Fusion of sensor data, knowledge sources and algorithms for extraction and classification of topographic objects

baltsavias, emmanuel p.

Bibliographic data

Monograph

Persistent identifier:: 856473650

Author:: Baltsavias, Emmanuel P.

Title:: Fusion of sensor data, knowledge sources and algorithms for extraction and classification of topographic objects

Sub title:: Joint ISPRS/EARSeL Workshop ; 3 - 4 June 1999, Valladolid, Spain

Scope:: III, 209 Seiten

Year of publication:: 1999

Place of publication:: Coventry

Publisher of the original:: RICS Books

Identifier (digital):: 856473650

Illustration:: Illustrationen, Diagramme, Karten

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Monograph

Collection:: Earth sciences

Chapter

Title:: TECHNICAL SESSION 3 OBJECT AND IMAGE CLASSIFICATION

Document type:: Monograph

Structure type:: Chapter

Chapter

Title:: BAYESIAN METHODS: APPLICATIONS IN INFORMATION AGGREGATION AND IMAGE DATA MINING. Mihai Datcu and Klaus Seidel

Document type:: Monograph

Structure type:: Chapter

International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999 a measure of error. The inference requires the knowledge of the prior model p(Q\M.) and the data prediction term or forward model p(D\Q, M.) pursues Bayes’ rule and is applied separately for each of the models {Af,}: p(D\Q, M.)p(Q\M.) =—jimr) <•> The information extraction is a Maximum A Posteriori (MAP) estimation: 0 = argmaxp(@\D, M.) (2) The evidence termp(D\M.) in the denominator of (1) is generally neglected in the model fitting, but is important in the second level of inference, and here lies the novelty of the Bayesian approach in data inversion. Model comparison. The task of the second level of the Bayesian inference is to find the most plausible model, given the data. The inference applies in the space of models: The objective of this work is to use the Bayesian inference in order to obtain an estimate of a given physical parameter, using observations acquired with different sensors. We assume a model for the desired physical parameter and try to estimate it by fitting this model to the data. If we take into consideration two datasets D/ and D 2 separately for observations, the information extraction can be splitted into two separated problems with solutions given by the maximum of the following a posteriori probabilities (MAP): p(0|D 1 ,M 1 ) p(D^e,M { )-p(e\M x ) p(d v m 1 ) (4) 0, M 2 ) • p(0|M 2 ) p(£> 2 |m 2 ) (5) where 0 is the desired physical parameter, and p(0IA/,) encapsulates our a priori knowledge. The measure of fidelity to the observed data is given in terms of the conditional probabilities p(D,|0, Mf, i=l,2. In Fig. 2 we introduce a first paradigm for data fusion. It refers mainly to the extraction of image content information. P(° 2 p(G\d 2 ,m 2 ) = piM^ocpiDlMJpWt) (3) The inference relies on the evidence of Af, carried by p(D\Mf and the subjective prior over the assumed hypothesis space p(Mf. p(M i ) shows how plausible we thought the alternative models were, before the data arrived. Inference of probability distributions from observation of sensory data aims at finding the best stochastic models able to consistently characterize classes of images (Datcu et al., 1998; Minka and Picard, 1997). The Bayesian approach for data modelling is used. The information contained in a dataset (provided by a unique sensor) is extracted in different assumptions. The assumptions are represented by different prior models (Fig. 1). In the case of a multispectral sensor, the assumed prior models can characterize either the spectral components or the texture structures. The extracted information according to these two models is not commensurable, it represents different qualities. Fig. 1. Information extraction using qualitatively different models. We call the process to extract information from sensory data using different prior models, data fission. Fig. 2. First paradigm for sensory information extraction and data fusion. Here, we can identify three cases. The first case, the case of a unique source of information, was treated as data fission. A second situation is the extraction of information from different sources using the same prior model. The estimated parameters will have identical representation, however their meaning can be different. A simple example is texture parameter estimation from data with different resolution. The scale plays the role of meta information, thus the direct interpretation of the estimated parameters is not consistent. The third case assumes information extraction from different sources using different prior models. The resulted information has incommensurable representations. A full Bayesian approach for information fusion can be formulated as maximizing the following a posteriori probability: p(Q\d v d 2 ,m v m 2 ) = p(D x |0, M^piD^Q, M 2 ) • P{p(G\M x )p{Q\M 2 )} (6 ) p(D v £> 2 | m i> M i) where F is an operator representing the prior information in the assumption of two different models. We observe that the problem of fusion of information from two datasets is extended with fusion of knowledge, in form of the specification of the a priori

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