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Publications sur MAP
Résultat de la recherche dans la liste des publications :
Article |
1 - Invariant Bayesian estimation on manifolds.
I. H. Jermyn. Annals of Statistics, 33(2): pages 583--605, avril 2005.
Mots-clés : Estimation bayesienne, MAP, MMSE, Invariant, Metrique, Jeffrey's.
@ARTICLE{jermyn_annstat05,
|
| author |
= |
{Jermyn, I. H.}, |
| title |
= |
{Invariant Bayesian estimation on manifolds}, |
| year |
= |
{2005}, |
| month |
= |
{avril}, |
| journal |
= |
{Annals of Statistics}, |
| volume |
= |
{33}, |
| number |
= |
{2}, |
| pages |
= |
{583--605}, |
| url |
= |
{http://dx.doi.org/10.1214/009053604000001273}, |
| pdf |
= |
{ftp://ftp-sop.inria.fr/ariana/Articles/jermyn_annstat05.pdf}, |
| keyword |
= |
{Estimation bayesienne, MAP, MMSE, Invariant, Metrique, Jeffrey's} |
| } |
Abstract :
A frequent and well-founded criticism of the maximum em a posteriori (MAP) and minimum mean squared error (MMSE) estimates of a continuous parameter param taking values in a differentiable manifold paramspace is that they are not invariant to arbitrary `reparametrizations' of paramspace. This paper clarifies the issues surrounding this problem, by pointing out the difference between coordinate invariance, which is a em sine qua non for a mathematically well-defined problem, and diffeomorphism invariance, which is a substantial issue, and then provides a solution. We first show that the presence of a metric structure on paramspace can be used to define coordinate-invariant MAP and MMSE estimates, and we argue that this is the natural way to proceed. We then discuss the choice of a metric structure on paramspace. By imposing an invariance criterion natural within a Bayesian framework, we show that this choice is essentially unique. It does not necessarily correspond to a choice of coordinates. In cases of complete prior ignorance, when Jeffreys' prior is used, the invariant MAP estimate reduces to the maximum likelihood estimate. The invariant MAP estimate coincides with the minimum message length (MML) estimate, but no discretization or approximation is used in its derivation. |
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Rapport de recherche et Rapport technique |
1 - Building Extraction and Change Detection in Multitemporal Aerial and Satellite Images in a Joint Stochastic Approach.
C. Benedek et X. Descombes et J. Zerubia. Rapport de Recherche 7143, INRIA, Sophia Antipolis, décembre 2009.
Mots-clés : Change detection, Building extraction, Processus ponctuels marques, MAP, multiple birth-and-death dynamics.
@TECHREPORT{benedekRR_09,
|
| author |
= |
{Benedek, C. and Descombes, X. and Zerubia, J.}, |
| title |
= |
{Building Extraction and Change Detection in Multitemporal Aerial and Satellite Images in a Joint Stochastic Approach}, |
| year |
= |
{2009}, |
| month |
= |
{décembre}, |
| institution |
= |
{INRIA}, |
| type |
= |
{Research Report}, |
| number |
= |
{7143}, |
| address |
= |
{Sophia Antipolis}, |
| url |
= |
{http://hal.archives-ouvertes.fr/inria-00426615}, |
| keyword |
= |
{Change detection, Building extraction, Processus ponctuels marques, MAP, multiple birth-and-death dynamics} |
| } |
Résumé :
Dans ce rapport, nous proposons une nouvelle méthode probabiliste qui intègre l'extraction de bâtiments et la détection de changements à partir de paires d'images de télédétection. Un algorithme d'optimisation globale permet de trouver la configuration optimale de bâtiments en considérant des observations, des connaissances a priori et des interactions entre des parties voisines de bâtiments. La précision est assurée par une vérification d'un modèle objet bayésien; le coût du calcul est considérablement réduit en utilisant un processus stochastique non-uniforme de naissance d'objets fondé sur des caractéristiques bas-niveaux des images, qui génère des objets pertinents ayant une grande probabilité. |
Abstract :
In this report we introduce a new probabilistic method which integrates building extraction with change detection in remotely sensed image pairs. A global optimization process attempts to find the optimal configuration of buildings, considering the observed data, prior knowledge, and interactions between the neighboring building parts. The accuracy is ensured by a Bayesian object model verification, meanwhile the computational cost is significantly decreased by a non-uniform stochastic object birth process, which proposes relevant objects with higher probability based on low-level image features. |
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