile of the structure from a training set of images and boundaries. Specifically, we model the intensity distribution as a function of signed distance from the object boundary, instead of modeling only the intensity of the object as a whole. A curvature profile acts as a boundary regularization term specific to the shape being extracted, as opposed to simply penalizing high curvature. Using the prior model, the segmentation process estimates a maximum a posteriori higher dimensional surface whose zero level set converges on the boundary of the object to be segmented. Segmentation results are demonstrated on synthetic data and magnetic resonance imagery.

67 citations

Journal ArticleDOI
TL;DR: A deterministic relaxation method based on mean field annealing with a compound Gauss-Markov random (CGMRF) field model is proposed and a set of iterative equations for the mean values of the intensity and both horizontal and vertical line processes with or without taking into account some interaction between them are presented.
Abstract: The authors consider the problem of edge detection and image estimation in nonstationary images corrupted by additive Gaussian noise. The noise-free image is represented using the compound Gauss-Markov random field developed by F.C. Jeng and J.W. Woods (1990), and the problem of image estimation and edge detection is posed as a maximum a posteriori estimation problem. Since the a posteriori probability function is nonconvex, computationally intensive stochastic relaxation algorithms are normally required. A deterministic relaxation method based on mean field annealing with a compound Gauss-Markov random (CGMRF) field model is proposed. The authors present a set of iterative equations for the mean values of the intensity and both horizontal and vertical line processes with or without taking into account some interaction between them. The relationship between this technique and two other methods is considered. Edge detection and image estimation results on several noisy images are included. >

67 citations


Network Information
Related Topics (5)
Estimator
97.3K papers, 2.6M citations
86% related
Deep learning
79.8K papers, 2.1M citations
85% related
Convolutional neural network
74.7K papers, 2M citations
85% related
Feature extraction
111.8K papers, 2.1M citations
85% related
Image processing
229.9K papers, 3.5M citations
84% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202364
2022125
2021211
2020244
2019250
2018236